Need help with these asap

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)?

tangare [24]

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
$g(x)=0.5(x-(-3))$
$g(x)=0.5(x+3)$
$g(x)=0.5x+1.5$

4 0

4 years ago

Help!! I need answer ASAP!!!

Zolol [24]

Answer:

11 cm. if your first base is 11cm, and your second base is 13, then you need height. A=(a+b)/2 h=(13+11)/2 × 11= 132

5 0

3 years ago

Find the unknown side length, x. Write your answer in simple

Bumek [7]

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 32² = 48²

x² + 1024 = 2304 ( subtract 1024 from both sides )

x² = 1280 ( take the square root of both sides )

x = $\sqrt{1280}$

= $\sqrt{256(5)}$

= $\sqrt{256}$ × $\sqrt{5}$

= 16 $\sqrt{5}$ → C

8 0

3 years ago

The graph of f(x) is shown below, if f(x) and its inverse function,

Yuki888 [10]

Before defining the inverse of a function we need to have the right mental image of function.

Consider the function f(x) = 2x + 1. We know how to evaluate f at 3, f(3) = 2*3 + 1 = 7. In this section it helps to think of f as transforming a 3 into a 7, and f transforms a 5 into an 11, etc.

Now that we think of f as "acting on" numbers and transforming them, we can define the inverse of f as the function that "undoes" what f did. In other words, the inverse of f needs to take 7 back to 3, and take -3 back to -2, etc.

Let g(x) = (x - 1)/2. Then g(7) = 3, g(-3) = -2, and g(11) = 5, so g seems to be undoing what f did, at least for these three values. To prove that g is the inverse of f we must show that this is true for any value of x in the domain of f. In other words, g must take f(x) back to x for all values of x in the domain of f. So, g(f(x)) = x must hold for all x in the domain of f. The way to check this condition is to see that the formula for g(f(x)) simplifies to x.

g(f(x)) = g(2x + 1) = (2x + 1 -1)/2 = 2x/2 = x.

This simplification shows that if we choose any number and let f act it, then applying g to the result recovers our original number. We also need to see that this process works in reverse, or that f also undoes what g does.

f(g(x)) = f((x - 1)/2) = 2(x - 1)/2 + 1 = x - 1 + 1 = x.

Letting f-1 denote the inverse of f, we have just shown that g = f-1. http://dl.uncw.edu/digilib/mathematics/algebra/mat111hb/functions/inverse/inverse.html

5 0

4 years ago

The variables x and y vary. Write an equation relating x and y. Then find y when x=-2. x=7, y=2.

Sphinxa [80]

Answer:

<h2>equation x=y</h2>

Step-by-step explanation:

6 0

3 years ago