5

-5

40

x

Select all of the following ordered pairs that are in

the solution set of the inequality shown.

(-10,-10)

(0, 0)

(0, 10)

(10,0)

(20, 0)

(100, 100)

The only solution that satisfies the inequality is the **point (0,0)**

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Write an exponential

function y = ab∧x

whose

graph passes through the

points

(2, –50), (4, –1250)

The **exponential function **will be** y= -2(3)^**x.

What are **exponential functions**?

An **exponential function **is a Mathematical function in the form f (x) = a^x, where “x” is a **variable **and “a” is a **constant **which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the **transcendental number **e, which is approximately equal to 2.71828.

Now,

Given **points **for exponential function are (2, –50), (4, –1250).

and exponential function is y=ab^x

To find a and b put points in the function

-50=ab^2 -->1

-1250=ab^4 --->2

From **equation **1

a=-50/b^2

Put value of a into 2

-1250=-50/b^2*b^4

b^2=25

b=5

For b=5, a=-50/5^2=-2

Hence, a=-2

Therefore,

The **exponential function **will be** y= -2*5^x**.

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Find a set of four integers such that their order and the order of their absolute valúes are the same

The set of 4 integers are is given by the **equation **A = { 1 , 2 , 3 , 4 }

**Equations **are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an **equation**. The "=" sign and terms on both sides must always be present when writing an **equation**.

Given data ,

Let the set of 4 integers be represented as set A

Now , the **equation **will be

Let the first **number **be 1

The absolute value of 1 is | 1 | = 1

Let the second **number **be 2

The absolute value of 2 is | 2 | = 2

Let the third **number **be 3

The absolute value of 3 is | 3 | = 3

Let the fourth **number **be 4

The absolute value of 4 is | 4 | = 4

And , | 1 | < | 2 | < | 3 | < | 4 |

Hence , the set of integers are { 1 , 2 , 3 , 4 }

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Kellen is having a party at a restaurant that charges $350 to rent a room and $12.50 per person for the meal. His maximum budget is $1500 . He will have x people at the party. Which of the following must be satisfied by x if Kellen does not exceed his budget?

**Answer:**

**Step-by-step explanation:**

350 + x people = 1500

x = 1500 - 350

x = 1150 / 12.50

x = 92 people

Find four pairs of integers that add up to 1.

**Answer:**

5 & -4

4 & -3

3 & -2

2 & -1

**Step-by-step explanation:**

5 + (-4) = 1

4 + (-3) = 1

3 + (-2) = 1

2 + (-1) = 1

ella has 0.5 lb of sugar how much water should she add to make the following concentrations? tell ella how much syrup she will have in each case. 75% syrup ella should add _ lb water and she will have to add _lb syrup

**Answer: The answer provided is based on the following calculation:**

**To make a 75% syrup, Ella should add enough water to the sugar to create a solution that is 25% sugar and 75% water.**

**To calculate how much water to add, you can use the formula: (desired % of sugar) / (100 - desired % of sugar) * (amount of sugar).**

**In this case, it would be: (0.75) / (100 - 0.75) * (0.5 lb) = 0.67 lb of water.**

**To calculate the total amount of syrup, you add the amount of sugar and the amount of water: 0.5 lb + 0.67 lb = 1.17 lb.**

**So Ella should add 0.67 lb of water to make a 75% syrup and will have a total of 1.17 lb syrup.**

**Step-by-step explanation:**

**Answer:**

**for the 75% syrup: 0.167lbs**

**For the 1.5% syrup: 32.83 lbs**

Can somebody please tell me how do we solve this? Thank you.

The correct option is E. the roots of the **auxiliary **equation are √6 and -√6.

Differential equations are defined as the **equations **in which consist of one or more terms which consist of the a dependent variable and it's derivatives with respect to the **independent **variable.

