hurry please

The** resulting expression **would** **be** **8b + 4v + 13.

**What is an Expression?**

An **expression** consists of one or more **numbers** or **variables** along with one more **operation**.

If we **combine** like **terms** in 4b - 2v + 4b + 6v + 13 the **resulting** **expression** would be, **8b + 4v + 13.**

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The resulting **expression** would be **8b + 4v + 13.**

An **expression** is created by combining one or more variables or numbers with another operation. A **mathematical** expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or **subtraction** of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math **Operator**)

You must substitute a number for each **variable** and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the **variable** x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before **evaluating** the expression.

If we combine **like terms **in 4b - 2v + 4b + 6v + 13 the resulting **expression** would be, 8b + 4v + 13.

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1.On the accompanying grid, sketch the graphs of y = 2^x and 3y = 7x + 3 over the interval

-3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.

As a result, the coordinates of the** equations** y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.

When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a **two-dimensional plane** requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact** locations**. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.

given

y = 2^x and 3y = 7x + 3 over the interval -3 ≤ x ≤ 4.

as x = -3

y = 2^x= 2^-3 = -8

y = 8

3y = 7x+3

3y= 7*-3 +3

3y = -21 + 3

y = -6

As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.

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QUIZ:

Composite Figures

What is the area of this polygon

Area of given **polygon **is **39 unit².**

As seen above, a polygon is a **geometric shape** that is described as "consisting of a number of points (called vertices) and an equal number of line **segments **(called sides), namely a cyclically ordered set of points in a plane, with no three successive **points **collinear, as well as the line segments joining the points."

A polygon has flat surfaces throughout. A **polygon **must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. We can quickly determine the **geometry **of a polygon based on how many sides it has.

For the given **polygon**,

Below is the given image of partition,

We will calculate the **area **by dividing the figure in different portions,

**triangle **and **rectangle**,

**Area **of **triangle **= 1/2 × Base × Height

Base = 6 units

Height = 3 units

= 1/2 × 6 × 3 = **9 unit²**

**Area **of **rectangle **= length × breadth

length = 5 units

breadth = 6 units

**Area **= 5 × 6 = **30 unit²**

Total area = area of triangle + area of rectangle = 9 + 30 = **39 unit²**

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PLEASE HELP

The graph for the equation y = 2 x minus 2 is shown below.

On a coordinate plane, a line goes through points (0, negative 2) and (1, 0).

If another equation is graphed so that the system has one solution, which equation could that be?

y = 2 (x + 1)

y = 2 (x minus 1)

y = 2 (x minus 2)

y = negative 2 (x + 1)

From the graph **solution** of system of equations is (0, -2). Therefore, option D is the correct answer.

A system of **linear** **equations** consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given equation is y=2x-2.

**Graph** the line using the slope and y-intercept, or two points.

Slope: 2

y-intercept: (0, -2)

Now,

A) y=2(x+1)

2x-2=2(x+1)

No solution

B) y=2(x-1)

2x-2=2(x-1)

No solution

C) y=2(x-2)

2x-2=2(x-2)

No solution

D) y=-2(x+1)

2x-2=-2(x+1)

2x-2=-2x-2

4x=0

x=0

Substitute x=0 in y=-2(x+1), we get y=-2

Therefore, option D is the correct answer.

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A ball is dropped from the top of a building 74 ft tall, How long will it take to fall to ground level?

**To determine how long it will take for a ball to fall from the top of a building 74 ft tall to ground level, we can use the formula:**

**t = √(2*d/g)**

**where t is the time in seconds, d is the distance in feet, and g is the acceleration due to gravity (approximately 32.2 ft/s^2 on Earth).**

**Plugging in the values:**

**t = √(2*74 / 32.2)**

**t ≈ 3.63 seconds**

**So the ball will take approximately 3.63 seconds to fall to the ground level.**

**It's important to note that this calculation assumes that there's no air resistance and the ball is dropped vertically. In reality, air resistance and the ball's trajectory would affect the time it takes to fall.**

Above is correct I took the test

Dan is mailing packages. Each small package costs him $2.30 to send. Each large package costs him $3.90. How much will it cost him to send 4 small packages and 6 large packages?

