In Exercises 13-15, use f(x) = x² and g(x) = 4x - 6 to find h(x).

13. h(x) = f(x) - g(x)

14. h(x) = f(g(x))

15. h(x) is the inverse of g(x)

The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image

y = - 1/2x + 3

In order to graph the equation of the line:

First, find the value of x when y = 0:

y = - 1/2x + 3 , when y = 0:

0 = - 1/2x + 3

1/2x = 3

x = 3 × 2

x = 6

Also, find the value of y when x = 0:

y = - 1/2x + 3, when x = 0:

y = - 1/2(0) + 3

y = 3

Therefore,  the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached

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Using the Algebraic tile method we get x=2 solution for equation model

The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.

In the question, we have 3 kinds of tile

Equation will be :

⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1

⇒ 3x - 2 = 4

⇒ 3x = 6

⇒ x = 2

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The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.

Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.

Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.

Thus;

[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]

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Answer:

Step-by-step explanation:

y= 265

The rate of change of the equation is 25.

The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.

Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.

Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.

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The profits last year were $2041.66

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900

                            x=4900/2.4

                            x=2041.66

Hence, The profits last year were $2041.66

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The money invested in a  account with 3% interest is $3000 and the money invested in a  account with 6% interest is $6000.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, Susan invested a total of $9000 in two account.

One account pays 3% interest and the other account pays 6% interest.

Let the money invested in a  account with 3% interest be x.

Then, the money invested in a  account with 6% interest be 9000-x.

The total return from both accounts was $450.

Here, (x×3×1)/100 + ((9000-x)×6×1)/100 =450

3x+54000-6x=45000

54000-3x=45000

3x=9000

x=$3000

So, 9000-x=$6000

Therefore, the money invested in a  account with 3% interest is $3000 and the money invested in a  account with 6% interest is $6000.

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Answer:

D

Step-by-step explanation:

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex]  Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]

7[tex]\frac{9}{8}[/tex]

7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex]  Another name for [tex]\frac{8}{8}[/tex] is 1

7 + 1 + [tex]\frac{1}{8}[/tex]

8[tex]\frac{1}{8}[/tex]

Answer: x = -5, y = 4

Step-by-step explanation:

Align the two equations according to their terms:

[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]

Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:

[tex]3y = 12\\y = 4[/tex]

Plug in y = 4 into the first equation:

[tex]-3x - 3(4) = 3\\[/tex]

Solve for x:

[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]

Check by plugging in both x and y:

[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]

So, x = -5 and y = 4

Answer:

D+Q = 31

10D + 25Q = 595

10D + 10Q = 310

subtract to get

15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes

Answer:

(2,-2)

Step-by-step explanation:

The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.

hope this helps :)

Answer:

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

From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:

The first line is given y = 1/2x - 3, equate both to get:

Then the value of y:

The solution is (2, - 2).

The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96

The amount of interest that Latoya paid was $ 980.96

The total amount paid by Latoya for the machinery can be found as :

= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )

= 1, 800 + ( 313. 36 x 12 x 3 )

= $ 13, 080 .96

The total interest paid on the loan was :

= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment

= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800

= $ 980.96

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Dirk will make 70 pars or better.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.

Out of 90 holes, Dirk made par or better on 42 holes.

At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.

Then, Out of 150 holes, Dirk will make par or better on -

(42/90 x 150) holes

(42/90 x 150)

70

Therefore, Dirk will make 70 pars or better.

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Answer:

4

Step-by-step explanation:

The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.

Hope this helps! :)

The value of x is 10°.

What is a measure of an angle?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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The value of x is 10°.

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]

Add the square of the scaling factor s to the area of ​​the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of ​​the figure after dilation Ad. a d = s2a p .

To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of ​​the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]

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When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

area of the polygon ( triangle ) = 1/2 * b * h

= 1/2 * 4 * 4

= 8 units

so When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

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Answer:

going to have to to get the house ready

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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The answer is: 55 crayons.

Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

What does rate of change mean?

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Surafce area of a prism is equal to

2(Area of base) + (perimeter of base)(height)

2b^2+4bh

[tex]S=2b^2+4bh[/tex]

[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]

It is given that db/dt= -7 and dh/dt -=10.

At a particular instant b= 4km, h=9 km.

Now we will substitute the values in this formula:

[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

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The essays that she can review in 1 hour would be; 2 2/3.

A fraction represents a part of a number or any number of equal parts.

We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.

Thus, Fraction of the essay reviewed = 2/3

Amount of time used = 1/4

Therefore, the fraction of essay for an hour can be calculated as;

= Fraction of the essay reviewed / Amount of time used

= 2/3 ÷ 1/4

= 2/3 × 4

= 8/3

= 2 2/3

Hence, She will review 2 2/3 essay.

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On solving the provided question, we can say that - the linear equation

y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y=mx+b

x=gallons of fuel

y=total weight of plane including fuel

m=slope=6.4

b=weight of plane, no fuel....a constant to be calc'd

[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]

82gallons fuel is 2424.80 lbs

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Answer: -2, -3, and -4.

Step-by-step explanation:

The range is all the Y Values the graph uses, and the Y values range from -0.5 to -5.5, making every number in between those included.

Answer:

1.8 meters

Step-by-step explanation:

Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.

Answer: 1.8

Step-by-step explanation:

Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.

The function's general shape is a downward-opening parabola.

From the question, we have the following parameters that can be used in our computation:

f(x)=-x^4+8x^3+8x^2-96x-144

Express properly

So, we have

f(x) = -x⁴ + 8x³ +8x² - 96x - 144

Next, we plot the graph (see attachment)

From the attached graph, we can see that the function opens down

This means that the general shape is a downward-opening parabola.

The function faces down (as shown on the graph)

Here, we set x = 0

So, we have

f(0) = -(0)⁴ + 8(0)³ + 8(0)² - 96(0) - 144

Evaluate

f(0) = -144

So, the y-intercept is -144

We start by setting the factor to 0

So, we have

x - 6 = 0

Solve for x

x = 6

From the graph;

When x = 6, y = 0

This means that x - 6 is a factor

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Answer: 0.155

Step-by-step explanation:

To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:

P(k) = (μ^k * e^(-μ)) / k!

Where:

Plugging in the given values, we get:

P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550

So the probability of the event occurring 5 times is approximately 15.5%.

h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.

Here,

We can draw the graph as

h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)

h(x) = f(x) + 5

The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.

Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

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The closest to the number of yards of ribbon Mario had altogether will be ;

⇒ 11 yards

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Now,

Since, Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards

                                                                        = 41/5 + 11/4

                                                                        = (164 + 55) / 20

                                                                         = 219 / 20 yards

                                                                         = 10.95 yards

                                                                         ≈ 11 yards

Thus, Total ribbon for the project Mario have = 11 yards

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Answer: atleast alot

Step-by-step explanation:

Yes, the expression; y = x³ is a function because it passes the vertical line test.

Function from a set x to a set y assigns to each element of x exactly one element of y. The set x is called the domain of the function and the set y is called the codomain of the function.

There are 4 types of functions:

On this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

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