Given differential equation,

[tex]\frac{d^{2} y}{dx^{2} }[/tex] - 6y = 0

This can be also written as,

y'' - 6y = 0, where y'' indicates the second **derivative **of y.

Auxiliary equation is the **polynomial **equation which is found by replacing the right member of a **standard **differential equation by zero.

To find the roots of auxiliary equation can be found by,

Let m = y', then m² = y''

m² - 6 = 0

m² = 6

m = ± √6

So the **roots **are √6 and -√6.

Hence the roots of the auxiliary equation of the given differential equation are √6 and -√6.

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Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)

f(x) = √5x + 4

X = ?

**Answer:**

**-4/√5**

**Step-by-step explanation:**

when f(x) = 0.

we can set the function equal to 0 and solve for x:

√5x + 4 = 0

√5x = -4

x = -4/√5

So the zero of the function is x = -4/√5

Which of the following describes the domain and range of the function?

The **domain** and **range **of the piecewise function is;

B) Domain: x < 2 or x ≥ 3.; range: y > -3

What is the domain and range of the function?The **piecewise function** is given as;

f(x) = {-¹/₂x - 2, if x < 2

{2x - 4, if x ≥ 3

The **domain** of a function is the set of all possible input values of the function and as such in this case the domain is x < 2 or x ≥ 3.

The **range** is defined as the set of all possible output values of the function and in this case, we have;

For -¹/₂x - 2; If x < 2

At x = 2; -¹/₂(2) - 2 = -3

**Range** is; y > -3

Similarly, for 2x - 4, if x ≥ 3

At x = 3; 2(3) - 4 = 2

**Range** is; y ≥ 2

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A coin with a head on one side and a tail on the other is tossed, followed by a six-sided die with faces marked 1 through 6 being rolled. If each outcome is equally likely, what is the probability of each outcome?

The **probability **of **each outcome** is given as follows:

1/12.

How to obtain the probability?A **probability **is obtained as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that the **total number** of outcomes is of twelve, as:

Hence:

6 x 2 = 12.

(applying the Fundamental Counting Theorem).

Meaning that the probability of each outcome is given as follows:

1/12.

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1. Antonio sets his remote-controlled car at the start of the racetrack and starts its run on the track. His car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance and then stops for good. It is 38m from the starting line. How long is the racetrack? (a) Let x = the length of the racetrack. Write an equation that fits the story (b) Solve the equation from Part a. (How long is the racetrack?) Show your work. (c) How much farther did Antonio’s car have to go to the finish line? Show your work.

The total **length **of the **race track **that Antonio remote** controlled** car runs on is 70 m.

An equation is an **expression** that shows how numbers and variables relate with each other.

Equations can either be** linear, quadratic a**nd so on depending on the degree of the polynomial

Let x represent the **length** of the racetrack.

Antonio car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s **total distance**. It can be represented by the equation:

(2/5)x + 10 = 38

(2/5)x = 28

x = (28 * 5)/2

x = 70

The **length **of the **race track **is 70 m.

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Select the correct answer. What is the solution for x in the equation? -4 + 5x − 7 = 10 + 3x − 2x A. x = 4 21 B. x = 4 13 C. x = 13 4 D.

x = 21/4

First combine like terms on both sides of the equation: -4 + 5x - 7 = 10 + 3x - 2x

5x - 11 = 10 + x

Now, we want to isolate the variable, x, to one side. Preform the opposite operation (for + you subtract and for - you add) to combine like terms again.

5x -11 = 10 + x

+ 11 - x

These will cancel out and move to the other side of the equal sign.

5x - x = 10 + 11

4x = 21

Finally, divide each side by 6 to get x alone.

x = 21/4 or 5.25.

First combine like terms on both sides of the equation: -4 + 5x - 7 = 10 + 3x - 2x

5x - 11 = 10 + x

Now, we want to isolate the variable, x, to one side. Preform the opposite operation (for + you subtract and for - you add) to combine like terms again.

