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Ivahew [28]
3 years ago
12

Work out the area of the trapezium ABDE. A В. 7.5 cm 2.5 cm С 5 cm E

Mathematics
1 answer:
baherus [9]3 years ago
7 0

Answer:

Area = 50 cm²

Step-by-step explanation:

Area of a trapezium ABDE = ½(a + b)h

where,

a = BD = 2.5 cm

b = AE = 7.5 cm

h = DE = ?

We need to find DE ti be able to calculate the area.

DE = CE - CD

DE = CE - 5

Since ∆ACE is similar to ∆BCD, therefore:

AE/BD = CE/CD

Plug in the values

7.5/2.5 = CE/5

Cross multiply

CE*2.5 = 7.5*5

CE*2.5 = 37.5

Divide both side any 2.5

CE = 37.5/2.5

CE = 15

Thus, DE = CE - 5 = 15 - 5

DE = 10

✅Area of trapezium = ½(BD + AE)DE

= ½(2.5 + 7.5)*10

= ½(10)10

= 50 cm²

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Shalnov [3]
(x - d) + x + (x + d) = 12 --> Create an equation using the first piece of information - "Three consecutive terms... have a sum of 12"

x - d + x + x + d = 12 --> Simplify the left side of this equation (d cancels out)

3x = 12 --> Divide both sides by 3

<u>x = 4
</u>


Use the value of x (x = 4) to find the value of d. To do this, set up another equation using the second piece of information.

(x - d) * (x + d) * x = - 80 --> "Three consecutive terms... have... a product of -80". Then, substitute the value of x (4) into this equation.

(4 - d) * (4 + d) * 4 = - 80 --> Multiply out the sets of brackets, the * 4 is dealt with afterwards

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4(16 - d²) = - 80 --> Multiply out these brackets by the 4

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<u>d = 6

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Now, find the values of the terms of the sequence by using substituting the values of x and d into the expressions given.
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<u />1. x - d = 4 - 6 = <u>- 2
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The three terms are - 2, 4, 10.
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5 0
3 years ago
Suppose you would like to save P9000 invested at 8% compounded quarterly for 5 years and 6 months. (Note: Round off your answer
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Answer:

a) 13913

b) 4913.82

Step-by-step explanation:

The compound interest formula is given by:

A(t) = P(1 + \frac{r}{n})^{nt}

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

In this question:

Investment of 9000, so P = 9000

Interest rate of 8%, so r = 0.08

Compounded quarterly, so n = 4

5 years and 6 months, that is, 5 years and half, so t = 5.5

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A(t) = P(1 + \frac{r}{n})^{nt}

A(5.5) = 9000(1 + \frac{0.08}{4})^{4*5.5} = 13913.82

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