Graph XY with endpoints X(-3, 1) and Y(4, 5) and its
image after the composition.
Rotation: 180° about the origin
Translation: (x, y)→(x-1, y + 1)
Write a coordinate rule for the composition.
(x, y)→

The ball hits the ground after x = 6 seconds.

Two or more expressions with an equal sign are defined as an equation.

The given equation is h(x) = -2x² + 8x + 24.

(a) when the ball is thrown, the time is t = 0 sec.

Therefore, the height of the ball when it is thrown is,

h(0) = -2(0)² +8(0) +24

h(0) = 24

(b) The derivative of the function is,

h'(x) = -4x + 8

Substitute h'(x) = 0 into the above equation,

0 = -4x +8

4x = 8

x = 2

The second derivative of the function is,

h''(x) = -4

Since the second derivative of the function is negative, the function is maximum at x = 2.

(c) The maximum height of the ball is,

h(2) = -2(2)² + 8(2) +24

h(2) = -8 +16 +24

h(2) = 32

(d) The ball hits the ground when h(x)= 0, therefore,

0 = -2x² +8x +24

0 = -2x² +12x - 4x + 24

0 = -2x(x - 6) - 4(x - 6)

0 = (x - 6)(-2x - 4)

(x - 6) = 0 or (-2x-4) = 0

x = 6 or x = -2

Since time cannot be negative, it follows, x = 6 seconds.

Hence, the ball hits the ground after x = 6 seconds.

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Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.

As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.

When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.

Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

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Answer:

a

Step-by-step explanation:edge

Answer: 44.35

Step-by-step explanation:

0.07x20=1.4

45.75-1.4

Proved that the length of AB ≅ the length of CD

The conditions are given that

The line BC and the line AD are parallel lines

The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other

Similarly

The measure of angle BAD is equal to the measure of angle DCB

If angle BAD = angle DCB, then we can say that the given shape is a parallelogram

In the parallelogram the opposite sides will be equal

Then the length of the length of AB equal to the length of CD

Hence, proved that the length of AB ≅ the length of CD

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The number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80 from the algebraic equation is; 12 pounds

Let x represent the number of pounds of Chamomile tea needed.

We are told to find the number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80.

Therefore,

9x + 6(8) = 7.8(8 + x)

9x + 48 = 62.4 + 7.8x

9x - 7.8x = 62.4 - 48

1.2x = 14.4

x = 14.4/1.2

x = 12

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The correct numbers from the box below are 5/6 - 1/3 = 1/2.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A table with five different fractions.

Now, 5/6 - 1/3 we will check and the result must fall in the fractions given in the table.

5/6 - 1/3.

= (5 - 2)/6.

= 3/6.

= 1/2.

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Answer:

-6 is the y-intercept, as in the point that crosses the y axis

Answer:

Assuming w=2 and r=3, we plug in these values

2+5*3 = 2+15 = 17

Step-by-step explanation:

A. The equation that can be used to determine the number of weeks is $999=225+42w

B. The number of weeks it will take Hannah to repay is 18weeks

An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. 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. In the case of one variable, there is only one solution. For example, the equation x + 3 = 0 has only one solution as x = -2.

the total amount of money Hannah repaid is $225+$43×w, where w is the number of weeks to repay $43.

therefore $999= $225+$43w

$43w=$ (999+225)

$43w= $1224

divide both side by $43

w= $1224/$43

w= 18 weeks

therefore it will take Hannah 18weeks to repay the money.

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Answer:

-1.1

Step-by-step explanation:

:)

Answer:

12a + 13b

Step-by-step explanation:

3(5a + 4b) - 3a + b

multiply 3 by 5a and 4b

15a + 12b - 3a + b

Now add the a terms together and b terms together

15a - 3a + 12b + b

12a + 13b

Answer:

12a + 13b

Step-by-step explanation:

3(5a+4b)-3a+b

To simplify the expression, we need to distribute the 3 to all terms inside the parentheses

3*5a+3*4b-3a+b

15a+12b-3a+b

Combine like terms

12a + 13b

Answer:

x = 6

Step-by-step explanation:

2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )

x = - 3 × - 2 = 6

x = 6

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Answer:

There are two solutions. The parabola and the line intersect at two different points.