5x -11 = 10 + x

+ 11 - x

These will cancel out and move to the other side of the equal sign.

5x - x = 10 + 11

4x = 21

Finally, divide each side by 6 to get x alone.

x = 21/4 or 5.25.

Please help!!! please! which letter represent the opposite of 1 1/3 on the number line below

**Answer:**

K

**Step-by-step explanation:**

K represents negative 1 ⅓.

to find the opposite of a number you must look to see if its negative. if its negative then its opposite would be a positive. If its a positive then its opposite would be a negative. Opposites are always the number in opposite signs like 7 and -7.

I found K to be 1⅓ because there are 2 spaces in between numbers so it would be ¹ ⅓ ⅔ 1. so I went to the number 1 and went one space back/where K because I know it would be 1 ⅓

Write the slope-intercept form of the equation of each line: 1) x − y = −3, 2) 2x + y = −6, 3) 4x + y = −7

The **slope - intercept form** of the **equations **of each of the given lines is:

The** slope - intercept form** is:

y = mx + b

Where

m = slope

b = y - intercept

Basically, given the **equations **of each **line**, you are to move y such that it goes to the left of the equation and remains there alone, while the other figures stay on the right side.

Equation 1:

x − y = −3

x + 3 = y

y = x + 3

Equation 2:

2x + y = −6

y = - 6 - 2 x

y = - 2x - 6

Equation 3 :

4x + y = −7

y = - 4x - 7

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h(t)=-16t^(2)+130t+2 how many seconds does the ball attain its height round to the nearest hundredth

The **number **of **seconds **that the ball attains its height round to the nearest **hundredth **will be 4.06 seconds.

For the **maximum **value of the function if f''(x) < 0 and for the **minimum **value of the function if f''(x) > 0.

The **maximum **and **minimum **value of the function is at f'(x) = 0.

The **function **is given below.

h(t) = -16t² + 130t + 2

**Differentiate **the function with respect to t. Then we have

h'(t) = -32t + 130

h'(t) = 0

- 32t + 130 = 0

t = 130 / 32

t = 4.0625 seconds

The **number **of **seconds **that the ball attains its height round to the nearest **hundredth **will be 4.06 seconds.

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4. A model kit for the Dornier Do17 airplane has a wingspan of approximately 10 inches. If the kit has a

scale of 1 inch to 72 inches, what is the wingspan of the actual Dornier Do17? Show all your work.

**Answer: If the model kit for the Dornier Do17 airplane has a wingspan of 10 inches and the scale of the kit is 1 inch to 72 inches. This means that for every inch on the model, the equivalent measurement on the actual Dornier Do17 airplane is 72 inches.**

**We know that the wingspan of the model is 10 inches and we want to find the actual wingspan of the airplane so we'll use the scale factor of 1:72**

**To find the actual wingspan, we'll multiply the wingspan of the model by the scale factor.**

**10 inches * 72 inches/1 inch = 720 inches**

**Therefore, the actual wingspan of the Dornier Do17 airplane is 720 inches or 60 feet.**

**Step-by-step explanation:**

Find three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.

**Answer:**

2, 4, 6

**Step-by-step explanation:**

You want three **consecutive even integers** such that the sum of **twice the first** and **three times the second** is **4 more** than **twice the third**.

Let x represent the middle integer. Then the first is (x-2) and the third is (x+2). The given relation is ...

2(x -2) + 3x = 2(x +2) +4

SolutionSimplifying the equation gives ...

2x -4 +3x = 2x +4 +4

5x -4 = 2x +8 . . . . . . . collect terms

3x = 12 . . . . . . . . . . . add 4-2x

x = 4 . . . . . . the middle integer

**The integers are 2, 4, 6**.

__

*Additional comment*

It often simplifies the equation if the variable is used to represent the middle of the consecutive integers in problems like this. In this particular problem, there is not a great advantage.

