Answer:
|x y 1|
|7 -3 1| = 0
|4 -8 1|
x*(-3*1 - (-8)*1) - y*(7*1 - 4*1) + 1*(7*-8 - 4*-3) = 0
5x - 3y - 44 = 0
Step-by-step explanation:
3 + 4x = 33
-3 on both sides
4x = 30
/4 on both sides
x = 7.5
Answer:
Rod is 7 1/2 years old
<span>3(2v + 1)= -15(5v + 16)
6v + 3 = -75v - 240 (Add 75v onto each side)
+75v +75v
81v + 3 = 240 (Subtract 3 on each side)
-3 -3
81v = -243
v = -3
</span>
Answer:
y - 2 = - 
(x - 7)
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 4 ← is in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= -
The equation of a line in point- slope form is
y - b = m(x - a)
m is the slope and (a, b) a point on the line
Here m = - and (a, b) = (7, 2), thus
y - 2 = - (x - 7) ← equation of perpendicular line
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.
