Find the vertex of the function f(x) = x2

A landscape business charges $50 to deliver rocks. The cost of the rocks are $27 per cubic yard. write and solve a linear equati

Nuetrik [128]

<h2>Answer: 27x + 50 = y, $266</h2>

Step-by-step explanation:

First, let's form a linear equation that will help us find out how much that will cost.

Let's set x = the cubic yards of rocks delivered and y = total cost.

First, we know that the business charges 27 dollars for every x that you buy. That can be shown with a multiplication expression:

27x

Next, we know that the business charges a fixed fee of $50 for their services. This fee would be <em>added on</em> to the amount that they charge for the rocks that you buy.

That's our linear expression! Next, we need to find out the <em>total cost</em>, y, when you need 8 cubic yards of rocks delivered, x.

To solve this, we need to substitute values for at least one of our variables.

Since 8 describes the cubic yards of rocks delivered, we can substitute 8 for x.

But we don't know y, the total cost- that's what we're solving for! In other words, we're solving for y.

Let's just substitute in what we know:

27(8) + 50 = y.

216 + 50 = y

So, we know that it would cost $266 dollars to have 8 cubic yards of rocks delivered to a site.

By the way, you can also graph your linear equation to find the corresponding y-value to 8 as another way to solve your problem.

7 0

3 years ago

For the function g(x)=3-8(1/4)^2-x

Reika [66]

Using function concepts, it is found that:

a) The y-intercept is y = 2.5.

b) The horizontal asymptote is x = 3.

c) The function is decreasing.

d) The domain is $(-\infty,\infty)$ and the range is $(-\infty,3)$ .
e) The graph is given at the end of the answer.

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

The given function is:

$g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}$

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

Question a:

The y-intercept is g(0), thus:

$g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5$

The y-intercept is y = 2.5.

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

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

$\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3$

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$\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty$

Thus, the horizontal asymptote is x = 3.

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

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

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Question d:

Exponential function has no restrictions in the domain, so it is all real values, that is $(-\infty,\infty)$ .
From the limits in item c, the range is: $(-\infty,3)$

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The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

8 0

2 years ago

The ratio of boys to girls in a class is 4:5, what fraction of the class is boys

scoundrel [369]

Boys:girls = 4/5

boys = 4/(4+5) = 4/9 of the class

8 0

3 years ago

Read 2 more answers

Peter and sai were buying presents. Their parents had given them each an allowance of $7 per week. Each of them saved their mone

Lady bird [3.3K]

They each have $42 because 7 times 6 is 42 and combined they have $84 because 42 + 42=84.

6 0

3 years ago

Read 2 more answers

What does AB congruent symbol CD mean? AB and CD here have lines over them How is it different than AB=CD?

masha68 [24]

Answer:

Suppose that we have two line segments, AB and CD. We know that they have the same length.

I know that AB¯¯¯¯¯¯¯¯=CD¯¯¯¯¯¯¯¯ means AB is identical to CD (aka. They are the same lines), and also that AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ means that AB and CD have the same size, but what does AB=CD mean?

Step-by-step explanation:

4 0

3 years ago

Find the vertex of the function f(x) = x2 - 8x + 15.