Answer:

Two

Step-by-step explanation:

there are two slope lines, so you need two equations for each lines.

A linear graph with a negative slope indicates that as the independent variable decreases, the dependent variable increases.The line with a negative slope is sloping down to the right.

This relationship is represented by a line sloping down to the right. A line with a negative slope indicates that there is a negative correlation between the two variables. This means that as one variable decreases, the other variable increases.

This is because the line is going down from left to right, which means that the y-value is increasing as the x-value decreases. This relationship is known as a negative correlation.It is also known as an inverse relationship. In an inverse relationship, the two variables move in opposite directions. As one variable decreases, the other variable increases.

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There are 33 numbers that are less than 200 and divisible 4 but not divisible 12. this can be solved with the help of simplification.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Main body:

Given that,

To determine how many natural numbers less than 200 are divisible by 4, but not divisible by 12.

Here,

Let the largest number divisible by 4 less than 200 is 198

The total numbers divisible by 4 and less than 200 is,

= 198 / 4 = 49

Similarly

The total number divisible by 12 and less than 200 is,

= 192/ 12 = 16

So the numbers that are less than 200 but divisible 4 not by 12 is,

= 49 - 16

= 33

Hence, there are 33 numbers that are less than 200 and divisible 4 but not divisible 12.

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The volume of the cylindrical jar be 1130.97 in³.

Also, 56 whole marbles can fit in the jar.

Given, a cylindrical jar has a radius of 6 inches and a height of 10 inches.

The jar is filled with marbles that have a volume of 20 in³.

(a) The volume of the cylindrical jar be,

Volume = πr²h

Volume = (3.14)(6)²(10)

Volume = 1130.97 in³

(b) Now, if each marble has the volume of 20 in³

then, the number of marbles that can be fit in the jar be,

The number of marbles = 1130.97/20

The number of marbles = 56.

Hence, the volume of the cylindrical jar be 1130.97 in³.

Also, 56 whole marbles can fit in the jar.

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Answer:

(x - 3)

Step-by-step explanation:

4x² - 12x ← factor out 4x from each term

= 4x(x - 3)

the factors are 4x and (x - 3)

The equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.

Given: A line is perpendicular to line y = 4x – 7  and passes through point A (8, 2).

We know that,

Slope of line perpendicular to another line is negative reciprocal of its slope.

So, m(slope) = -1/4

Equation of line is given as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 8)

y + (1/4)x = 4

Therefore, the equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

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Answer:

y = 8/5

Step-by-step explanation:

Formula we use,

→ y = kx

Then the value of y will be,

→ y = kx

→ y = (-2/5) × (-4)

→ y = (-2 × -4)/5

→ [ y = 8/5 ]

Hence, the value of y is 8/5.

Answer:

[tex]y=3x-13[/tex]

Step-by-step explanation:

Parallel lines have the same slope. So, the equation is:

[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]

Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

Since we're subtracting the entire quadratic, we can place the second equation in parentheses and distribute the subtraction sign.

[tex]2x^2-9x+8-(6x^2-5x-12)\\2x^2-9x+8-6x^2+5x+12\\2x^2-6x^2-9x+5x+8+12\\-4x^2-4x+20[/tex]

Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

To find the difference of the two quadratic expressions, subtract the second expression from the first expression:

[tex]\implies (2x^2-9x+8)-(6x^2-5x-12)[/tex]

Remove the parentheses and apply the distributive law
[tex]-\left(a-b\right)=-a+b[/tex]

[tex]\implies 2x^2-9x+8-6x^2+5x+12[/tex]

Collect like terms:

[tex]\implies 2x^2-6x^2+5x-9x+8+12[/tex]

Combine like terms:

[tex]\implies -4x^2-4x+20[/tex]

Therefore, the difference of the two quadratic expressions is:

[tex]\large \boxed{-4x^2-4x+20}[/tex]

The linear model that represents the total cost of recording is f(x) = 75x + 50.

