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

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

Need 45 ! compare the rates at which each of the three students read: which student read at a fa

Answer from: Quest

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

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