The functions fx) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?

The average rate of change over the entire slide is [tex]\( \frac{1}{10} \)[/tex] feet per foot.

To find the average rate of change over the entire slide, we need to calculate the change in height divided by the change in distance over the entire slide.

Let's denote:

- [tex]\( h_1 \)[/tex] as the initial height (when x = 0),

- [tex]\( h_2 \)[/tex] as the final height (when x = 20).

Given that the height of the slide is 2 feet when ( x = 20 ), we have:

[tex]\[ h_2 = 2 \, \text{feet} \][/tex]

We also know that the height of the slide is 0 feet when ( x = 0 ), so:

[tex]\[ h_1 = 0 \, \text{feet} \][/tex]

Now, the change in height ([tex]\( \Delta h \)[/tex]) over the entire slide is:

[tex]\[ \Delta h = h_2 - h_1 = 2 \, \text{feet} - 0 \, \text{feet} = 2 \, \text{feet} \][/tex]

The change in distance ([tex]\( \Delta x \)[/tex]) over the entire slide is simply the distance traveled, which is:

[tex]\[ \Delta x = 20 \, \text{feet} \][/tex]

The average rate of change over the entire slide ([tex]\( \text{Avg ROC} \)[/tex]) is then:

[tex]\[ \text{Avg ROC} = \frac{\Delta h}{\Delta x} \][/tex]

[tex]\[ \text{Avg ROC} = \frac{2 \, \text{feet}}{20 \, \text{feet}} \][/tex]

[tex]\[ \text{Avg ROC} = \frac{1}{10} \][/tex]

The average rate of change of the slide height is calculated as 0.1 feet per foot, indicating that the height increases by 0.1 feet for every foot along the slide.

Step by step calculation:

The average rate of change of a function over an interval is calculated using the formula:

       Average Rate of Change = (2 - 0) / (20 - 0) = 2 / 20 = 0.1 feet per foot

This means the height increases by 0.1 feet for every foot traveled along the length of the slide.

Answer:

9 cups of milk

Step-by-step explanation:

2 cups of flour - 3 cups of milk

4- cups of flower - 6 cups of milk

6 cups of flower - 9 cups of milk

Please mark brainliest and have a great day!

Answer:

9 cups of milk

Step-by-step explanation:

2 cups of flour need 3 cups of milk

1 cup of milk needs 3/2 cups of milk

:. 6 cups of milk will need

(6 x 3/2) = 18/2

= 9 cups of milk

Hello!

Answer:

[tex]\boxed{-10x+7.5}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

[tex]-2.5*4x-(-2.5)*3[/tex]

[tex]-4*2.5x+3*2.5[/tex]

Simplify.

[tex]4*2.5=10[/tex]

[tex]3*2.5=7.5[/tex]

[tex]=-10x+7.5[/tex]

[tex]\boxed{-10x+7.5}[/tex], which is our final answer.

I hope this helps you!

Have a nice day! :)

Thanks!

Answer:

The answer is -10x+7.5

Step-by-step explanation:

Answer:

350 lightbulbs

Step-by-step explanation:

First, we need to find the rate of lightbulbs that are inspected. This can be calculated as the division between the number of lightbulbs selected for inspection and the number of light bulbs produced. This is:

Rate = 7/400 =0.0175

That means that for every lightbulb produced, 0.0175 are inspected. Then if the factory produces 20000 light bulbs, the number of light bulbs inspected is:

20000*0.0175 = 350 lightbulbs

By solving for the unknown, the number of lightbulbs inspected can be determined as 350.

The quality control manager selects 7 lightbulbs out of 400 for inspection.

To find the number of lightbulbs inspected, we set up a proportion:

7 lightbulbs / 400 lightbulbs = x lightbulbs / 20000 lightbulbs

Solving for x gives:

x = (7/400) * 20000 = 350 lightbulbs inspected.

Answer:

C

Step-by-step explanation:

Given the inequality

(x - 3)(x + 5) ≤ 0

Find the zeros by equating to zero

(x - 3)(x + 5) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 5 = 0 ⇒ x = - 5

Thus the domain is split into 3 intervals

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

- ∞ < x ≤ - 5 → (1)

- 5 ≤ x ≤ 3 → (2)

3 ≤ x < + ∞ → (3)

Select a test point in each interval and check validity

x = - 10 → (- 13)(- 5) = 65 > 0 ← not valid

x = 0 → (- 3)(5) = - 15 < 0 ← valid

x = 10 → (7)(15) = 105 > 0 ← not valid

Solution is { x | - 5 ≤ x ≤ 3 }

Answer:

The quotient is [tex]\frac{7}{12c}[/tex]

Step-by-step explanation:

Given expression is:  [tex]\frac{5}{4c^2}\div \frac{15}{7c}[/tex]

While dividing two fractions, first we need to change the division sign into multiplication and then flip the second fraction.

