Which of the following represents the range of the graph of F(x) below

Answer:

B. 84 deg

Step-by-step explanation:

Sides DE and FE are congruent since they both have the same length.

That makes angles D and F congruent.

m<D = m<F = 48

The sum of the measures of the angles of a triangle equals 180 deg.

m<E + m<D + m<F = 180

m<E + 48 + 48 = 180

m<E = 84

Answer:

I think it is C

Step-by-step explanation:

Answer:

Point is at x = 4 m

Step-by-step explanation:

From the question, we can write the formula for intensity as;

I = strength/distance²

Now,

- Let x be the position from the stronger source

- Let k be the strength of the weaker light source

- 8k will be the strength of the stronger light source.

We are told that the two sources are 6 meters apart and one of them is 8 times stronger than the other.

Thus, the total illumination is;

I(x) = (8k/x²) + k/(6 - x)²

Using chain rule to get the critical points, let's find the first derivative and equate to zero;

I'(x) = -16k/x³ + 2k/(6 - x)³ = 0

Adding -16k/x³ to both sides, we have;

2k/(6 - x)³ = 16k/x³

Cross multiply to get;

2kx³ = 16k(6 - x)³

Dividing both sides by 16k to give;

x³/8 = (6 - x)³

Taking cube root of both sides to give;

x/2 = 6 - x

Multiply both sides by 2 to give;

x = 12 - 2x

x + 2x = 12

3x = 12

x = 12/3

x = 4 m

Answer:

4 (20) + 6(6) = 120

4(20) + 4 (6) = 100

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations with the information given:

Build time (hours) = 4c + 6a = 120

Test time (hours) = 4c + 4 a = 100

Where c represents the number of child bikes and a represents adult bikes.

So, for 20 child bikes and 6 adult bikes:

4 (20) + 6(6) = 120

4(20) + 4 (6) = 100

Feel free to ask for more if needed or if you did not understand something.

Answer:

see below

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius is 9 and the height is 20

V = pi  ( 9)^2 ( 20)

V = 1620 pi

If we approximate pi by 3.14

V =5086.80 cm^3

If we approximate pi by pi button

V =5089.3800099 cm^3

Answer:

V=5089.380099cm^3

Step-by-step explanation:

V=πr^2h

V=π(9)^2(20)

V=π(9)^2(20)

V=5089.380099cm^3

Answer:

x= 150

Step-by-step explanation:

X/5 = 30

x = 5×30

x= 150

Answer:

150

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] = 30

→ Multiply both sides by 5 to isolate x

x = 150

Answer:

1(a)1,030,000+0.13x

(b)$1,030,026

2. (a)Base and Index

(b)See Explanation

Ste-by-Step Explanation

(a)Total Amount to be paid to the four actors

=500,000+(300,000+0.02x)+(150,000+0.03x)+(80,000+0.08x)

Collect like terms

=500,000+300,000+150,000+80,000+0.02x+0.03x+0.08x

[tex]\text{Total Amount Paid= }1,030,000+0.13x[/tex]

(b)When x=200

[tex]\text{Total Amount Paid= }1,030,000+0.13(200)\\=1,030,000+26\\=$1,030,026[/tex]

Question 2

(a)The two parts of a power are the base and index.

Take, for example, the expression: [tex]a^b\\[/tex]

[tex]a$ is the base\\b is the index[/tex]

Another example using numbers is: [tex]10^3[/tex]

In this case:

[tex]10$ is the base\\3 is the index[/tex]

(b)Like terms are terms that have the same letter/variable attached to them.

For example, the following pairs are like terms

These, however, are not like terms

Hey there! :)

Answer:

y + 32 = 3(x + 8)

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates of the points into the equation:

[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]

Simplify:

[tex]m = \frac{33}{11}[/tex]

m = 3.

Point-slope form is:

y-y₁=m(x-x₁)

Plug in the coordinates of the first point, as well as the slope:

y - (-32) = 3(x - (-8)

y + 32 = 3(x + 8)

Answer:    y+32=3(x+8)

Step-by-step explanation:

First  you need to find the slope.The slope is the change in y divided by the change in x values.

