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2 years ago

Plz help!!! I have a bad grade as it is and i don't want to drop it

Mathematics

1 answer:

Travka [436]2 years ago

5 0

$Answer: \\ The\: area\: of\: the\: shaded\: region\\ =Area\: of\: square - Area\: of\: circle\\ = {28}^{2} - 3.14 \times {14}^{2} = 784 - 615.44 = 168.56 \: {in}^{2}$

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Give the factors for the numerator [n] and denominator [d] after reducing.

Burka [1]

Answer:

The factors for the numerator [n] and denominator [d] after reducing will be:

$\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}$

Step-by-step explanation:

Given the expression

$\frac{x^2-25}{x^2-4x}\div \frac{2x^2+2x-40}{x^3-x}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{x^2-25}{x^2-4x}\times \frac{x^3-x}{2x^2+2x-40}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{\left(x^2-25\right)\left(x^3-x\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}$

$=\frac{\left(x^2-25\right)x\left(x^2-1\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}$

$\mathrm{Cancel\:the\:common\:factor:}\:x$

$=\frac{\left(x^2-25\right)\left(x^2-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}$

∵ As factor $\left(x^2-25\right)\left(x^2-1\right)=\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)$

so the expression becomes

$=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}$

∵ As factor $2\left(x-4\right)\left(x^2+x-20\right)=2\left(x-4\right)^2\left(x+5\right)$

so the expression becomes

$=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2\left(x+5\right)}$

$\mathrm{Cancel\:the\:common\:factor:}\:x+5$

$=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}$

Therefore, the factors for the numerator [n] and denominator [d] after reducing will be:

$\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}$

8 0

3 years ago

Solve x 2 + 6x - 5 = 0 by completing the square. Which equation is used in the process?

ella [17]

$x ^2 + 6x - 5 = 0\\\\ x^2+6x+9-14=0\\\\ (x+3)^2=14\\\\ x+3=\sqrt{14} \vee x+3=-\sqrt{14}\\\\ x=-3+\sqrt{14} \vee x=-3-\sqrt{14}$

8 0

3 years ago

The sum of two numbers is 18 . the difference of the two numbers is -2 find the numbers

saveliy_v [14]

A and b is a numbers
a + b = 18
a - b = -2

2a = 16
a = 8

8 + b = 18
b = 10

5 0

2 years ago

Diego is building a kitchen table and a coffee table the legs of a kitchen table must be twice the height of a coffee table and

Jobisdone [24]

X represents the height of the leg of the coffee table, plug it in and we'll see

4(2x) + 4(x)
= 4 (2*coffeetableleg) + 4 (coffeetableleg)
= 4 (kitchentableleg) + 4 (coffeetableleg)
= total length of kitchen table legs + total length of coffee table legs
= Total length measurement of table legs needed to build a kitchen table and a coffee table

meme

3 0

2 years ago

Andy constructed a triangle. Angle 1 and 2 are the same size and angle 3 has a measurement of 100 degrees. What is the measureme

Jlenok [28]

Answer:

Angle 1: 40

Angle 2: 40

Step-by-step explanation:

A triangle's angles will ALWAYS add up to 180 degrees total, therefore you can subtract 100 from 180 to find what the measure of A and B are combined.

180 - 100 = 80

So now we know Angles A and B add to 80 degrees, but individually, each is half of that, so both are 40 degrees.

3 0

2 years ago