Mathematics, 08.07.2019 18:30 cathyfrawley

Perform the following operations and prove closure. show your work.
(x/x+3) + (x+2/x+5)

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Answer from: mystaxkkks

$\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}$

Step-by-step explanation:

We need to sum the following two expressions:

$\frac{x}{x+3} + \frac{x+2}{x+5}$

$\frac{x(x+5) + (x+2)(x+3)}{(x+3)(x+5)}$

expanding the polynomial in the numerator:

$\frac{2x^{2} + 10x + 6}{(x+3)(x+5)}$

$\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}$

This is the most simplified form we can get:

$\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}$

Answer from: shelbylynn17

$\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}$

Step-by-step explanation:

The given expression is $\frac{x}{x+3}+\frac{x+2}{x+5}$

We have to simplify the given expression

$\frac{x}{x+3}+\frac{x+2}{x+5}$

= $\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}$ [Distributive law]

= $\frac{x^{2}+5x+x^{2}+3x+2x+6}{(x+3)(x+5)}$

= $\frac{2x^{2}+10x+6}{(x+3)(x+5)}$

= $\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}$

Finally the simplified form of the given expression is $\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}$

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6 = 0.00000180

1.80 x 10-4 = 0.000180 (bigger, or "less small", than the former one)

1.8 x 10-2 = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

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Perform the following operations and prove closure. show your work.
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