Factor the expression 3x? - 75 completely. (select one answer)

Vivian is a salon owner. Yesterday she did 2 haircuts and colored the hair of 4 clients, charging a total of $422. Today, she di

harina [27]

Answer:

Haircuts cost $50.33

Hair Color costs $80.33

Step-by-step explanation:

Let haircut be cost "a"

coloring be cost "b"

2 haircut, 4 coloring equals 422, we can write:

2a + 4b = 422 {Equation 1}

5 haircut, 4 coloring, equals 573, we can write:

5a + 4b = 573 {Equation 2}

We now multiply equation 1 with -1 and add it with Equation 2 to get:

-1(2a + 4b = 422) = -2a - 4b = -422

Now,

-2a - 4b = -422

5a + 4b = 573

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

3a = 151

a = 151/3 = $50.33

Now, to find b, we plug in this value into any equation and solve for b:

2a + 4b = 422

2(50.33) + 4b = 422

4b = 422 - 100.66

b = $80.33

Haircuts cost $50.33

Hair Color costs $80.33

4 0

3 years ago

(50 points!) Whats 7x + 5z(x-z) ÷ 9y, when x = 5, z = 8, and y = 23. Whoever Gives me an answer AND REALLY GOOD EXPLANATION FIRS

Oliga [24]

Answer: First we will substitute the numbers given for the variables.

Then we will use order of operations to simplify.

7x + 5z(x - z) ÷ 9y would be equal to

7(5) + 5(8) * (5 - 8) ÷ 9(23)

Simplify:

35 + 40(-3) ÷ 207

Use order of operations to multiply 40 and -3; the equation now looks like:

35 + (-120) ÷ 207

Use order of operations to divide -120 and 207; the equation now looks like:

35 + (-0.6)

Add 35 and -0.6:

34.4

The solution to this equation is 34.4.

8 0

3 years ago

Read 2 more answers

What was its average speed in miles per hour if a plane flew 1898.4 miles in 5.6 hours?

Stells [14]

1898.4mi/5.6hr = 339mi/hr

3 0

3 years ago

Evaluate the expression below at x=6.

ziro4ka [17]

Remember to use Orders of Operations, or PEMDAS.

6(3 * 6^2 - 7 * 6)
6(3 * 36 - 7 * 6)
6(108 - 42)
6(66)
396

The answer is 396.

6 0

3 years ago

Read 2 more answers

Prove algebraically that the sum of the squares of two consecutive intgers is always an odd number

musickatia [10]

Answer:

See below.

Step-by-step explanation:

Let's let our first integer be n.

Then, our second, consecutive integer must be (n+1).

We want to prove that the sum of the square of two consecutive integers is always odd.

So, let's square our two expressions and add them up:

$(n)^2+(n+1)^2$

Square. Use the perfect square trinomial pattern. So:

$=n^2+(n^2+2n+1)$

Combine like terms:

$=2n^2+2n+1$

Notice that the first term 2n² has a 2 in front. Anything multiplied by 2 is even. So, regardless of what integer n is, 2n² is always even.

Our second term 2n also has a 2 in front. So, whatever n is, 2n is also always even.

So far, 2n² and 2n are both even. Therefore, the sum of 2n² and 2n is also even.

Lastly, we have the constant term 1. It doesn't matter what n is, we know that (2n² + 2n) is definitely and is always even. So, if we add 1 to this, we will get an odd number.

Q.E.D.

3 0

3 years ago