So, we will get.....

[tex]\frac{5}{4c^2}\div \frac{15}{7c}\\ \\ =\frac{5}{4c^2}\times \frac{7c}{15}\\ \\ =\frac{35c}{60c^2}\\ \\ = \frac{7}{12c} \ \ [Dividing\ both\ numerator\ and\ denominator\ by\ 5c][/tex]

So, the quotient is [tex]\frac{7}{12c}[/tex]

Answer:

the answer is B

Step-by-step explanation:

just did the assignment on edge

Answer:

The new function is g(x) = Ix - 5I - 7 ⇒ answer C

Step-by-step explanation:

* Lets revise the translation of a function

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ f(x) = IxI

∵ f(x) is shifted 5 units to the right

∵ If the function f(x) shifted to the right  by h units

∴ g(x) = f(x - h)

- Change IxI to Ix - 5I ⇒ (1)

∵ f(x) is shifted 7 uints down

∵ If the function f(x) shifted down  by k units

∴ g(x) = f(x) - k

- Change f(x) to f(x) - 7 ⇒ (2)

- From (1) and (2) the new function is:

 g(x) = Ix - 5I - 7

* The new function is g(x) = Ix - 5I - 7

Answer:

ive got you fam  <3 your answer is x= -8

Step-by-step explanation:

isolate the variable by dividing each side by factors that dont contsin the variable

For this case we have the following expression:

[tex]a + b[/tex]

We must evaluate the expression to:

[tex]a = 2\\b = 3[/tex]

Substituting the values in the expression we have:

[tex]2 + 3[/tex]

Equal signs are added and the same sign is placed.

So:

[tex]2 + 3 = 5[/tex]

Finally, the value of the expression is 5.

Answer:

[tex]a + b = 5[/tex]for[tex]a = 2[/tex] and[tex]b = 3[/tex]

Answer:

12.21

Step-by-step explanation:

Step 1: You got to find the distance between your x's

Step 2: You got to find the distance between your y's

Step 3: Apply Pythagorean Theorem:  That is do:

[tex]\sqrt{ (\text{ distance of x})^2+( \text{ distance of y})^2}\\[/tex]

So x distance is 10    (I just did 6-(-4))

So y distance is 7      (I just did 8-1 )

As per the formula, I'm going to square both... Then add those squared results together like so 100+49=149

Last step is the square root...

[tex]\sqrt{149} \approx 12.21 [/tex]

Answer:

12.21

Step-by-step explanation:

hope it helps

Answer: 0.3 times

Step-by-step explanation:

Answer:

1.3 times

Step-by-step explanation:

The function [tex]f(x)=603(1.3)^{x}[/tex] represents the number of students enrolled at a university, x years after it was founded.

So the sequence will be formed to represent the number of students will be

f(1) = 603(1.3)

f(2) = 603(1.3)²

f(3) = 603(1.3)³

and so on.

Now the common ratio between second and first term will be

= [tex]\frac{(603)(1.3)^{2}}{603(1.3)}=1.3[/tex]

Therefore, second term of the sequence will be 1.3 times of the first term.

Answer will be - "Each year, the number of students will be 1.3 times the number the year before".

To find the number of 5-digit numbers that can be formed using the digits 0-6 without repetition, we use permutations. The answer is 5,040.

To find the number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 (without repetition), we need to use the concept of permutations.

Since repetition is not allowed, for the first digit, we have 7 choices (0 cannot be the first digit). For the second digit, we have 6 choices (since one digit has been used). For the third digit, we have 5 choices (since two digits have been used), and so on.

Therefore, the number of 5-digit numbers that can be formed is 7 x 6 x 5 x 4 x 3 = 5,040.

Answer:

16 chlildren

Step-by-step explanation:

5x+8y=80

y=0

5x=80

x=8-0/5=16

Answer:

Step-by-step explanation:

The answer is B.16

Since the equation is 5x+8y=80

There are no parents so it equation will turn into 5x+8(0)=80, AKA, 5x=80

Using algebra, 5x=80 will x=80/5

which is 16

That is true.

The diameter is a line that passes through the center of a circle.

Answer: True is the answer

Answer:

C. 140

Step-by-step explanation:

We want m^2 to be the largest value it can be, so ignoring the sign of m the largest value of |m| is 12

(-12)^2 = 144 which is the largest value of m^2

We want n^2 to be the smallest it can be, so ignoring the sign of n the smallest value of |n| is 2

(2)^2 =4

m^2 -n^2

144-4 = 140

Answer:

Option B.  AA

Step-by-step explanation:

we know that

Angle-Angle (AA) Similarity Postulate, states that If two angles of one triangle are congruent to two angles of another, then the triangles must be similar

In this problem

In the triangle XYZ

∠X=70°

∠Y=90°

∠Z=90°-70°=20° (remember that angle X and angle Z are complementary)

