Logarhythm

Is this missing any details? On my screen I can't see the numbers... 

Let s = soft shell tacos, and h = hard shell tacos

6s + 2h = 12

3s + 1h = 6

Im not sure you can even write a system for this since they are proportionate. 

(3s + 1h = 6) * 2 --> 6s + 2h = 12, which is the first sentence. If you wrote a system, it would just be "0 + 0 = 0"; you can't cancel anything out.

However, you could make a good guess to what the answer might be since the numbers aren't big. 

s could equal 1 and h could equal 3. 

50.25 * 3 = $150.75 a day

150.75 * 7 = B) $1055.25, which is your answer :)

1/a + 1/b = (b + a) / ab

1/b - 1/a = (a - b) / ab

When multiplied, you get: (a + b)(a - b) / a²b²

                                              = (a² - b²) / a²b²

                                      = 1/b² - 1/a²

This means you want b = 3, since you want it to be the smallest it can be. Then you want a = -1, since you want it to be the biggest it can be. 

This gives you:
 

1/3² - 1/(-1)²

= 1/9 - 1

= -8/9, which is your answer :)

3.5 / 3 = 6.5   (3.5 + 3)

32.5 ÷ 6.5 = 5, which means he needs to make 5 batches.

3.5 gallons of fruit punch concentrate per batch, which means he'll need 3.5 * 5 = 17.5 gallons of fruit punch concentrate :)

The ratio of quarters to dimes right now is 3:12

If we look at this like a fraction, it's 3/12, but we want to get it to 1/2. 

1/2 = 6/12, which means there needs to be 3 more quarters in order for the ratio to be 6:12, or 1:2. 

7x²⁰¹⁴ / 4x²⁰¹³ = 7x/4 

2x²⁰¹² / 28x²⁰¹¹ = x/14

9x²⁰⁰⁷ / x²⁰⁰⁸ = 9/x

8x²⁰⁰⁹ / 6x²⁰¹⁰ = 4/3x

= (252x²) / (168x²)

= 252 / 168

= 3/2, which is your answer :)

Let m = multiple choice, and s = short response

23m + 10s = 86

28m + 5s = 76

56m + 10s = 152

23m + 10s = 86

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

33m = 66

    m = 2

28m + 5s = 76

28(2) + 5s = 76

56 + 5s = 76

5s = 20

s = 4

Which means each multiple choice answer is worth 2 points and short responses are worth 4 points :)
 

A = P(1 + r/n)^nt

where,

A = final amount

P = initial investment 

r = interest rate

n = number of times interest is applied

t = number of time periods

Cedric:
A = P(1 + r/n)^nt

   = 12000(1 + 0.05/1)^(1*15)

   = 12000(1.05)¹⁵

   ≈ 12000(2.0789)

   ≈ $24 947.14

Daniel:
A = P(1 + r/n)^nt

   = 12000(1 + 0.07/1)^(1*15)   

   = 12000(1.07)¹⁵

   ≈ 12000(2.759)

   ≈ $33 108.38

33108.38 - 24947.14 = $8161.24, which is your answer :)

(-5x³ - 5x² - 7x + 1)(-x² + 6x + 1) 

To find the coefficient of x², we can just multiply the terms that would have x².

(-5x²)(1) + (-7x)(6x) + (1)(-x²) 

= -5x² - 42x² - x²

= -48x²

Which means your coefficient is -48, which is also your answer :)