**Answer: $32.60**

**Step-by-step explanation:**

**(4)(2.30) + (6)(3.90)**

**= 32.60**

**Answer:**

for him it send 4 small packages it will cost 9.20

For him to send 6 large packages it will cost 23.40

23.40 + 9.20 = 32.60

**Step-by-step explanation:**

Formula: Quanity x Cost = Total

After Totals + Costs = Exact Total

LESSON 7 SESSION 2

Develop Using the Standard Algorithm

to Add and Subtract Decimals

Read and try to solve the problem below.

How much greater is the mass of a dollar coin than the combined

masses of a dime and a quarter?

TRY

IT

put

Math Toolkit base-ten blocks, base-ten grid paper,

grid paper, number lines, place-value charts

Mass of U.S. Coins

Periny: 2.5 g

Dime: 2.268 g

Nicket: 5. g

Quarter: 5.67 g

Half-Dollar: 11.34 g Dollar 8.1 g

Exploring Base **Ten Blocks **: Measure 1 x 1 x 1 cm with units of "ones."

Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.

Hundred times flats Count 1 cm by 10 cm by 10 cm.

Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.

How do you solve a base ten block?Our base **ten number system** is spatially represented by Base Ten Blocks. The four separate concrete representations known as "Base Ten Blocks" are generally used in middle school arithmetic after being introduced in elementary school.

Measure 1 x 1 x 1 cm with units of** "ones."**

Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.

Hundred times flats Count 1 cm by 10 cm by 10 cm.

Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.

When names are given based on shape rather than value, it is possible to rename the pieces as needed. For instance, a class learning decimals can use the flat to represent a unit and then determine the value of the other components.

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Juan has a blueprint of a professional basketball court. The scale is 1 inch to 4 feet. If the

professional basketball court is 50 feet wide, how wide is the drawing of the court on the blueprint?

Use the questions below to help you solve.

a. Write the scale as a ratio.

b. Use your answer from part (a) and the information in the problem to write a scale

proportion.

c. Solve the scale proportion you wrote in part (b) to determine the width of the

professional basketball court in the blueprint. Show all your work.

**Answer: **

**a. The scale is 1 inch to 4 feet. This can be written as a ratio: 1:4**

**b. Using the ratio from part a, the scale proportion is: 1/4 = width of the drawing/50 feet**

**c. To find the width of the drawing, we will use cross multiplication and solving for the width, we have 1/4 * 50 feet = width of the drawing/50 feet = 1* 50/4 =12.5 inches.**

**The width of the drawing on the blueprint is 12.5 inches.**

**Step-by-step explanation:**

The **answer** to each part is mentioned below.

Given is that Juan has a blueprint of a professional basketball court. The scale is **1 inch to 4 feet** and the professional basketball court is **50 feet** wide.

After the dilation, the relation between **final** and **initial **dimensions of the image is -

y = Kx

where -

{K} is a dimensionless quantity called **scale factor**.

**{a} -**

the scale as a ratio can be written as -

K = (1 inch/4 feet) = (1/12 feet/4 feet) = (1/48) = 1 : 48

**K = 1 : 48**

**{b} -**

We can write the scale proportion as -

**(1/48) = (x/50)**

**{c} -**

The width of the professional basketball court in the blueprint is -

x = 50/48

**x = 1.05 feet**

Therefore, the **answer** to each part is mentioned above.

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Explain in your own words:

What is a linear function?

A linear function is a function that represents a straight line on a coordinate plane. (not sure if this helps)

Gary found 72 shells and 40 coins at the beach. he wants to give them to some of his friends. Each friend will receive the same number of shells and the same number of coins. What is the greatest number of friends Gary can give shells and coins to? How many shells will each friend receive? How many coins? Select your answers from the drop-down lists.

