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3 years ago

Write a function g with the parent function f(x) = x4 that has a vertex at (3, -6).

Mathematics

1 answer:

Irina18 [472]3 years ago

5 0

Answer:

$g(x)=(x-3)^4-6$

Step-by-step explanation:

The parent function is $f(x)=x^4$ .

We want to transform this function so that its vertex will move from the origin to (3,-6).

In other words, we translate the parent function 3 units to the right and 6 units down,

Let g(x) be the new function then:

$g(x)=f(x-3)-6$

$\implies g(x)=(x-3)^4-6$

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Pete estimates that he has spent $64.50 on supplies for his lawn mower. He charges $12 per lawn for his service. Write a linear

nadya68 [22]

Answer:

The equation representing the Amount of profit Peter earns is $y=12x-64.5$ .

Step-by-step explanation:

Given:

Money spent on supplies = $64.50

Per lawn charge for mowing lawn = $12

Solution:

Let the amount of profit Pete earns be represented by 'y'.

Let the number of lawns to be mowed be represented by 'x'

Now we can say that:

Amount of profit Pete earns is equal to Per lawn charge for mowing lawn multiplied by number of lawns to be mowed minus Money spent on supplies.

framing in equation form we get;

$y=12x-64.5$

Hence The equation representing the Amount of profit Peter earns is $y=12x-64.5$ .

7 0

4 years ago

PLEASE help !!! I’m struggling and I suck at math. Can someone answer this for me? For points and brainly !

Helen [10]

Answer:

$\huge\boxed{2329 \ \text{pounds}}$

Step-by-step explanation:

In order to solve this equation, let's see what we already know.

We know two points on the graph <em>which we can use to find the slope</em>

That's about it.

However, this can come useful to find the slope between the two points, which is the slope for the entire graph (since this is linear). The slope between two points is usually defined as $\frac{\Delta y}{\Delta x}$ (change in y / change in x). Our two points are (18, 2017) and (48, 2212).

The change in y between our two points is $2212-2017 = 195$ , and the change in x is $48 - 18 = 30$ . Our slope will then be $\frac{195}{30}$ , which comes out to be approximately 6.5. Therefore, our slope is 6.5.

Now that we know the slope, we can substitute inside our equation in slope intercept form.

$y = 6.5x+b$

We have yet to find b, the y-intercept (how much the plane itself weighs). To find b, we can substitute a point on the graph into the equation and solve for b. We know that the point (18, 2017) is on the graph so let's use that.