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2 years ago

Please help me out with these 2 questions! Legit answers only please!

Mathematics

1 answer:

geniusboy [140]2 years ago

5 0

Answer:

1.) 12 hours 2.) She made a multiplying error in the table.

Step-by-step explanation:

1.)

First, let's find the slope of this equation:

m = 135 - 81 / 5 - 3

m = 54/2

m = 27

Therefore, the equation should be y = 27x.

Now we substitute 324 for y and solve for x:

324 = 27x

12 = x (Divided 27 on both sides.)

Therefore, someone would have to work 12 hours in order to earn $324.

2.)

For this problem, it appears Amanda has found the correct equation for her recipe. When taking a look at the table, however, it seems as though she has made a multiplying error.

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Please help! Thanks in advance.

alukav5142 [94]

In this problem, we need to plug in the given x values for $f(x)=0$ and find a and b.

When we plug in 1, we get: $2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0$

Simplify:
$2 - 5 - 14 + a + b = 0$
$- 17 + a + b = 0$
$a + b = 17$

We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
$2 \times {4}^{4} - 5 \times {4}^{3} - 14 \times {4}^{2} + a \times 4 + b = 0$
$512 - 320 - 224 + 4a + b = 0$
$- 32 + 4a + b = 0$
$4a + b = 32$

Now we have our second one. We can combine them:
$a + b = 17 \\ 4a + b = 32$

I use elimination method which is easier here.

Multiply the top equation by -1: $- a - b = - 17 \\ 4a + b = 32$

Add them up:
$3a = 15$

Simplify:
$a = 5$

Now we have a, we can plug in one of those equations to find b:
$5 + b = 17$
$b = 17 - 5$
$b = 12$

So, the answers are $a=5$ and $b=12$ .

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