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kati45 [8]
3 years ago
8

Fill in the missing justifications in the correct order.

Mathematics
1 answer:
Vinil7 [7]3 years ago
7 0

Answer:

A ) Distributive property, subtraction property of equality, subtraction property of equality, division property of equality.

Step-by-step explanation:

The given equation:

4 ( x + 5 ) = 2 x + 2

4 x + 20 = 2 x + 2 ( Distributive property ),

because: 4 · x + 4 · 5 = 4 x + 20

Then follows :  4 x - 2 x + 20 = 2 x - 2 x + 2  ( Subtraction property of equality )

2 x + 20 = 2

After that:

2 x + 20 - 20 = 2 - 20  ( Subtraction property of equality )

2 x = - 18

Finally:

x = - 18 : 2  ( Division property of equality )

x = - 9

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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 area of the following circle of the radius is 4=r
maria [59]

Answer:

50.24 (unit squared! cm2, m2, etc.)

Step-by-step explanation:

Area is: Pi x r^2

3.14 x 4^2 = 3.14 x 16 = 50.24

8 0
3 years ago
Read 2 more answers
Write the expression in expanded form that is equivalent to 3(7d +4e)
pickupchik [31]

Answer:

21+4

Step-by-step explanation:

3 times 7=21

3 times4=12

21d+4e

4 0
3 years ago
Read 2 more answers
What is the factored form of the polynomal? x2-12x+27
lianna [129]

Answer:

The answer is (x-9) (x-3).

Step-by-step explanation:

This is because when you multiply them together you get

x^{2}, -9x, -3x, and 27

When you add the like terms you get,

x^{2} - 12x +27

6 0
3 years ago
Phyllis invested 50000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7
Elodia [21]

Answer:

The amount invested at 5% was $39,000 and the amount invested at 7% was $11,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x-----> the amount invested at 5%

50,000-x -----> the amount invested at 7%

so

t=1\ year\\ I=\$2,720\\r_1=0.05\\r_2=0.07\\P_1=\$x\\P_2=\$(50,000-x)

substitute in the formula above

2,720=x(0.05*1)+(50,000-x)(0.07*1)

solve for x

2,720=0.05x+3,500-0.07x

0.07x-0.05x=3,500-2,720\\0.02x=780\\x=\$39,000

(50,000-x)=\$11,000

therefore

The amount invested at 5% was $39,000 and the amount invested at 7% was $11,000

5 0
3 years ago
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