Answer:
x=3/2
Step-by-step explanation:
2^2x=2^3
2x=3
x=3/2
1. Zoe stacked the most brownies. She stacked 27 brownies out of the 50 brownies.
2. 15
3. 43 + 3n ≥ 70, so n ≥ 9
4. D. 58x + 13 + 58y
5. The answer would be ≤4
6. 9.94 + 10.01p ≤ 70, so p ≤ 6
7. C 40 89
8. D. x+(x+5)=77
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Both the negative and positive counterparts of a number have the same absolute value, or distance from 0.
The two numbers are 16 and -16.
They both have the same absolute value, 16.
Answer: The equation of an ellipse:
(
x
−
h
)
2
a
2
+
(
y
−
k
)
2
b
2
=
1
;
a
>
b
Has vertices at
(
h
±
a
,
k
)
Has foci at
(
h
±
√
a
2
−
b
2
,
k
)
Use the vertices to write 3 equations:
k
=
4
[1]
h
−
a
=
−
6
[2]
h
+
a
=
10
[3]
Use equations [2] and [3] to solve for h and a:
2
h
=
4
h
=
2
a
=
8
Use the focus to write another equation:
8
=
h
+
√
a
2
−
b
2
Substitute values for h and a:
8
=
2
+
√
8
2
−
b
2
6
=
√
64
−
b
2
36
=
64
−
b
2
b
2
=
64
−
36
b
2
=
28
b
=
√
28
Substitute the values into the standard form:
(
x
−
2
)
2
8
2
+
(
y
−
4
)
2
(
√
28
)
2
=
1
1. Multiply the hourly rate by the number of hours worked ( 22.5h) add that to the flat fee ( 22.5h +35) and that needs to be equal to or greater than what he expects to make:
A. 22.5h + 35 ≥ 215 , with a solution of h ≥ 8
2. Same method as number 1:
C. $3 + 1.80m ≤ $25
3. Each fraction would need 1 negative sign and have the same numerator and denominator, so the answer would be B.6/-7