Let 
be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use 
gal of the 70% solution.
You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means
so the answer is B.
Answer:
2
Step-by-step explanation:
If A = (2, 3) then a dilation of scale factor 2 means that the x and y coordinates are multiplied by 2, so x = 2 x 2 = 4 and y = 3 x 2 = 6, so A' = (4, 6)
<h2>
Answer:</h2>
<h2>
Step-by-step explanation:</h2>
The question in this problem is:
<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>
<em />
First of all, let's name the first variable which is the smaller number. Accordingly, the lager number will be 
given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:
So:
1. The sum of 2 consecutive integers can be written as:
2. Nine times the smaller and 5 times the larger can be written as:
Finally, the whole statement:
The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:
The two numbers are:
Answer:
no solution
Step-by-step explanation:
-9x +5 < 17 AND 13x + 25 < -1
Solve each part separately and then put back together
-9x +5 < 17
Subtract 5 from each side
-9x+5-5< 17-5
-9x < 12
Divide each side by -9 remembering to flip the inequality
-9x/-9>12/-9
x > -4/3
and
13x + 25 < -1
subtract 25 from each side
13x +25-25 < -1-25
13x <-26
Divide by 13
13x/13 < -26/13
x <-2
There is no overlap so there is no solution
Answer:
x = 17
Step-by-step explanation:
∠ DCE = ∠ ACE ( vertically opposite angles )
The sum of the 3 angles in a triangle = 180° , then
∠ DCE = 180° - (100 +x) = 180 - 100 - x = 80 - x
∠ ACE = 180 - (49 + 4x) = 180 - 49 - 4x = 131 - 4x
Equating the 2 angles
80 - x = 131 - 4x ( add 4x to both sides )
80 + 3x = 131 ( subtract 80 from both sides )
3x = 51 ( divide both sides by 3 )
x = 17