The greatest number of friends Gary can give shells and coins to is ___

friends. Each friend will receive ___

shells and ___

coins.

The greatest number of friends** Gary c**an giv**e shells **and **coins** to is 8

friends. Each friend will receive 9 shells and 5 coins.

How to solve for the number of friendsWe have to find the** factors of 72**

72/ 2 = 36 / 2 = 18/ 2 = 9/ 3 = 3

72 = 2 * 2* 2 * 3

We would find the **factors of 40**

40 / 2 = 20 / 2 = 10 / 2 = 5

40 = 2 * 2 * 2 * 5

Then we would find the common factors they have

2 * 2 * 2 = 8

This is the number of f**riends t**hat Gary can have

Then 72 / 8 = 9

40 / 8 = 5

The greatest number of friends Gary can give shells and coins to is 8

friends. Each friend will receive 9 shells and 5 coins.

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a warehouse 40 yards long, and 25 yards wide, and it is piled with cartons to a height of 3 yards. what is the area of the warehouse floor? what is the total volume of the cartons? (assume there is no space between cartons.)

The area of the warehouse floor is 1000 square yards. This can be **calculated **using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.

The calculated answer is the result of a mathematical equation or calculation. Calculations can range from simple addition and subtraction to complex integrations and derivatives. By using mathematical formulas, equations, and **algorithms**, the calculated answer can be used to solve problems and make predictions. Calculated answers can be used in fields such as science, engineering, economics, and finance. Calculated answers can also be used to make decisions about investments, projects, and other business decisions. In addition, calculated answers can be used to analyze data and make decisions based on the results.

The area of the warehouse floor is 1000 **square **yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.

The total volume of the cartons is 12500 cubic yards. This can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Therefore, in this case V = 40 x 25 x 3 = 12500.

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Improper fraction 2x2/3

2x2=4 | 4/3. In decimal 1.25 or 1 1/3

Fuel consumption is commonly measured in miles per gallon (mi/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the range, variance, and standard deviation for the sample data. Is the decrease of 4 mi/gal unusual? Why or why not? 2 1 2 1 3 3 4 2 2 2 2 2 2 2 2 3 2 2 2 2 2 The range of the sample data is mi/gal. (Type an integer or a decimal.) The variance of the sample data is . (Round to one decimal place as needed.) mi/gal. The standard deviation of the sample data is mi/gal.

(Round to one decimal place as needed.) Is the largest decrease, 4 mi/gal, unusual? Why or why not? O A. The decrease of 4 mi/gal is unusual because the smallest value in a data set is usually an outlier. O B. The decrease of 4 mi/gal is unusual because it is more than two standard deviations from the mean. O C. The decrease of 4 mi/gal is not unusual because the sample is a simple random sample, in which no values are considered unusual. O D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean.

A. The **range** of the sample data is 4 mi/gal.

B. The **variance** of the sample data is 0.98 mi/gal.

C. The **standard** **deviation** of the sample data is 0.99 mi/gal.

D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean (4 mi/gal is less than 2*0.99 mi/gal).

A. To find the **range** of the sample data, we need to find the difference between the largest and smallest values in the sample. In this case, the largest value is 4 mi/gal and the smallest value is 1 mi/gal. The range is the difference between these two values, which is 4 mi/gal - 1 mi/gal = 3 mi/gal.

B. To find the **variance** of the sample data, we first need to find the **mean** of the sample. The mean is calculated by summing all the values in the sample and dividing by the number of values in the sample. In this case, the mean is [tex]\frac{(2+1+2+1+3+3+4+2+2+2+2+2+2+2+2+3+2+2+2+2+2)}{20} = 2.05[/tex].