In the triangle UWV

∠V=20°

∠W=90°

∠U=90°-20°=70° (remember that angle V and angle U are complementary)

therefore

Traingles XYZ and UWV are similar by AA Similarity Postulate

Answer:

degrees apart in latitude: 91.22

degrees apart in longitude: 147.95

Step-by-step explanation:

Liverpool and Melbourne are two cities that are located very far away from each other. Liverpool is located in the northwestern part of England, while Melbourne is located in the southeastern part of Australia, so understandably their latitudes and longitudes are very different. In order to get to the distance in degrees between these two cities in latitude and longitude, we just simply need to sum the degrees of both of them and we will get to the result. The reason why simple summing will do the job is because they are on separate hemispheres, with Liverpool being on the Northern and Western Hemisphere, while Melbourne being on the Southern and Western Hemisphere.

Latitude distance:

53.41 + 37.81 = 91.22

Longitude distance:

2.99 + 144.96 = 147.95

Answer:

degrees apart in latitude: 91.22

degrees apart in longitude: 147.95

Answer:

y= -1/3x+5

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

Given expression is:

[tex]\frac{(2mn)^{4}}{6m^{-3}n^{-2}} \\=\frac{2^{4}m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{16m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{8*2*m^{4}*n^{4}}{2*3*m^{-3}*n^{-2}} \\=\frac{8*m^{4+3}n^{4+2}}{3}\\=\frac{8m^{7}n^{6}}{3}[/tex]

So option 1 is the correct answer ..

Answer:

c

Step-by-step explanation:

Follow below steps:

The area of the hexagonal base of the cake:

Calculate the volume of the cake: 32 ounces * 3.125 = 100 cubic inches.

The volume of a hexagonal prism: Volume = area of base * height. Since height is 5 inches, the area of the base is 100 / 5 = 20 square inches.

Answer:

You start at the bottom

Distance, often assigned the variable d, is a measure of the space contained by a straight line between two points. Distance can refer to the space between two stationary points (for instance, a person's height is the distance from the bottom of his or her feet to the top of his or her head) or can refer to the space between the current position of a moving object and its starting location.

Answer:

Step-by-step explanation:

[tex]f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

We need to find the pattern as the exponent decreases.

the first value in the table is 125.

if we divide 125 by 5 i.e 125/5 we get 25

the next value in the table is 25

if we divide 25 by 5 i.e 25/5 we get 5

the next value in the table is 5

if we divide 5 by 5 i.e 5/5 we get 1

the next value in the table is 1

if we divide 1 by 5 i.e 1/5 we get 1/5

the next value in the table is 1/5

if we divide 1/5 by 5 i.e 1/5*5 we get 1/25

the next value in the table is 1/25

So, the pattern is if we divide the previous value by 5 we get the next value in the table.

So, Option C is correct.

Answer:

The answer is C

Step-by-step explanation:

I just took the test

Answer: Step 4

Step-by-step explanation:

Rena made the first mistake in step 4 because she left the terms [tex]2^{3} and (-1)^{21}[/tex] in the denominator, when in the previous step they were also in the denominator but raised to -1, which means that they should be in the numerator.

The right step 4 would be:

[tex]\frac{2^{3} (-1)^{21} }{2^{6} } =\frac{-1}{2^{3} } =\frac{-1}{8}[/tex]

Answer: step 4

!!

Step-by-step explanation:

Answer:

No, the power multiplied to 8.64 should havean exponent of zero.

HOPE THIS WILL HELP YOU

Answer:its the second one or b

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Givens

Let child one = x

Let child two = y

Let child three = z

Equations

x^2 + y^2 + z^2 = 100

xy + xz + yz = 150

Solution

There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).

(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz

Take out 2 as a common factor from the last three terms.

(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )

Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150

(x + y + z)^2 = 100 + 2*150

(x + y + z)^2 = 100 + 300

(x + y + z)^2 = 400

Take the square root of both sides.

sqrt(x+y+z)^2 = sqrt(400)

x + y + z = 20

Note

This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.

Answer:

A. x = √2

B. x = 1

D. x = -1

E. x = -√2

Step-by-step explanation:

Correct 100%

Without the complete equation, we cannot provide a definitive solution. However, it seems like you are dealing with a quadratic equation where possible solutions can be found using the quadratic formula, '-b ± √ (b² - 4ac) / 2a'. Please provide the full equation for a more precise answer.

The original equation mentioned in your question is missing, but I'll assume you are referring to solutions of the equation x² = √ ( 2x² - 1 ). This equation can be solved by first simplifying the condition as 2(x² - 1)² ≤ 1. Following the standard method for solving quadratic equations, we can use the quadratic formula -b ± √ (b² - 4ac) / 2a. Unfortunately, without a full equation, we cannot provide a comprehensive answer. Please, provide the complete equation for a more accurate solution.

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