Answer:
D. $8 per hour
Step-by-step explanation:
The rate of pay is found by dividing the pay by the number of hours it is for.
$40/(5 h) = $8/h
The worker gets paid $8 per hour.
-9x + y = 17
9x + 9y = 19
------------------add
10y = 36
y = 36/10 = 18/5 <==
A knitter with 14 skeins of yarn can make 7 scarves
Explanation:
We can use a proportion to solve this
4 skeins of yarn
-----------------------
2 scarves
That is the information we know. What we want to do is find out how many scarves for 14 skeins of yarn, like this
4 14
-- = ---
2 ?
To get from 4 to 14, you multiply by 3.5. We must to the same thing to the bottom as well. So we multiply 2 by 3.5, which gives us 7
x3.5
4 14
-- = ---
2 7
x3.5
<h3>
Answers: x = 30 and y = 150</h3>
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Explanation:
For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.
One pair of such angles is A and C
A+C = 180
x+y = 180 is one equation to form
The other pair of supplementary angles is B and D
B+D = 180
y-45+2x+15 = 180
2x+y-30 = 180
2x+y = 180+30
2x+y = 210 is the other equation to form
--------------
So the system of equations we have is

Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.
- The x terms subtract to x-2x = -x
- The y terms subtract to y-y = 0y = 0, so the y terms go away
- The right hand sides subtract to 180-210 = -30
We end up with -x = -30 which solves to x = 30
--------------
Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y
Let's say we picked on the first equation
x+y = 180
30+y = 180
y = 180-30
y = 150
Or we could pick on the second equation
2x+y = 210
2(30) + y = 210
60+y = 210
y = 210-60
y = 150
Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.
Do I understand coorectly, you have the following equation
6x+1=4x+19
and you want to know what x is?
first, let's put all the expressions with x on one side and all else on the other side:
6x-4x=19-1
and calculate this 2x=18
and divide by 2:
x=9
and this is the answer!