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Ivan
3 years ago
14

Choose the correct simplification of the expression (a^4/b^2)^3

Mathematics
1 answer:
Oksanka [162]3 years ago
4 0
The answer is B: <span> a^12/b^6

Proof:

Simplify the following:
(a^4/b^2)^3

Multiply each exponent in a^4/b^2 by 3:
(a^(3×4))/((b^2)^3)

3×4 = 12:
a^12/(b^2)^3

Multiply exponents. (b^2)^3 = b^(2×3):
a^12/b^(2×3)
2×3 = 6:
Answer:  a^12/b^6</span>
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The diagram shows the cross-section of a wall of a cinema. It has to be painted. Work out the area that needs to be painted.
mestny [16]

Answer:

Area = 370 m²

Cost to paint = £105

Step-by-step explanation:

Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)

Area of a trapezoid = \frac{1}{2}(b_1+b_2)h

where b_1 and b_2 are the parallel sides and h is the distance between these sides.

Area of trapezoid (1) = \frac{1}{2}(11+12)\times 6

                                  = 69 m²

Area of the rectangle (2) = Length × Width

                                         = 12 × 15

                                         = 180 m²

Area of the trapezoid (3) = \frac{1}{2}(12+10)\times 11

                                         = 121 m²

Now area of the wall = 69 + 180 + 121

                                   = 370 m²

One tin covers the area = 25 m²

Number of tins required to paint the wall = \frac{\text{Total area}}{\text{Area covered by one tin}}

= \frac{370}{25}

= 14.8

Therefore, number of tins to be purchased = 15

Cost to paint the complete wall = 15 × £7

                                                       = £105

8 0
3 years ago
What is the slope of the following line?
serg [7]
U use y=mx+b to find the slope, and the answer would be m=-3
8 0
2 years ago
What are my like terms here: <br><br> 4b, b, 7, 9b
netineya [11]

Answer:

4b, b, and 9b are like terms

Step-by-step explanation:

7 0
3 years ago
Use doubles mines one to solve 8+7.Write the number sentence.
vlada-n [284]

Answer:

15

Step-by-step explanation:

8+8 would be the doubles and that would equal 16.

Then take one away from 16 and that would equal 15

7 0
3 years ago
Y=2x+6 and y=-3x+16 for solving the system
Butoxors [25]
Substitution

Step 1: Solve for x or y in either of the two equations. In the equations that you are given, y is already solved for you.

Step 2: Plug in 2x + 6 into the opposite equation.

   2x + 6 = -3x + 16
         - 6              - 6
------------------------------
   2x = -3x + 10
+ 3x  + 3x
------------------------------
   5x  =  10
 ------   ------
    5        5

x = 2

Step 3: Plug in the x value into either equation.

y = 2(2) + 6
y = 4 + 6
y = 10

The final answer gets expressed as a coordinate pair: (x,y) (2,10)

I hope this helps you :)




4 0
3 years ago
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