1) 2m - 16 = 2m + 4
2m - 2m = 4 + 16
0 = 20 (no solution)
2) -4(r + 2) = 4(2 - 2r)
-(r + 2) = 2 - 2r
-r - 2 = 2 - 2r
-r + 2r = 2 + 2
r = 4
3) 12(5 + 2y) = 4y - (6 - 9y)
60 + 24y = 4y - 6 + 9y
60 + 24y = 13y - 6
24y - 13y = -6 - 60
11y = -66
y = -6
Answer:
Step-by-step explanation:
Volume = 198 ft
length * width * height = 198
(x - 1) * (x + 4) * 3 = 198
(x - 1) * (x + 4) = 198/3
(x - 1) * (x + 4) = 66
x*x + x*4 -1*x - 1*4 = 66 {Use FOIL method to multiply}
x² + 4x - x - 4 = 66
x² + 3x - 4 =66
x² + 3x - 4 - 66 = 0
x² + 3x - 70 = 0
Now factorize.
x² + 10x - 7x - 7*10 = 0
x(x +10) - 7(x + 10 ) = 0
(x + 10)(x - 7) = 0
x - 7 = 0 {x + 10 is ignored because measurement cannot be in negative}
x = 7
length = x - 1 = 7 - 1 = 6ft
Width = x + 4 = 7 + 4 = 11 ft
Answer:
To find the constant of proportionality from the coordinates of
one point on the graph are as follows :-
1.) Find two easy points.
2.) Start with the leftmost point and count how many squares you need to up to get to your second point.
3.) Count how many squares you need to go to the right.
4.) Simplify, and you've found your constant of proportionality.
3/4 Of X(Capacity) = 18 Gallons
X = 18*4/3
= 6*4
= 24 Gallons
Capacity of Tank = 24Gallons
<h2><em>y
2
+
6
y
−
16
=
(
y
+
8
)
(
y
−
2
)
</em></h2><h2 /><h2><em>Explanation:
</em></h2><h2><em>Note that in general:
</em></h2><h2 /><h2><em>(
y
+
a
)
(y
−
b
)
=
y
2
+
(
a
−
b
)
y
−
a
b
</em></h2><h2 /><h2><em>So we want to find a pair of factors a and b of 16 which differ by 6
. </em></h2><h2><em>The pair 8
,
2 works in that 8−
2
=
6 and 8
⋅
2=
16
.
</em></h2><h2 /><h2><em>Hence:
</em></h2><h2><em>
y
2
+
6
y
−
16
=
(
y+
8
)
(
y
−
2
)</em></h2><h2><em>y=2,-8</em></h2>
