Answer:
x=4 x=-2
Step-by-step explanation:
x+4 x
----------- = ------------
4 x-2
Using cross products
(x+4)(x-2) = 4x
FOIL
x^2 -2x +4x -8 = 4x
Combine like terms
x^2 +2x -8 = 4x
Subtract 4x from each side
x^2 +2x-4x -8 = 4x-4x
x^2 -2x-8 =0
Factor
What 2 numbers multiply to -8 and add to -2
-4*2 =-8
-4+2 = -2
(x-4) (x+2) =0
Using the zero product property
x-4+4 =0+4 x+2-2=0-2
x=4 x=-2
Answer:
1414 kL
Step-by-step explanation:
The volume of the donut-shaped moat is the product of its surface area and depth. The area is the product of its centerline length and its width.
<h3>Moat area</h3>
The diameter of the centerline of the moat is (50 m -5 m) = 45 m. The length of that centerline is ...
C = πd = π(45 m) = 45π m
The area is this length times the width of the moat:
moat area = (45π m)(5 m) = 225π m²
<h3>Moat volume</h3>
The volume is the product of the area and the depth of the moat:
V = Ah = (225π m²)(2 m) = 450π m³ ≈ 1413.72 m³
1 cubic meter is 1000 liters, 1 kiloliter.
The volume of the moat is about 1414 kL.
Answer:$7855.94
Step-by-step explanation:
Answer:
A 3^4 * 3^-4 / 3^6
C 1 / 3^6
Step-by-step explanation:
( 3^2 * 3^-2)
------------------- all the the power of 2
3^3
First simplify the numerator
We know a^b* a^c = a^(b*c)
( 3^(2+-2))
------------------- all to the power of 2
3^3
( 3^(0))
------------------- all to the power of 2
3^3
( 3^(0))
------------------- all to the power of 2
3^3
We know a^b/ a^c = a^(b-c)
3^(0-3) all to the power of 2
3^-3 all to the power of 2
3^-3 ^2
We know that a^b^c = a^(b*c)
3^(-3*2)
3^ -6
We know the negative exponent takes if from the numerator to the denominator
1 / 3^6
The other correct choice is A
3^4 * 3^-4 = 3^0 which is 1
1/3^6 is the same answer
Q1: The answer is A. pyramid.
A pyramid has one polygon base. A prism has two polygon bases. A cone has one circular base. A cylinder has two circular bases.
Q6: The answer is false.
Surface area of a rectangular prism is:
A = 2(wl + hl + hw)
A1 = 2(4*5 + 6*5 + 6*4) = 2(20+30+24) = 2*74 = 148
A2 = 2(6*4 + 5*4 + 5*6) = 2(24+20+30) = 2*74 = 148
Q7. The answer is A. 6 feet
The volume of rectangular prism is:
V = w * l * h
w = ?
So, just replace the knowing facts:
288 = w * 8 * 6
288 = w * 48
w = 288/48 = 6
Q8: The answer is 216 ft³
The volume of the cube is:
V = a³
Since a = 6, then:
V = 6³ = 216