Answer: Choice C) Infinitely many solutions
If you solve the first equation for y, you get
2y = 14 - 2x
2y = 14 + (-2x)
2y = -2x + 14
2y/2 = (-2x)/2 + 14/2 ... divide every term by 2
y = -x + 7
This result of y = -x+7 is identical to the second equation in the system. So the two graphs are going to be the same. We only produce one line. One graph is right on top of the other. The two lines will intersect infinitely many times. Any point on the blue line is a solution to the system.
1.b)
Fred has F cards. Bill has B cards. Tim has T cards.
B + F + T = 167
B = 5F
T = 4F - 3
5F + F + 4F - 3 = 167
10F - 3 = 167
10F = 170
F = 17
Fred has 17 cards.
B = 5F = 5(17) = 85
Bill has 85 cards.
T = 4F - 3 = 4(17) - 3 = 65
Tim has 65 cards.
2.a)
length = L
width = W
L = W + 5
perimeter = 2L + 2W = 168
2L + 2W = 168
2(W + 5) + 2W = 168
2W + 10 + 2W = 168
4W = 158
W = 39.5
L = W + 5 = 39.5 + 5 = 44.5
Length = 44.5 inches
Width = 39.5 inches
2.b)
Original rectangle:
width = W
length = 2W
New rectangle:
width = W - 1
length = 2W + 4
perimeter = 198 inches
perimeter = 2L + 2W = 198
2(2W + 4) + 2(W - 1) = 198
4W + 8 + 2W - 2 = 198
6W + 6 = 198
6W = 192
W = 32
L = 2W = 64
width = 32 inches
length = 64 inches
3.a)
Now:
Sam's age = S
John's age = 3S
In 5 years:
John's age = 3S + 5
Sam's age = S + 5
3S + 5 = 2(S + 5)
3S + 5 = 2S + 10
S = 5
Sam's age is 5.
John's age is 15.
This is all I have time for now. Post the rest of the problems in a different post, and I'll try to help later.
a +b = 7
a-b = 3
Rewrite the second equation as a = 3+b
Replace a in the first equation with that:
3+b + b = 7
Simplify:
3 +2b = 7
Subtract 3 from both sides:
2b = 4
Divide both sides by 2:
b = 4/2 = 2
Now replace b in the first equation with 2 to solve for a:
a + 2 =7
a = 7-2 = 5
so you now have a and b.
Now solve the given equation:
2^a * 2^b
2^5 * 2^2
32*4
128
The answer is 128.
Answer:
F = 
Step-by-step explanation:
Given
C = 
( multiply both sides by 9 to clear the fraction )
9C = 5(F - 32) ← distribute
9C = 5F - 160 ( add 160 to both sides )
9C + 160 = 5F ( divide both sides by 5 )
= F