Next, we need to subtract the mean from each value in the sample, square the result, and divide it by the number of values in the sample. The variance is

[tex][(2-2.05)^2 + (1-2.05)^2 + (2-2.05)^2 + (1-2.05)^2 + (3-2.05)^2 + (3-2.05)^2 + (4-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (3-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2] = 19.6[/tex]

[tex]\frac{19.6}{20} = 0.98 mi/gal.[/tex]

C. To find the **standard deviation**, we take the square root of the variance. The standard deviation is [tex]\sqrt{0.98} = 0.99 mi/gal[/tex]

D. The standard deviation measures the amount of variation or dispersion in the data. The standard deviation is used to determine how much the values in a sample differ from the mean. If a value is more than two standard deviations away from the mean, it is considered unusual. In this case, the value of 4 mi/gal is less than 2*0.99 mi/gal = 1.98 mi/gal away from the mean, so it is not considered unusual.

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2. Solve for BC using Law of Sines. Round to the nearest tenth when necessary

**Answer:**

the answer to the question is 9.9 in the nearest tenth

i need help with this

5x(15-2x) = 5x(15) - 5x(2x) = 75x - 10x^2

The order of operation first is parenthesis then the x^2, x, / and *, then + and - from left to right. The equation is simplified as 75x - 10x^2.

The order of operation first is parenthesis then the x^2, x, / and *, then + and - from left to right. The equation is simplified as 75x - 10x^2.

Find the measures of all of the angles.

The measure of all the angles are given as follows;

<XVR = 125° [**Sum of angle on a straight line**]

<RVS = 55° [Angle on a straight line or Opposite Angles]

< WVS = 125° [Opposite Angles]

< RST = 125° [Angle on a straight line] Note that ΔRVS is an equilateral

< RSV = 55° [Equilateral Triangle]

<VSU = 125° [VSU and RST are Opposite angles]

<UST = 55° [**Opposite Angles**]

<TUS = 54° [Sum of angles in a Triangle.

What is the sum of Angles on a Straight Line?A **straight line's **angles add up to 180°. Angles may also be calculated using this information.

**Opposite angles **are non-adjacent angles created by two intersecting lines, which is also a mathematical truth.

Angles that are opposite each other are congruent (equal in measure). They are also known as vertically opposing angles and are occasionally referred to as vertical ones. Because they are vertically opposing' at the same **vertex**, the two angles labeled 'a' are equal.

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describe three different methods that you could use to prove that quadrilateral abcd is a parallelogram.

Quadrilateral ABCD is a Parallelogram can be proved by many postulates. The most important** three Postulates **are:-

1. The two opposite side pairs are parallel.

2. The two opposing side pairs are both congruent.

3. One set of opposite sides is parallel and congruent.

In geometry, you'll frequently be required to provide evidence that a particular shape actually exists. For instance, you can be asked to demonstrate that a** quadrilateral** is a** **parallelogram after being shown it. Do not forget that a quadrilateral is a flat, four-sided shape. A quadrilateral with two sets of opposing, parallel sides is referred to as a parallelogram.

A **quadrilateral ABCD** is a Parallelogram

The five approaches to demonstrate that a quadrilateral is a parallelogram will be discussed first, though. You'll employ one of these five methods, depending on the data you've got to work with.

1. Establish the parallelism of the two pairs of opposite sides.

This one is just the opposite of what a parallelogram is. If you can demonstrate that the** quadrilateral **satisfies the requirements for a parallelogram, then it is one.

2. Establish the congruence of both pairs of opposite sides.

There will always be two opposite pairs of parallel sides in a **quadrilatera**l if both pairs of opposite sides are congruent. They measure similarly when objects are congruent.

3. Establish that one pair of opposing sides is parallel and congruent.

The previous procedure and this one are quite comparable. It simply presents the evidence in a different manner. Actually, four toothpicks will work for this experiment. Try it by aligning two toothpicks in a parallel but opposing direction. Now join these two toothpicks to the other two toothpicks at both ends. You'll see that your second pair of toothpicks will always be parallel, regardless of how you arrange your first set.

Hence, **Quadrilateral establish parallelogram.**

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The APR on your credit card is current 31.2%. What is your monthly periodic rate?

If the **APR **on your credit card is current 31.2%. your **monthly **periodic rate is: 2.6%.