The initial fee is $50 for recording an album.

There is an additional cost per hour i.e. $75.

number of hours = x

Now based on the above information, the linear model should be f(x)=75x+50

Here 50 represent the initial fee i.e. equivalent to y-intercept

And, 75 represent the slope

Therefore we can conclude that the linear model that represents the total cost of recording is f(x) = 75x + 50.

The interest rate that would be required for Emma to end up with $2440 in her bank account is 6.8%

Given,

P = $720

A = $2440

t = 18 years.

r = n[(A/P)^1/nt - 1]

r = 12 × [(2440/720)¹/⁽¹²⁾¹⁸ - 1]

r = 0.06799764

Then convert r to R as a percentage.

R = r × 100

R = 0.06799764 × 100

R = 6.8%/year

Hence the rate of interest is 6.8%

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Answer:

Angle 6 is 78 degrees Angle 7 is 102 degrees

Step-by-step explanation:

Since both lines are parallel, you can assume that Angle 6 plus Angle 7 are a linear pair. Angle 1 corresponds to Angle 5 by the corresponding parts. Angle 5 is congruent to Angle 7 by Vertical angles so therefore Angle 7 is 102. Since Angle 6 + Angle 7 equal 180 degrees, you can put the equation like this,

[tex]Angle 6 + 102 = 108. Angle 6 = 78.[/tex]

Therefore you get your two answers

Answer:

the exact form is 419/104

decimal for:4.02884615...

mixed number form: 4 3/104

Step-by-step explanation:

calculator

Answer:

picture it to pixilated

Step-by-step explanation:

The x-intercept and y-intercept of the equation will be (-1, 0) and (0, 2). The graph is given below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The linear equation is given below.

y = 2x + 2

Convert the equation into intercept form, then we have

y = 2x + 2

y - 2x = 2

y / 2 - x / 1 = 1

The x-capture and y-block of the situation will be (- 1, 0) and (0, 2). The chart is given beneath.

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Answer:

Step-by-step explanation: 34

Answer:

x = [tex]\frac{11}{26}[/tex]

Step-by-step explanation

Expand 2(9x - 1):  18x - 2

Expand - ( x - 9 - 7x:     -8 + 9

Add 2 to both sides 18x - 2 +2 =  -8x + 9 + 2

Simplify

18x = -8x + 11

Add 8x to both sides

18x + 8x =  -8x + 11 + 8x

Simplify

26x = 11

Divide both sides by 26

[tex]\frac{26x}{26}[/tex] = [tex]\frac{11}{26}[/tex]

Simplify

x = [tex]\frac{11}{26}[/tex]

The corresponding standard deviation percentage area for -2 to -1,  0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85%

To find the Standard Deviation Percentage Area, you have to consider the lower and upper points:

-2 to -1

The gap between -2 and -1 is 1 step, you will subtract -1 from -2:

-2 to -1 =>  0.4772 - 0.3413 = 0.1359 = 13.59%

Note: the values for -2 and +2 are the same. The same also applies to -1 and +1 and others

0 to +1

Check the value under 1. That is 0.3413 = 34.13%

0 to +2

Check the value under 2. That is 0.4772 = 47.72%

+1 to +3

The gap between +1 and +3 is 2 steps, you will subtract  1 from 3:

+1 to +3 =>  0.4987-0.3413 = 0.1574 = 15.74%

-1 to +2

-1 to +2 is the same as moving -1 to 0 and then moving from 0 to +2, you will add the values for -1 and +2:

-1 to +2 => 0.3413 + 0.4772 = 0.8185 = 81.85%

Therefore, the Standard Deviation Percentage Area for -2 to -1,  0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85% respectively

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