<95141404393>

A red and a blue die are thrown. Both dice are fair. The events A and B are defined as follows:

A: The blue die shows a number greater than 2.

B: The red die shows a number less than 5

What is p(A|B)? (Round to four decimal places.)

P(A|B) read as the **probability** of the event A given the **event** B is equal to 0.5000 rounded up to four decimal place.

**Conditional** probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome. The conditional **probability** P(A|B) occur only in the case of dependent events. It gives the conditional probability of A given that B has occurred.

P(A|B) = P(A∩B) / P(B)

P(A∩B) = **Probability** of happening of both A and B

When a die is rolled, the sample space = {1, 2, 3, 4, 5, 6}.

A is the **event** the blue die shows a number greater than 2, So;

A = {3, 4, 5, 6}

B is the **event** the red die shows a number less than 5. So;

B = {1, 2, 3, 4}.

Then A∩B = {3, 4}

P(A∩B) = 2/6 = 1/3

P(B) = 4/6 = 2/3

P(A|B) = 1/3 ÷ 2/3

P(A|B) = 1/3 × 3/2 {changing division to multiplication}

P(A|B) = 1/2

Therefore, the **conditional** **probability** of the event A given the event B denoted by P(A|B) is equal to 1/2 or 0.5000 to four decimal place.

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Find all the missing side and angles < p

Therefore , the solution of the given problem of **triangle** comes out to be ∠P = 30° , PQ = 4√3 and PN = 2.

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having **angles** A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a **polygon.** The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given : A right triangle,

=> ∠P + 60° + 90° = 180°

=> ∠P = 180° - 150°

=> ∠P = 30°

For PQ

=> Tan 60° = √3

=> PQ /4 = √3

=> PQ = 4√3

For PN ,

=> Sin 60° = √3/2

=> 4√3 / PN = √3/2

=> PN = 2

Therefore , the solution of the given problem of triangle comes out to be

∠P = 30° , PQ = 4√3 and PN = 2.

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What are the solutions of 2 - 5x+7=0?

○ A. x = 5+3² or x =

OB. x =

5+1v2 or 2 = 5-√2

OC. x =

- 5+₁v²

5+√2

2

or x =

○ D. x = 5+√³ or x =

5-i√2

**The solution** to **the equation** x^2-5x+7=0 are x=5/2+3/2i and x=5/2-3/2i

A mathematical statement that has an **"equal to" **symbol between two expressions with** equal values** is called an equation. as in 3x + 5 Equals 15, for instance.** Equations** come in a variety of forms, including linear, quadratic, cubic, and others. In this** tutorial**, let's study more about math equations.

There are three major forms of **linear equations**: point-slope form, standard form, and slope-intercept form.

According to the given question, we see

by solving **the inequality **we get

x=5/2+3/2i and x=5/2-3/2i

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A toy car and a battery together costs £44. The ratio of the cost of the car to the battery is 10:1. How much did the battery cost?

**Answer:**

4,4

**Step-by-step explanation:**

44x1/10

What is the graph of the solution to the following compound inequality?

7x+3 ≤ 52 and 3-x<9

O A.

O B.

О с.

O D.

-10-9-8-7 -6 -5 4 -3 -2 -1 0 1 2 3 4

5 6 7 8 9 10

-10-9-8-7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

-10-9-8-7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B

-10-9-8-7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Here, on solving the provide question to us, we got to know that - **equation **210 feet represents = 825/4

Since equations are essentially questions, efforts to **systematically **find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or **multiplication **to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Here,

15 feet represents = 1/8 of an inch

1 feet represents = 1/8 X 15

The growth of mathematics has been fueled by efforts to methodically find answers to equations, which are basically questions. There are many distinct forms of equations that range in complexity, from simple algebraic equations that just need addition or multiplication to differential equations, exponential equations that employ exponential expressions, and integral equations 210 feet represents = 1/8 X 15 X 210 = 825/4

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"Find all the second partial derivatives

f(x,y)= sin^(2) (mx+ny)"

Therefore , the solution to the given problem of **derivative** comes out to be 2cos(mx+ny) for both the cases of partial derivative.

