Divide. Write the quotient in lowest terms.

What is the value of x?<br><br> Enter your answer in the box.

Goshia [24]

Answer:

x = 111°

Step-by-step explanation:

180 x (7 - 1) - (120 + 158 + 126 + 125 + 121 + 139) =

900 - 789 = 111

8 0

2 years ago

Solve the system by substitution. 4x+3y=5x=4y+6Options: A. The solution is ____B. There are infinitely many solutions. C. There

zvonat [6]

So we have the following system of equations:

$\begin{gathered} 4x+3y=5 \\ x=4y+6 \end{gathered}$

We need to solve it by substitution. This means that we have to take the expression for x given by the second equation and replace x with it in the first equation:

$\begin{gathered} 4x+3y=5 \\ 4\cdot(4y+6)+3y=5 \\ 16y+24+3y=5 \\ 16y+3y=5-24 \\ 19y=-19 \\ y=-\frac{19}{19}=-1 \end{gathered}$

So y=-1. If we use this value in the second equation:

$\begin{gathered} x=4y+6 \\ x=4\cdot(-1)+6 \\ x=-4+6 \\ x=2 \end{gathered}$

So we have x=2 and y=-1 which means that there's one solution. Then the correct answer is A and the solution is (2,-1).

5 0

11 months ago

In a race between 18 people, how many ways can the top 5 finishers be arranged?

snow_lady [41]

Answer:

Step-by-step explanation:

This is permutation, since order matters. The formula for us is

₁₈P₅ = $\frac{18!}{(18-5)!}$ which simplifies to

₁₈P₅ = $\frac{18*17*16*15*14*13!}{13!}$

The factorial of 13 cancels out on the top and bottom leaving you with

₁₈P₅ = 18 × 17 × 16 × 15 × 14

which comes to 1,028,160 ways

Another way to look at it is: the first 5 people of 18 finish and the others you don't care about. Once the first place person is first, there are only 4 of the 18 left to finish in second place. Then there are only 3 left to finish in third place, etc. So if we use that reasoning, we don't even need to use the formula, we can just say

18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.

8 0

3 years ago

What is 6c+b÷6,when c=8

worty [1.4K]

6(8)+b/6
48+b/6
b/6=-48
b=-48/6
b=-288

5 0

3 years ago

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand co

jok3333 [9.3K]

Answer:

76 mL of 8% and 304 mL of 13%

Step-by-step explanation:

Set up a table like this (this is the same table for any mixture problem):

mL total * % vinegar = % vinegar/mL

8%

13%

total %

What you do with this table is multiply the first 2 columns and they equal the last column. We already know the middle column's entries from what we are given. But remember that a percent needs to be expressed as a decimal:

mL total * % vinegar = % vinegar/mL

8% .08

13% .13

total %

Now we also know that the total he wants to make is 380 mL that is 12%, so all that info goes into the last row:

mL total * % vinegar = % vinegar/mL

8% .08

13% .13

total % 380 .12

If he wants this total mixture to come from the 8% and the 13% vinegars, he is mixing them together, or adding them. We need to know how much 8% + how much 13% will give us 380 mL of 12%. So we can fill in the amounts accordingly. If he has x mL of 8%, then he will have 380 - x of 13%. The table tells us that we are multiplying the first 2 columns to get the third, so we will do that at the same time:

mL total * % vinegar = % vinegar/mL

8% x * .08 = .08x

13% 380 - x * .13 = .13(380 - x)

total % 380 * .12 = 45.6

Since we are adding the different vinegars together to get the total, we can do that with the last column as well. This is our equation:

.08x + .13(380 - x) = 45.6 Multiply everything through by 100 to get rid of the decimals now:

8x + 13(380 - x) = 4560 and

8x + 4940 - 13x = 4560 and

-5x = -380 so

x = 76

This means that there is 76 mL of 8% and 380 - 76 = 304 mL of 13%

8 0

3 years ago