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3 years ago

Write the equation for g(x).

Mathematics

1 answer:

MrRissso [65]3 years ago

5 0

Answer:

g(x) = $5x^{2}$

Step-by-step explanation:

This problem may seem tricky at first, but after you understand the basic concepts about vertical stretches and vertical shrinks, this problem will become much simpler. Additionally, if you use the online tool: DESMOS, you will be able visualize things better.

First, you may notice the graph is more narrow than the original "f(x)" graph. This means that the g(x) graph is a vertical shrink. A vertical shrink can be achieved by adding a whole-number as a coefficient to the " $x^{2} \\$ " formula. Adding a coefficient of "5" would result in coordinates like (1,5), just like adding a coefficient of "2" for example would result in coordinates like (1,2).

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4 (2x-6)=10x-6. solve for x

Reika [66]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

4*(2*x-6)-(10*x-6)=0

2x - 6 = 2 • (x - 3)

8 • (x - 3) - (10x - 6) = 0

-2x - 18 = -2 • (x + 9)

-2 • (x + 9) = 0

Solve : -2 = 0

<span>This equation has no solution.
</span>A a non-zero constant never equals zero.

Solving a Single Variable Equation :
Solve : x+9 = 0

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</span>Subtract 9 from both sides of the equation :<span>
</span> x = -9

7 0

3 years ago

A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6

Burka [1]

Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

Length of street light AB = 25 ft

Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate ( $\frac{dw}{dt}$ ) of the tip (D) of the girl's shadow (BD) moving away from th

light.

Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, $\frac{dx}{dt}=6$ feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

$\frac{x}{21}=\frac{x+y}{25}$

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = $\frac{4x}{21}$

Now we take the derivative on both the sides,

$\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}$

= $\frac{4}{21}\times 6$

= $\frac{8}{7}$

≈ 1.14 ft per sec.

Since w = x + y

Therefore, $\frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}$

$\frac{dw}{dt}=6+1.14$

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

3 0

3 years ago

-2 1/4 - ( - 3/4) =<br>

Grace [21]

Answer: -1.5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

240,000 written as a whole number multiplied by the power of ten

Stolb23 [73]

This question can be also asked as what is the scientific notation of the number 240,000. The scientific notation is written as <span>a whole number multiplied by the power of ten. It should be written as follows:

2.4 x 10^5

Hope this helps. Have a nice day.</span>

8 0

3 years ago

A water tank is built in the form of a right rectangular prism, with dimensions that measure 13.4 ft by 8.7 ft by 7.5 ft. How ma

Alex17521 [72]

The volume of water that the rectangular prism will hold when it is full is: 874.35 ft³.

<h3>What is the Volume of Rectangular Prism?</h3>

Volume = length × width × height

Given:

Length = 13.4 ft
Width = 8.7 ft
Height = 7.5 ft

Thus:

Volume of water = 13.4 × 8.7 × 7.5

Volume of water = 874.35 ft³

Thus, the volume of water that the rectangular prism will hold when it is full is: 874.35 ft³.

Learn more about volume of rectangular prism on:

brainly.com/question/12917973

7 0

2 years ago