The product is: 25x^2-5xy-6y^2
"The total number of stamps is 35" is the statement among the following choices given in the question that is correct. The correct option among all the options that are given in the question is the third option or the penultimate option. I hope that this is the answer that has actually come to your great help.
If the grid is an 8x8:
To solve this we need to convert 3/4 into a fraction x/8 so that they have the same denominator.
To do this we can set a porportion and find a common denominator. 4 x 2 = 8 so the common denominator would be 8 and the rule would be x 2 so 4 x 2 = 8 and 3 x 2 = 6
So we get 7/8 and 6/8
From top to bottom shade 7 spaces in a row
From left to right shade 6 spaces in a row
Fill in the spaces in between to make a square
I hope this helps!
26 , 8-6=2 so you do 24+6
<span>1,
During a 1-hr television program, there were 22 commercials, Some
commercials were 15 sec and some were 30 sec long. Find the number of
15- sec commercials and the number of 30 sec commercial if the total
playing time for commercial was 9.5 minutes.
</span>a) <span>show how to formulate your system of equations for your problem,
Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language
b) state the two equations:
- translate the word statement into algebraic equations:
</span><span>* there were 22 commercials => x + y = 22
* the total playing
time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>
Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y = 570
c) state which method you will use to solve either addition or substitution
Answer:
adition: multiply the first equation times - 15 and add the two equations.
d) solve your system showing and explaining each step of the process
Answer:
- muliply eq (1) times - 15
-15x - 15y = - 330
- add that to the eq (2):
-15x + 15x - 15y + 30y = -330 + 570
- add like terms: 15y = 240
- divide both members by 15: 15y/15 = 240 / 15 => y = 16
- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6
Solution: x = 6, y = 16
e) Be sure to check your solution!
x + y = 22
6 + 16 = 22
22 = 22 --> check
15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check
f) Once a solution is found explain what this solution means in the context
of the problem, write the answer to the word problem in words</span><span>
The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.
2, How many quarts of water should be mixed with a 30% vinegar solution
to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>
a) variables:
- state the variables
x: number of quarters of water
y: number of quarters of vinegar
- translate the words into mathematical language
12 qt 25% vinegar solution
=> total number of quarts = 12 = x + y
balance in vinegar:
vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution
0 + 0.3y = 0.25 (x + y)
c) Equations
Eq (1) x + y = 12
Eq (2): 0.3y = 0.25x + 0.25y
=> 0.25x - 0.05y = 0
d) solve
- multiply eq (1) times 0.05 and add to eq (2)
0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6
x = 0.6 / 0.3 = 2
x + y = 12 => y = 12 - y = 12 - 2 = 10
Solution: x = 2, y = 10
e) check:
x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check
vinegar:
10*0.3 = 12*0.25
3 = 3 -> check
f) Explanation of the solution
The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.
