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3 years ago

The graph of g(x) is the result of translating the graph of f(x) (1\2)x = three units to the left. What is the equation of g(x)?

Mathematics

1 answer:

tangare [24]3 years ago

4 0

The equation $f(x)= \frac{1}{2}x$ is plotted on graph below (red line)

Translating $f(x)$ three units to the left can be done by choosing any coordinates on $f(x)$ .

Let choose (0,0) and (2,1)
Translating 3 units on to the left gives the new coordinates (0-3, 0)=(-3,0) and (2-3, 1)=(-1, 1)

The gradient of the two functions will stay the same since the lines are parallel to each other, so m = 0.5

By joining the two coordinates (-3,0) and (-1,1), we see that the translated line crosses y-axis at 1.5

The equation of translated line is given
$g(x)=0.5(x-(-3))$
$g(x)=0.5(x+3)$
$g(x)=0.5x+1.5$

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3 years ago

Express as a single power of 2

den301095 [7]

When you multiply powers, they add, and when you divide them they subtract.
So I would first add the 2^a + 2^b +2^c to get 2^(a+b+c)
Then, divide by 2^(a+b). Because when you divide powers they subtract, you will be taking away the (a+b) from the (a+b+c) and you will be left with c on its own.
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3 years ago

Two kinds of perfume are packaged in square pyramidal bottles. Perfume A is packaged in a bottle with a base of 3 inches square

kondor19780726 [428]

Answer:

The bottle of perfume A contains more glass

Step-by-step explanation:

we know that

The surface area of the square pyramid is equal to the area of the square base plus the area of its four triangular faces

step 1

Find the surface area of Perfume A

$SA=3^{2} +4[\frac{1}{2}(3)(2.5)]=24\ in^{2}$

step 2

Find the surface area of Perfume B

$SA=2.5^{2} +4[\frac{1}{2}(2.5)(3)]=21.25\ in^{2}$

step 3

Compare the surface areas

$24\ in^{2}>21.25\ in^{2}$

therefore

The bottle of perfume A contains more glass

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3 years ago

Help please!! Solve the equation -5m = -20. m = 1/4 m = -1/4 m = -4 m = 4

koban [17]

Answer:

m=4

Step-by-step explanation:

-5m=-20

m= - 20/-5

m=4

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3 years ago

Complete the following statement: f(3)=_____

victus00 [196]

Using this equation, f(3) = 23.

In order to find the value of f(3), we need to take the f(x) equation and put 3 everywhere we see x. Then we follow the order of operations to solve. So, let's start with the original.

f(x) = 2x^2 + 5sqrt(x - 2)

Now place 3 in for each x.

f(3) = 2(3)^2 + 5sqrt(3 - 2)

Now square the 3.

f(3) = 2(9) + 5 sqrt(3 - 2)

Do the subtraction inside of the parenthesis.

f(3) = 2(9) + 5sqrt(1)

Take the square root

f(3) = 2(9) + 5(1)

Multiply.

f(3) = 18 + 5

And add.

f(3) = 23

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3 years ago