1. This must be greater than or equal to 0 (there can't be any negatives!)
8 - .5t ≥ 0.
8 ≥ .5t
t ≤ 16
D.
2. 4(2x-1) = 2x + 35
8x - 4 = 2x + 35
6x = 39
x = 6.5
H.
3. c = .8(x-15) = .8x-12
A.
4. m = number of marble cupcakes
s = number of strawberry shortcake cupcakes
6m + 8.5s = 391
m = 1/2s
6(.5s)+8.5s = 391
11.5s = 391
s = 34
m = 17
F.
5. B
6. Use substitution
2x + 3x = 10
5x = 10
x = 2
7. (sorry I'm not sure!)
8. G
9. L = number of balls
B = number of bats
L + B = 100
B = 100 - L
4.5L+20B = 822
4.5L + 20(100-L) = 822
4.5L -20L + 2000 = 822
1178 = 15.5L
L = 76
10. J
Answer:
5 withdrawals
Step-by-step explanation:
Since $10.50 ends in $0.50, you know that she must have made at least one $2.50 transaction.
10.50 - 2.50 = 8
8/2 = 4 (she made four $2 transactions)
She made 4 $2 transactions and 1 $2.50 transaction.
4 + 1 = 5
She made 5 transactions total.
Each petal of the region
is the intersection of two circles, both of diameter 10. Each petal in turn is twice the area of a circular segment bounded by a chord of length
, which implies the segment is subtended by an angle of
. This means the area of the segment is
This means the area of one petal is
, and the area of
is four times this, or
.
Meanwhile, the area of
is simply the area of the square minus the area of
, or
.
So
(provided these regions are indeed disjoint; it's hard to tell from the picture)
The answer is 7.5 liters that should of evaporated
f(h(x))= 2x -21
Step-by-step explanation:
f(x)= x^3 - 6
h(x)=\sqrt[3]{2x-15}
WE need to find f(h(x)), use composition of functions
Plug in h(x)
f(h(x))=f(\sqrt[3]{2x-15})
Now we plug in f(x) in f(x)
f(h(x))=f(\sqrt[3]{2x-15})=(\sqrt[3]{2x-15})^3 - 6
cube and cube root will get cancelled
f(h(x))= 2x-15 -6= 2 x-21