Using this formula to determine the monthly **periodic **rate

Monthly periodic rate = APR / 12 months

Where:

APR = Annual percentage **rate **= 31.2% or 0.312

Let plug in the formula

Monthly periodic rate = 0.312/12

Monthly periodic rate = 0.026 or 2.6%

Therefore we can conclude that the **monthly** periodic rate is 2.6%.

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A quadrilateral with vertices (2, 5) and (-3, -4) has point symmetry about the origin.

a. What transformation maps the quadrilateral onto itself?

b. What are the other two vertices of the quadrilateral?

The **transformation** that maps the quadrilateral into itself is [-1 0] and [ 0 -1] and the vertices of the** quadrilateral** is (-3,-4),(2,5),(-2,-5),(3,4)

a. A point symmetry about the origin is a transformation that maps a figure onto itself by reflecting it across the origin. This transformation is known as a central reflection or an isometry, and it is represented by the matrix (with respect to the standard basis)

[-1 0]

[ 0 -1]

b. To find the other two vertices of the quadrilateral, we can apply the transformation to the given vertices.

The **transformation** maps (2,5) to (-2,-5) and (-3,-4) to (3,4).

So, the other two vertices of the quadrilateral are (-2,-5) and (3,4)

So the quadrilateral will be (-3,-4),(2,5),(-2,-5),(3,4)

Note that a **quadrilateral** with point symmetry about the origin is called a kite.

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A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of

long-term-growth supplement and 50 pounds of weed killer. The new packages contain 65 pounds of

long-term-growth supplement and 45 pounds of weed killer. Using past experience, the farmer estimates that he

needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer for the fields. How many old

packages of fertilizer and how many new packages of fertilizer should he use?

**Answer: This is a linear equation problem. The farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer. We can create two equations to represent this information:**

**Let x be the number of old packages**

**x(60) + y(65) = 1550 (long-term-growth supplement)**

**x(50) + y(45) = 1200 (weed killer)**

**Now we can use the system of equation to find the number of old and new packages:**

**x(60) + y(65) = 1550**

**x(50) + y(45) = 1200**

**We can use any method of solving system of equations like substitution, elimination or graphing to find the solution.**

**Example using substitution method:**

**x(50) + y(45) = 1200**

**x = (1200 - y(45)) / 50**

**x(60) + y(65) = 1550**

**(1200 - y(45)) / 50 * 60 + y(65) = 1550**

**We can then solve for y and then x by substituting the value of y back into the first equation**

**y = (1550- (1200 - y(45)) / 50 * 60 ) / 65**

**Finally, the number of old packages is x and the number of new packages is y.**

**Step-by-step explanation:**

The number of **old packages** and the number of **new packages** is 15 and 10 respectively.

**Linear equations** are the equations of degree 1. It is the **equation** for the **straight line**. The solutions of linear equations will generate values, which when substituted for the unknown values, make the **equation** true.

Given that, the farmer needs 1550 pounds of **long-term-growth **supplement and 1200 pounds of weed killer.

We can create two **equations** to represent this information:

Let,

x = the number of old packages

y = the number of new packages

The **system of equations** that describes the situation is:

60x + 65y = 1550

12x+13y = 310......(i)

50x + 45y = 1200

10x+9y = 240......(ii)

Solving the equations,

**Multiply** the eq(i) by 10 and the eq(ii) by 12, and then **subtract**,

22y = 220

y = 10

Put y = 10 in eq(ii)

10x+90 = 240

10x = 150

x = 15

Hence, the number of **old packages** and the number of **new packages** is 15 and 10 respectively.

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What is the value of mm in the equation m+6=43m+6=43?

The **value** of m from the given equation is 37.

A mathematical **equation** is a formula that uses the equals sign to represent the equality of two expressions.

The given equation is m+6=43

We need to find the value of m from the given equation.

The group of values used to replace the unknowns in an equation to make it true is known as the **solution**.