The definition of a derivative is the simultaneous change that occurs at a certain place. Implicit & explicit **functions** are typically distinguished from one another. Explicit functions are those where the value of the known individual entity "x" directly determines the value of the known dependent **variable** "y."

Here,

Given : f(x,y)= sin^(2) (mx+ny)"

Partial derivative with respect to x

=> dx/dy = 2sin (mx+ ny) *m

=> d²x/dy = 2cos(mx+ny)

Partial derivative with respect to y

=> dx/dy = 2sin (mx+ ny) *n

=> d²x/dy = 2cos(mx+ny)

Therefore , the solution to the given problem of derivative comes out to be 2cos(mx+ny) for both the cases of partial derivative.

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In ΔGHI, g = 75 inches, mm∠H=151° and mm∠I=7°. Find the length of h, to the nearest 10th of an inch.

The **triangle** has length of the side h is equal to 97.1 inches approximately to the nearest tenth, using the **sine** **rule**.

The **sine** **rule** is a relationship between the size of an angle in a **triangle** and the opposing side.

For the **triangle** ΔGHI, by sine rule;

g/sinG = h/sinH = i/sinI

We first derive the angle G as follows:

151° + 7° + G = 180° {sum of interior angles of a triangle}

G = 180° - 158

G = 22°

Hence by **sine** **rule**;

75/sin22° = h/sin151°

h = (75 × sin151°)/sin22° {cross multiplication}

h = 97.1

Therefore, by application of the sine rule we have the length of the side h = 97.1 inches approximately to the nearest tenth

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Use the graph of y=f(x) to

A. Determine f(-1)

B. Find the range of f.

(A) ** f(-1) = 1**

(B) The **range** of the **function** **f(x) **is** [-4, ∞**).

**What is the range of the function?**

In mathematics, a **function's** **range** can refer to one of two closely related ideas: Its codomain is a **function**. The picture of the action Given two sets X and Y, a **binary** relation f between them is a **function** if and only if there is precisely one y in Y such that f connects x to y for every x in X.

For the given function we have to find the value of f(-1) and to find the **range** of the **function**.

From graph we can see that,

f(-1) = 1

The range of the function is the interval in which function cover the x - axis.

The range of the function is [-4, ∞).

Hence,

(A) ** f(-1) = 1**

(B) The **range** of the **function** **f(x) **is** [-4, ∞**).

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Reasoning with linear equations

The answer is D, I think. There’s parentheses and something outside of the parentheses which means that something outside of the parentheses will distributed to whatever is inside the parentheses

which scenarios are better represented by an equation in standard form vs. y=mx+b

The standard form is used to show **horizontal lines** and v**ertical lines**, while the slope intercept form shows the** slope** and y **intercept** of the linear equation.

An equation is an e**xpression** relating two or more numbers and variables.

The standard form of a** linear equation** is:

Ax + By = C

where A, B and C are** constants**

The** slope - intercept **form of a linear equation is:

y = mx + b

Where m is the** rate of change(slope)** and b is the **y intercep**t.

The standard form is used to show **horizontal lines **(A=0) and v**ertical lines **(B=0), while the slope intercept form shows the** slope** and y **intercept**.

