What is the next term of the following sequence? 20, 10, 5, 21/2, ...

Mathematics

1 answer:

ycow [4]3 years ago

6 0

Answer:

1 $\frac{1}{4}$

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

10 ÷ 20 = 5 ÷ 10 = 2 $\frac{1}{2}$ ÷ 5 = $\frac{1}{2}$

Thus to obtain the next term in the sequence multiply the previous term by $\frac{1}{2}$

2 $\frac{1}{2}$ × $\frac{1}{2}$ = 1 $\frac{1}{4}$

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Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides. The area of EFGH is 35 square units. What i

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*see attachment for the figure described

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Step-by-step explanation:

==>Given the figure attached below, let where FH and EG intercepted be K.

Since FH are midpoints of parallel lines, KE = KG = x.

Given that the area of the kite EFGH = 35 square units, and we know the length of one of the diagonals = HF = KF + KH = 2 + 5 = 7, we can solve for x using the formula for the area of a kite.

Area of kite = ½ × d1 × d2

Where d1 = KH = 7

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THUS:

35 = ½ × 7 × 2x

35 = 1 × 7 × x

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Divide both sides by 7

35/7 = x

x = 5