To solve given equation:

Transpose 6 to RHS of the equation, we get

m=43-6

Subtract 43 and 6 we get 37

So, m=37

Therefore, the **value** of m from the given equation is 37.

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You want to calculate the height of a tree in your yard. You stand 25 feet from the base of the tree and with a special instrument, you measure the angle of elevation from where you are on the ground to the top of the tree. You find that the angle of elevation is about 52°. What is the approximate height of the tree?

Between the horizontal line and the line of sight, an **angle** called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created.

The angle of elevation is defined in mathematics as "the angle created between the horizontal line and the line of sight when an observer looks upwards." It's always higher than the spectator, usually at a greater **height**. Angles of depression are created when a person looks downward, and they are the polar opposite of angles of elevation. While studying heights and distances in trigonometry, it is crucial to understand the angle of elevation and **depression**. Angle, horizontal line, and line of sight are the three general terms used to describe the angle of elevation.

To calculate the height of a tree using trigonometry, you would use the tangent function. Specifically, you would use the tangent of the angle of elevation (52° in this case) and the distance from the base of the tree to where you are standing (25 feet in this case).

The formula is:

height = distance * tangent(angle of elevation)

So, the height of the tree is approximately:

25 * tangent(52) = 25 * 1.19 = 29.75 feet

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Please help I’m struggling

**Answer:**

B

**Step-by-step explanation:**

Each floor, the rent is 3% more than the previous floor, so we multiply by 1.03.

Since we do this 17 times, the answer is [tex]1420 \cdot 1.03^{17}[/tex].

**Answer: B**

**Step-by-step explanation:**

You just need to find the formula, replace 17 with variable x and $2347.04 with y and graph. It will give you the right answer.

serious reply for finding the function to f(x+1)=3x squared +4x-2

The **numeric value **of the function f(x) = 3x² + 4x - 2 at x = x + 1 is obtained as follows:

f(x + 1) = 3x² + 10x + 3.

How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we **replace each instance **of the variable in the function or in the expression by the value at which we want to find the numeric value.

The **function **for this problem is defined as follows:

f(x) = 3x² + 4x - 2

The **numeric value** at x = x + 1 is found replacing both instances of x by x + 1, hence:

f(x + 1) = 3(x + 1)² + 4(x + 1) - 2

f(x + 1) = 3(x² + 2x + 1) + 4x + 4 - 4

f(x + 1) = 3x² + 6x + 3 + 4x

f(x + 1) = 3x² + 10x + 3.

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which equations are equivalent to -2y+3/2x+7/4

a) -1/2xy+7/4

b) 3/2x-2(y+7/2)

c) -1/4y+3/2 (y+x)

d-2y+1/2(3x+7/2)

e) 1/4 (-8y+6x+7)

The equations equivalent to the given equation are **-2y+1/2(3x+7/2) **and **1/4(-8y+6x+7)**.** **The solution has been obtained by using the **simplification** method.

**What is simplification?**

**Simplifying** in mathematics refers to the **process** of working with and understanding an **equation** in a way that makes it more **understandable **or transparent. The process of **grouping** similar **terms** together so that the problem can no longer be solved further is known as **simplification**.

We are given -2y + 3/2x + 7/4

In order to find which expression is equivalent to the given, we need to **simplify** the expressions.

a. -1/2xy+7/4

This is **not** the same expression as given.

b. 3/2x-2(y+7/2)

⇒ 3/2x - 2y - 7

This is **not** the same expression as given.

c. -1/4y+3/2 (y+x)

⇒ -1/4y + 3y/2 + 3x/2

This is **not** the same expression as given.

d. -2y+1/2(3x+7/2)

⇒** -2y + 3x/2 + 7/4**

This is the **same expression** as given.

e. 1/4 (-8y+6x+7)

⇒**-2y + 3x/2 + 7/4**

This is the **same expression** as given.

Hence, the equations equivalent to the given equation are **-2y+1/2(3x+7/2) **and **1/4(-8y+6x+7)**.