-32 - 1 = -33

-8 - 3 =    -11  

-33/-11 = 3   the slope is 3  

and in point-slope form is  like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.

it could be like   y-1=3(x-3) or y+32= 3(x+8)

Answer:

y = -3x + 8

Step-by-step explanation:

(1, 5)  ; (-2, 14)

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{14-5}{-2-1}\\\\=\frac{9}{-3}\\\\=-3[/tex]

m = -3   ; (1 , 5)

Equation: [tex]y-y_{1}=m(x-x_{1})[/tex]

y - 5 = (-3)(x - 1)

y - 5 = -3x + 3

y = -3x + 3 + 5

y = -3x + 8

Answer:

10 inches

Step-by-step explanation:

Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?

Hence, L1/L2 = W1/W2

∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches

Answer:

The center  is (-8/3,0) and the radius is 1

Step-by-step explanation:

(x+8/3)^2 + y^2 = 1

We know the equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

Rewriting

(x- -8/3)^2 + (y-0)^2 = 1^2

The center  is (-8/3,0) and the radius is 1

Answer:10

Step-by-step explanation:

8/80=1/10*100=10

Answer:

by using formula of median you can do it.

Answer:

put the numbers in order

20,20,23,39,60,64,82

Find the number in the middle

39 is in the middle because there is 3 numbers on each side so it is the median.

Divide by 3.

39 / 3 = 13

Hope this helps

Step-by-step explanation:

Answer:

(x, y) = (2, -1.5)

Step-by-step explanation:

x + 2y = -1

5x - 4y = 16

<=>

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

5x - 4y = 16

<=>

2x + 4y = -2

5x - 4y = 16

<=>

7x = 14

<=>

x = 2

(*)x + 2y = -1

=> 2 + 2y = -1

=> 2y = -3

=> y = -1.5

=> (x, y) = (2, -1.5)

Answer and Step-by-step explanation:

As it is mentoned in the question

Polygon ABCDE rotates around point F in clockwise direction to create polygon FGHIJ

And as we can see in the figure that

So we conclude that

A = F ⇒ 117°

B = G ⇒ 90°

C = H ⇒ 127°

D = I ⇒ 90°

E = J ⇒ 117°

Therefore this is the answer and the same is to be considered

Answer:

m∠ABC = 90117127°m∠BCD = 90117127°m∠DEA = 90117127°m∠CDE = 90117127°

Step-by-step explanation:

Answer:

  120

Step-by-step explanation:

n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.

n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.

The least common multiple of 6 and 40 is 120.

The smallest positive integer n is 120.

_____

Check

120^2/18 = 800

120^3/640 = 2700

Answer:

256 in ^2

Step-by-step explanation:

The area of the base B = 12*5 = 60 in ^2

The height is 14 inches

The perimeter of the base is

2 ( l+w) =2 ( 12+5) = 2 ( 17) = 34

The surface area  is  = 2B + Ph = 2 * 60 + 34*4

                                                    = 120 + 136

                                                    =256

Answer:

Terri’s speed can be calculated like this:

her speed- [tex]\frac{6km}{0.25h}[/tex]=24km/h

Step-by-step explanation:

Answer:

x = 1/9

Step-by-step explanation:

8x + 2 = 3 - x

Add x to both sides.

9x + 2 = 3

Subtract 2 from both sides.

9x = 1

Divide both sides by 9.

x = 1/9

Answer:

x = 1/9

Step-by-step explanation:

We are given the equation:

8x + 2 = 3 - x

In order to solve for the variable x, we need to isolate it; in other words, we need to combine all the x terms and move everything else to the other side.

First, add x to both sides:

8x + x + 2 = 3

9x + 2 = 3

Now subtract 2 from both sides:

9x = 3 - 2 = 1

Divide both sides by 9:

x = 1/9

The answer is thus 1/9.

~ an aesthetics lover

Answer:

False

Step-by-step explanation:

The negative reciprocal of -1/5 would be 5, and the negative reciprocal of -5 is 1/5. A way to double-check is all negative reciprocals add to -1.

-1/5 + -5= -5 1/5

Hope this helps and you understand negative reciprocals more for future problems ahead.

Answer:

(A)[tex]x + 3= x^2 + 2x-4[/tex]

Step-by-step explanation:

Given the equations:

[tex]y = x + 3\\y= x^2 + 2x-4[/tex]

Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.

