Mathematics, 15.12.2020 08:10 vazquezemmy8

Please solve these two questions

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Answer from: gottapass62

Question 4

Simplifying the expression $\frac{x^2-10x-24}{x^2-3x-108}$ we get $\frac{x-2}{x-9}$ and x≠9 or x≠2

Option D is correct option.

Question 5

Simplifying the expression: $\frac{8x-16}{x^2-13x+22}$ we get $\frac{8}{x-11}, x\neq 11$

Option C is correct.

Step-by-step explanation:

Question 4

Simplify completely $\frac{x^2-10x-24}{x^2-3x-108}$

For simplifying the above expression we have to find find factors of numerators and denominators

First finding factors of numerator x^2-10x-24

$x^2-10x-24\\ = x^2-12x+2x-24 \\= x(x-12)+2(x-12) \\=(x-12)(x-2)$

So, the factors of x^2-10x-24 are (x-12)(x-2)

Now finding factors of denominator x^2-3x-108

$x^2-3x-108\\=x^2-12x+9x-108\\=x(x-12)+9(x-12)\\=(x+9)(x-12)$

So, factors of x^2-3x-108 are (x-12)(x+9)

Now, replacing numerators and denominators with their factors

$\frac{x^2-10x-24}{x^2-3x-108}\\=\frac{(x-12)(x-2)}{(x+9)(x-12)}\\Cancelling\:(x-12) \: from\:numerator\:and\:denominator\\=\frac{x-2}{x-9}$

so, simplifying the expression $\frac{x^2-10x-24}{x^2-3x-108}$ we get $\frac{x-2}{x-9}$ and x≠9 or x≠2

Option D is correct option.

Question No 5

Simplify the expression: $\frac{8x-16}{x^2-13x+22}$

For simplifying the above expression we have to find find factors of numerators and denominators

First finding factors of numerator 8x-16

Taking 8 common:

$8x-16\\=8(x-2)$

So, factors of 8x-16 are 8(x-2)

Now finding factors of denominator : x^2-13x+22

$x^2-13x+22\\=x^2-11x-2x+22\\=x(x-11)-2(x-11)\\=(x-2)(x-11)$

Now, replacing numerators and denominators with their factors

$\frac{8x-16}{x^2-13x+22}\\=\frac{8(x-2)}{(x-11)(x-2)}\\Cancelling\:(x-2)\\=\frac{8}{x-11}, x\neq 11$

So, simplifying the expression: $\frac{8x-16}{x^2-13x+22}$ we get $\frac{8}{x-11}, x\neq 11$

Option C is correct.

Answer from: Quest

Answer: 10pi

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

Find the length of ac express your answer in terms of pi

Answer from: Quest

none cuz there are no "following statements" regarding the question

step-by-step explanation:

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