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Select the correct answer from each drop-down menu. A triangle ABC with base AC is shown. A line DE, parallel to line AC, passes through vertex B. Interior angle at vertex A is labeled 1, at vertex C is labeled 3, and at vertex B is labeled 2. The exterior opposite angles at vertex B are 4 and 5. Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°. Statement Reason Points A, B, and C form a triangle. given Let be a line passing through B and parallel to . definition of parallel lines ∠3 ≅ ∠5 and ∠1 ≅ ∠4 m∠1 = m∠4 and m∠3 = m∠5 m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line m∠1 + m∠2 + m∠3 = 180° substitution

The statement to prove that the **sum** of the interior angles of ΔABC is 180° should be completed as follows;

Statements Reasons

Points A, B, and C form a triangle. ⇒ Given

Let DE be a line passing through B and **parallel **to AC. ⇒ definition of **parallel** lines

∠3 ≅ ∠5 and ∠1 ≅ ∠4 ⇒ alternate interior angle theorem.

m∠1 = m∠4 and m∠3 = m∠5 ⇒ congruent angles have equal measures.

m∠4 + m∠2 + m∠5 = 180° ⇒ angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180° ⇒ substitution

What is the congruence of angles?In Mathematics, congruence of angles can be defined as a theorem which states that two (2) angles are **congruent** when the measure of their angles are equal.

This ultimately implies that, two (2) **congruent** angles would always have equal measures as depicted in triangle ABC with line DE;

m∠1 = m∠4 and m∠3 = m∠5

By applying the **Alternate Interior Angles** Theorem to triangle ABC and line DE, we have the following:

∠3 ≅ ∠5 and ∠1 ≅ ∠4

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Which linear equation represents the graph? Responses A y = 9x − 9y = 9x − 9 B y = −9x + 9y = −9x + 9 C y = 9x + 9y = 9x + 9 D y = −9x − 9

The **linear equation **y = -9x + 9 represents the **line **given in the **graph**. Thus, option D is correct.

**Linearity **is a property of equations with highest degree of 1. There isn't a single **variable **in it with an exponent greater than 1. The name "**linear** **equation**" comes from the fact that a **linear equation **always results in a straight line on a graph.

**Linear equations **in one **variable **and two **variables **are common in mathematics.

Two of lines' points on the plane are (1, 0)and (0, 9)

Lets put the value in the **slope formula**

y₂ - y₁ = m(x₂ - x₁)

9 - 0 = m(0 - 1)

9 = -m

m = -9

As we have the **slope **of the line lets put one of the values to get** slope intercept form**

y - y₁ = m(x - x₁)

y - 9 = -9(x - 0)

y = -9x + 9

Thus, The **linear equation **y = -9x + 9 represents the **line **given in the **graph**. Thus, option D is correct.

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You deposit $120 in an investment account that earns 6.4% annual interest compounded quarterly write a function that represents the balance y (in dollars) of the investment account after t years y= ? What is the balance of the account after 6 years

**Answer:1200**

**Step-by-step explanation:**

**Answer:**

[tex]\textsf{Function:} \quad y=120\left(1.016\right)^{4t}[/tex]

The **balance **of the account after 6 years is **$175.64** (nearest cent).

**Step-by-step explanation:**

To write a **function **that represents the **balance **y (in dollars) of the investment account after t years, substitute the given values into the **compound interest formula**.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

A = yP = $120r = 6.4% = 0.064n = 4 (quarterly)t = t yearsSubstitute these values into the **formula**:

[tex]\implies y=120\left(1+\dfrac{0.064}{4}\right)^{4t}[/tex]

[tex]\implies y=120\left(1+0.016\right)^{4t}[/tex]

[tex]\implies y=120\left(1.016\right)^{4t}[/tex]

To calculate the **balance **of the account after 6 years, **substitute t = 6 **into the function:

[tex]\implies y=120\left(1.016\right)^{4 \cdot 6}[/tex]

[tex]\implies y=120\left(1.016\right)^{24}[/tex]

[tex]\implies y=120\left(1.46368961...\right)^{24}[/tex]

[tex]\implies y=175.642753...[/tex]

Therefore, the **balance **of the account after 6 years is **$175.64** (nearest cent).

