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3 years ago

If EF = x + 5, DC = 2x + 4, and AB = 2x + 2. Find EF.

Mathematics

1 answer:

bonufazy [111]3 years ago

3 0

Answer:

B *second one down.

Step-by-step explanation:

EF = 1/2(AB + CD)

x+5 = 1/2 (2x + 2 + 2x+4) Combine the like terms on the right.

x+5 = 1/2 (4x + 6) Remove the brackets.

x+5 = 1/2*4x + 1/2*6

x+5 = 2x + 3 Subtract x from both sides

5 = 2x-x + 3

5 = x + 3 Subtract 3 from both sides

5-3 = x

x = 2

EF = x + 5

EF = 2 + 5

EF = 7

The answer is B

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

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Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

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3 years ago

NEED HELP QUICK!!

mrs_skeptik [129]

Answer:

(x - 2)² + (y - 6)² = 49

Step-by-step explanation:

Equation of a circle formula: (x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius

Given, center = (2, 6) and radius = 7

Substitute this information in the equation of a circle formula.

⇒ Equation of the circle: (x - 2)² + (y - 6)² = 49

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Answer:

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Step-by-step explanation:

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3 years ago

If EF = x + 5, DC = 2x + 4, and AB = 2x + 2. Find EF.​

If EF = x + 5, DC = 2x + 4, and AB = 2x + 2. Find EF.