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info about question in picture

The** coordinates** of the linear equation for (m, s) are; (0, 4), (2, 3), (-2, 5), (8, 0)

This is a one to one mapping and example of a function

How to solve linear equation problems?We are given the **equation **as;

2m + 4s = 16

Thus;

When m = 0, we have;

2(0) + 4s = 16

4s = 16

**divide** both sides by 4 to get;

s = 4

When s = 3;

2m + 4(3) = 16

2m + 12 = 16

2m = 16 - 12

**Divide** both sides by 2 to get;

m = 4/2

m = 2

When m = -2

we have;

2(-2) + 4s = 16

-4 + 4s = 16

4s = 20

divide both sides by 4 to get;

s = 5

When s = 0, we have;

2m + 4(0) = 16

2m + 0 = 16

2m = 16

Divide both sides by 2 to get;

m = 16/2

m = 8

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find the derivative of the function. f(x) = (5x6 + 4x3)4

The **derivate **of function f(x)=(5x⁶+4x³)⁴is **F'(x) = 4(30x³+12x²)(5x⁶+4x³)³**

The derivative of a function f(x) **represents **its rate of change and is denoted by** f'(x) **or **df/dx.**

The derivative Formula is given as:** **

**f1 (x)=lim△x→0 f(x+△x) − f(x)△x.**

Take the derivative: F'(x) = [tex]\frac{d}{dx} (5x^6+4x^3)^5[/tex]

**Substitute **the inner function by (5x⁶+4x³)

Apply the** chain rule**: [tex]\frac{d}{dx} (g)^4*\frac{d}{dx} (5x^6+4x^3)^4[/tex]

Calculate the derivative: [tex]4g^3*\frac{d}{dx} (5x^6+4x^3)^4[/tex]

Substitute back: [tex]4(5x^6+4x^3)^3*\frac{d}{dx} (5x^6+4x^3)[/tex]

Result after **applying **the chain rule: F'(x) = [tex]4(5x^6+4x^3)^3*\frac{d}{dx} (5x^6+4x^3)[/tex]

Calculate the derivative of the **sum **or **difference**:

F'(x) =[tex]4(5x^6+4x^3)^3*(\frac{d}{dx} (5x^6))+\frac{d}{dx} (4x^3))[/tex]

Take out the coefficients F'(x) = [tex]4(5x^6+4x^3)^3*(5*\frac{d}{dx} (x^6)+4\frac{d}{dx}(x^3))[/tex]

Apply the **power **rule: F'(x) = 4(5x⁶+4x³)³*(5*6x³+4*3x²)

Multiply the **monomials**: F'(x) = 4(5x⁶+4x³)³*(30x³+12x²)

Rewrite the expression: F'(x) = 4(30x³+12x²)*(5x⁶+4x³)³

So, the answer is F'(x) =4(30x³+12x²)*(5x⁶+4x³)³

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please help me with this

**Answer: B**

**Step-by-step explanation: 85.10 is total. 46 per minutes. $85/$/Min.46. The $ cancels and you get minutes.**

4) Daniella and Brayan have a joint checking account. They have a balance of $3,839.25 in the check register. The balance on the bank statement is $3,450.10. Not reported on the statement are deposits of $2,000, $135.67, $254.77, and $188.76 and four checks for $567.89, $23.83, $598.33, and $1.000. Reconcile the bank statement.

End Balance: $3,839.25 + $2,579.20 - $2,190.05 = $5,735.15, so the reconciled** balance** of $5,735.15.

This theory is used to compare the bank statements to the check register in order to properly reconcile the two balances.

The theory used in this question is the bank **reconciliation** theory.

Step 1: Begin by looking at the two balances - the check register balance and the bank statement balance.

In this case, the check register balance is $3,839.25 and the bank statement balance is $3,450.10.

Step 2: Add up all of the deposits that are not reported on the bank statement. In this case, the deposits are $2,000, $135.67, $254.77, and $188.76.

Step 3: Subtract all of the checks that are not reported on the bank statement. In this case, the checks are $567.89, $23.83, $598.33, and $1,000.

Step 4: Add the **deposits** and subtract the checks from the check register balance.

In this case, the check register balance ($3,839.25) plus the deposits ($2,579.20) minus the checks ($2,190.05) gives a reconciled balance of $5,735.15.

To learn more about **bank reconciliation theory**, visit

brainly.com/question/29097188

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