NO LINKS!!

Write an equation to represent the following graphs:

a. passes through (-2, 18.75 and (1, 1, 1.2)

a-value:___________ b-value:____________

Equation: _____________________

b. passes through (0, 6) and (2, 8.64)

a-value:_____________ b-value:_____________

Equation:________________________

**Answer:**

[tex]\textsf{a)\;\;passes\;through\;$(-2, 18.75)$\;and\;$(1, 1.2)$}[/tex]

[tex]\textsf{$a$-value:\;\;3 \quad $b$-value: \;\;0.4}[/tex]

[tex]\textsf{Equation: \quad $y=3 (0.4)^x$}[/tex]

[tex]\textsf{b)\;\;passes\;through\;$(0, 6)$\;and\;$(2, 8.64)$}[/tex]

[tex]\textsf{$a$-value:\;\;6 \quad $b$-value: \;\;1.2}[/tex]

[tex]\textsf{Equation: \quad $y=6 (1.2)^x$}[/tex]

**Step-by-step explanation:**

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Part (a)Given **points**:

**Substitute **both **points **into the **exponential function** formula to create **two equations**:

**Divide **the equations to **eliminate a**, then **solve for b**:

[tex]\implies \dfrac{18.75}{1.2}=\dfrac{ab^{-2}}{ab}[/tex]

[tex]\implies15.625=\dfrac{b^{-2}}{b}[/tex]

[tex]\implies15.625=b^{-2}b^{-1}[/tex]

[tex]\implies15.625=b^{-3}[/tex]

[tex]\implies15.625=\dfrac{1}{b^{3}}[/tex]

[tex]\implies b^{3}=\dfrac{1}{15.625}[/tex]

[tex]\implies b=0.4[/tex]

**Substitute **the found **value of b** into the second equation and** solve for b**:

[tex]\implies 1.2=0.4a[/tex]

[tex]\implies a=3[/tex]

Therefore, the **exponential equation **is:

[tex]y=3 (0.4)^x[/tex]

-------------------------------------------------------------------------------------------

Part (b)Given **points**:

**Substitute **point (0, 6) into the **exponential function** formula and **solve for a**:

[tex]\implies 6=ab^0[/tex]

[tex]\implies 6=a(1)[/tex]

[tex]\implies a=6[/tex]

**Substitute **the found **value of a** and point (2, 8.64) into the **exponential function** formula and **solve for b**:

[tex]\implies 8.64=6b^2[/tex]

[tex]\implies b^2=\dfrac{8.64}{6}[/tex]

[tex]\implies b^2=1.44[/tex]

[tex]\implies b=\sqrt{1.44}[/tex]

[tex]\implies b=1.2[/tex]

Therefore, the **exponential equation **is:

[tex]y=6 (1.2)^x[/tex]

Round the answer to the correct number of significant figures.

28.23

3.49

+ 5.3 = 13.389

**Answer:**

**13.389 = 13.4 **

For a goodness-of-fit test, the frequencies obtained from the performance of an experiment are the:

i) subjective frequencies

ii) observed frequencies

iii) expected frequencies

iv) objective frequencies

Option **B** : **observed frequencies** are the frequencies obtained from the **performance** of an experiment for a **goodness-of-fit test . **

The frequency, or outcomes, that are gathered during an experiment are known as **observed frequencies.** This is frequently the collection of data that is documented in mathematics. The distinction between an observed frequency and an expected frequency is described on the display poster. **Counts** derived from experimental data are known as observed frequencies. In other words, you really take measurements when the data is being collected. For instance, you might roll a die ten times and then tally the number of times each number appears. Following the experiment, the count is made. The observed frequencies are these numbers, and the sign for an **observed** frequency is O. There are k entries in the table. There are n total observed frequencies. Calculating **predicted** frequencies involves multiplying the probability.

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