taeijr

Given that a > 0, if f(g(a)) = 8, where f(x) = x^2 + 8 and g(x) = x^2 - 4, what is the value of a?

Substitute in g(x)

f(g(a)) = f(a^2 - 4)

f(a^2 - 4) = (a^2 - 4)^2 + 8

We bring that back into the original equation

(a^2 - 4)^2 + 8 = 8

(a^2 - 4)^2 = 0

a^2 - 4 = 0

a^2 = 4, a = 2

Answer: a = 2

Check:

f(0) = 0^2 + 8 = 8

:)

1. How much money does Kevin have?

We know that he has 18 dimes, 12 nickels, and 6 quarters

18 x 10 = 180 cents

12 x 5 = 60 cents

6 x 25 = 150 cents

180 + 60 + 150 = 390 cents

Kevin has 390 cents or $3.90

2. How many slices of pizza can Kevin buy?

Each slice of pizza is 75 cents, so to find the number of slices he can buy, we just divide 390 by 75

390/75 = 5.2

He can't buy 0.2 of a slice of pizza, so the max he can buy is 5 slices.

Kevin can buy 5 slices of pizza

Let me know if I made a careless error 

:)

Benny and Emmet have 135 altogether. Emmet has 53 more than Benny. How much does Benny have?

Benny = B, Emmet = E

We know that B + E = 135 and E = B + 53

This turns into a simple substitution

B + (B + 53) = 135

2B + 53 = 135

2B = 82

B = 41

Benny has 41

Check:

41 + (41 + 53) = 41 + 94 = 135 

:)

In order to find the equation, we first need to find the radius and the midpoint. We can find the midpoint simply by using these equations:

(x₁ + x₂)/2 and (y₁ + y₂)/2

If we do this, we find the the midpoint is (1, 6.5)

Now, we can find the radius. To do this, we pick one of the points listed in the question and use the distance formula.

The distance formula is: √(x₂ - x₁)² + (y₂ - y₁)²

I will just use the point (-5, 4) for this, and after plugging it in and doing some math, we find that the radius is 6.5 units.

Now we can easily find the equation of the circle. The standard form of the equation of this circle is:

(x - 1)² + (y - 6.5)² = 42.25

Please correct me if I'm wrong 

Here are the things we know about this problem:

Model A can print 80 books per day and Model B can print 60 books per day. (We will use "A" to represent Model A and "B" to represent Model B)

The total number of books printed, or "jobs", is 1260.

There are 18 printing presses.

Using this information, we can come up with an equation.

(80/1)(A) + (60/1)(B) = 1260

...There are two variables that we don't know. But, we do know that there are 18 total printing presses, so we can represent the variable B as (18 - A):

(80)(A) + (60)(18-A) = 1260

Now we just do the math.

(80A) + (-60A + 1080) = 1260

A = 9

Now we can go back and substitute A back in (18 - A) to find B.

18 - 9 = 9, B = 9

I haven't done these rate problems in a while so there's room for mistake, so please correct me if I'm wrong 

w a i t...

i think im wrong 

For one, we know that x cannot equal -2 because f(-2) is either undefined or indeterminate. 

To find the numbers that aren't in the domain of g(x), we set the bottom to 0. 

So 3x^2 + 11x + 10 = 0

(3x + 5)(x + 2) = 0,

x = -5/3, -2

-2 + (-2) + (-5/3) = -4 - (5/3) = -17/3

Uhm I'm not very good at functions and this stuff so there's a lot of room for errors :/. Please correct me if I'm wrong.

x + 15 = 3x + 5

2x = 10

x = 5

NM = OL = 5 + 15 = 20

The answer is "B" or the second one.

Please correct me if I'm wrong. 

4-0-0-0

3-1-0-0

2-2-0-0

2-1-1-0

1-1-1-1

We don't need things like 0-0-3-1, 0-0-2-2 etc. because they're identical and would be the same thing.

So there are only 5 cases. 

Hope that helps and please correct me if I'm wrong 

ohh yes sorry I assumed the value was 0 oops