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2 years ago

In parallelogram ABCD, AE=x^2-6 and CE=5x what is the value of x ? What is AC?

Mathematics

1 answer:

lutik1710 [3]2 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, hence

AE = EC, that is

x² - 6 = 5x ( subtract 5x from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 5

However x > 0 ⇒ x = 6

AC = x² - 6 + 5x = 6² - 6 + 5(6) = 36 - 6 + 30 = 60

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$\qquad\qquad\huge\underline{{\sf Answer}}♨$

Here's the solution ~

As we know, we can calculate the circumference of a circle in terms of its diameter as :

$\qquad \sf \dashrightarrow \:c = \pi d$

where, c = circumference and d = diameter

And also, circumference of circle is terms of radius (r) is :

$\qquad \sf \dashrightarrow \:c = 2\pi r$

Now, let's move on to questions ~

<h3>First </h3>

$\qquad \sf \dashrightarrow \:3.14 \times 5.9$

$\qquad \sf \dashrightarrow \: \approx18.53 \: ft$

<h3 />

・．━━━━━━━†━━━━━━━━━．・

<h3>Second</h3><h3 /><h3 /><h3 /><h3> $\qquad \sf \dashrightarrow \:3.14 \times 3.2$ </h3>

$\qquad \sf \dashrightarrow \: \approx10.048 \: ft$

・．━━━━━━━†━━━━━━━━━．・

<h3>Third</h3>

$\qquad \sf \dashrightarrow \:3.14 \times 6.1$

$\qquad \sf \dashrightarrow \: \approx19.15 \: ft$

・．━━━━━━━†━━━━━━━━━．・

<h3>Fourth</h3>

$\qquad \sf \dashrightarrow \:2×3.14 \times 3.7$

$\qquad \sf \dashrightarrow \: \approx2×11.62 \: m$

$\qquad \sf \dashrightarrow \: \approx23.24 \: m$

・．━━━━━━━†━━━━━━━━━．・

<h3>Fifth </h3>

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$\qquad \sf \dashrightarrow \: \approx38.94 \: m$

・．━━━━━━━†━━━━━━━━━．・

<h3>Sixth</h3>

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$\qquad \sf \dashrightarrow \: \approx \: 32.02m$

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So, we have:

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