Substitution of y into [tex]y=x^2 + 2x-4[/tex] gives us:

[tex]x + 3= x^2 + 2x-4[/tex]

The correct option is A.

Answer:

The correct option is;

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

A function defines an output given an input and the set of all the possible inputs to a function is the domain of a function such that there is an output, such that the domain is the set of x values which are points on the curve of the function

The set of outputs that are produced from a given input is the range of a function

The given function is f(x) = (x + 2)(x + 6)

From the curve we see that the minimum y-coordinate, f(x), value is at -4, which is the lower bound of the range, while the x-coordinate values, the domain can be seen extending past the graph sheet which from the expression for the function also (f(x) = (x + 2)(x + 6)) indicates that the x values is the set of all real numbers (on the number line)

Therefore, the correct option is;

The domain is all real numbers and the range is all real numbers greater than or equal to -4.

Answer:

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

Answer:

the answer is 126

Step-by-step explanation:

beacuse if you sell 7 bundles for every one you get 18 so 18+18+18+18+18+18+18=126

Answer:

126 books

Step-by-step explanation:

There are 18 books per bundle and 7 bundles

So you would multiply 7 with 18 and get your answer of 126 books to sell

Answer:

Ok, the first step to see the behavior of this data is doing a graph of it,

So we can see that it looks like an reversed V. (at the bottom of the answer you can see the graph)

Then, we can model this with a piecewise function like:

For the first part we can take the two pairs:

if 11 am is our t = 0h

(0, 85) and (6, 93)

then the linear equation

y = a*t + b

a = (93 - 85)/(6 -0) = 8/6.

and b = 85.

then the linear equation is:

y = (8/6)*t + 85. for 0h ≤ t ≤ 6h

The second part of this equation can be modeled with the points

(6, 93) and (11, 84)

then we have:

y = s*t + c

s = (84 - 93)/(11 - 6) = -7/5

and we can find the value of c as:

93 = (-7/5)*6 + c

93 + (7/5)*6 = 101.4

then this second part is:

y = (-7/5)*t + 101.4 for 6  ≤ t ≤ 11h

then, in conclusion we have:

         y = (8/6)*t + 85. for 0h ≤ t ≤ 6h

f(x) =

         y = (-7/5)*t + 101.4 for 6  ≤ t ≤ 11h

Answer:

y=7.496sin(0.3243x+0.315)+73.489

Step-by-step explanation:

simply put the data into a graph and graph each equation to see if its matched

Answer:

speed while going = 42, while returning home = 28

Step-by-step explanation:

let his speed on the way to his parents house is (x)

then his speed while returning is x - 14

Time = Distance / speed

528 / x + 528 / x -14 = 22

multiplying the denominator ...

528x + 528x +7392 = 22x^2 +14x

1056x + 7392 = 22x^2 + 308x

0 = 22x^2 -748x -7392

"dividing by 22"

0 = x^2 -34x-336

0 = (x+8) (x-42)

x must be 42

finally jon's speed while back home is  42 - 14 = 28

Answer: [tex]2(xy )^{2}[/tex]  the same thing as 2([tex]x^{2} y^{2}[/tex])

Step-by-step explanation:

You multiply 2 by x times y squared.

Answer:

solution,

[tex] \sqrt{16 {a}^{8} {b}^{ - 2} } \\ [/tex]

Use negative power rule:

[tex] {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]

[tex] \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ [/tex]

Simplify:

[tex] \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ [/tex]

Use this rule:

[tex] \sqrt{ab} = \sqrt{a} . \sqrt{b} [/tex]

[tex] \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } [/tex]

Since, 4*4=16 ,the square root of 16 is 4

[tex] \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } [/tex]

Simplify:

[tex] \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

No

Step-by-step explanation:

2 = 3 inches

2x5=10

10 = 3x5 of 15 inches

so no and it would take 8 minutes to fill up the tub

Equal steps mean each number is the same distance from the previous one

From -2 to 28 is 28 units

There are 4 spaces between the numbers

28/4 = 7

Each number is in increase of 7

-2 + 7 = 5

5+7 = 12

12+7 = 19

19+7 = 26

The third number would be 12

Answer:

d

Step-by-step explanation:

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