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agasfer [191]
2 years ago
14

Please help! All in the image:

Mathematics
2 answers:
charle [14.2K]2 years ago
8 0

Answer:

66 cm^2

Step-by-step explanation:

By equating the area we get x = 6.

spin [16.1K]2 years ago
6 0

Answer:The area of the inner rectangle is 66 cm^2

Step-by-step explanation:

The diagram is that of a rectangle with a certain thickness. The area of the outer rectangle is given as 99cm^2. The length I given as (x + 5) and the width is given as x + 3.

The formula for the area of a rectangle is expressed as length, ×width,w. Therefore,

(x + 5)((x + 3) = 99

x^2 + 3x + 5x + 15 = 99

x^2 + 3x + 5x + 15 - 99 = 0

x^2 + 8x - 84 = 0

x^2 + 14x - 6x - 84 = 0

x(x + 14) - 6(x + 84) = 0

(x + 14)(x - 6) = 0

x + 14 = 0 or x - 6 = 0

x = - 14 or x = 6

x cannot be negative so x = 6 cm

The length of the inner rectangle is 2x - 1 = 2×6 - 1 = 12 - 1 = 11 cm.

The width of inner rectangle is x = 6 cm. The area of the inner rectangle is

11×6 = 66 cm^2

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2 years ago
Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair
lubasha [3.4K]

Answer:

Additional <em>26</em> pendants are to be sold to make profit.

Step-by-step explanation:

Rent of booth at the craft fair = $200

Cost of material for each pendant = $7.80

Let Kelsey makes x number of pendants.

To calculate the total spending, we have to add the rent of booth at the craft fair and cost of material for x number of pendants.

Cost of material for x number of pendants = Cost of material for each pendant multiplied by number of pendants

Cost of material for x number of pendants = $7.80 \times x

So, total cost = $200 +  $7.80 \times x

Now, each pendant is sold at $13.50

So, total money made by selling  x pendants =  $13.50 \times x

For making profit, total money made must be greater than the total cost.

Therefore, the inequality becomes:

\bold{13.50 \times x  > 200+7.80\times x }

Let us solve the inequality now:

13.50x - 7.80x>200\\\Rightarrow 5.7x > 200\\\Rightarrow \bold{x > 35.08}

So, at least 36 pendants are to be sold to make a profit.

Additional 36-10  = <em>26</em> pendants are to be sold to make profit.

5 0
3 years ago
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marta [7]
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3 years ago
Jack's Lumber Yard receives 8,000 large trees each period that it subsequently processes into rough logs by stripping off the tr
nasty-shy [4]

Answer:

1. $3,960,000

2. $3,840,000

3. Sell the logs.

Step-by-step explanation:

The questions are incomplete:

<em>1. What is the contribution to income from selling the logs for log cabin construction?</em>

<em>2. What is the contribution to income from processing the logs into lumber?</em>

<em>3. Should Jack’s continue to sell the logs or process them further into lumber?</em>

1. The contribution income is the total income generated by the sales of the rough logs. Each one contributes with $495.

Contribution to income (log cabin construction) = $495*8,000 = $3,960,000

2. In this case, we have to calculate what is the profit after processing each board, then multypling by the amount of boards per log and lastly multiplying by the total amoun of logs.

Contribution to income (processed board) = $(0.75-0.15)*800*8000

Contribution to income (processed board) = $0.6*800*8000

Contribution to income (processed board) =  $480*8000 = $3,840,000

3. Jack should continue to sell logs for cabin construction because the profit per log is higher than for the processed board ($495/log versus $480/log).

4 0
2 years ago
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