Answer question 8,9 and 10 with full details.

Mathematics

1 answer:

Lelechka [254]2 years ago

4 0

Answer:

See Explanation

Step-by-step explanation:

8. (1)

Area of trapezoid = 1/2(sum of || sides) *perpendicular distance

36 =1/2(x+ y) * 6

36 = ((x + y)*3

36/3 = x + y

12 = x + y

x + y = 12.... (1)

8(2)

It is given that:

x = 2y....(2)

From equations (1) & (2)

2y + y = 12

3y = 12

y = 12/3

y = 4

From equation (2)

x = 2y = 2*4

x = 8

Area of square = 1 square m

Side of square = 1 m

Area of circle = 1 square m

$\pi {r}^{2} = 1 \\ {r}^{2} = \frac{1}{\pi} \\ r = \frac{1}{ \sqrt{\pi} } \\ c = 2\pi \: r \\ c = 2\pi \times \frac{1}{ \sqrt{\pi} } \\ c = 2 \sqrt{\pi} \\ c = 2 \sqrt{3.14} \\ c = 2 \times 1.77200451 \\ c = 3.54400902 \\ c = 3.544 \\ difference = 3.544 - 1 = 2.544 \\difference \approx \: 2.54$

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2 years ago

Which zero pair could be added to the function f(x)=x^2+12x+6 so that the function can be written in vertex form?

andrew11 [14]

f(x) = x² + 12x + 6 → y = x² + 12x + 6

Let us convert the standard form into vertex form.

1) Complete the squares. Isolate x² and x terms.
y - 6 = x² + 12x

2) Create the perfect square trinomial. Whatever number is added on one side must also be added on the other side.

y - 6 + 36 = x² + 12x + 36
y + 30 = (x + 6)²
y = (x + 6)² - 30 ← Vertex form

To check:

y = (x + 6) (x + 6) - 30
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The zero that could be added to the given function is 36, -36

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ratelena [41]

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Step-by-step explanation:

The formula for computing the sum of an infinite geometric series is

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