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3 years ago

Simplify the sum. State any restrictions on the variables. (x-2)/(x+3) + (10x)/(x^(2)-9)

Mathematics

2 answers:

Trava [24]3 years ago

7 0

Answer:

(x+2)/(x-3)

Step-by-step explanation:

(x-2)/(x+3) + (10x)/(x²+9)

(x-2)(x-3)+10x/(x+3)(x-3)

(x²-3x-2x+6+10x)/(x+3)(x-3)

(x²+5x+6)/(x+3)(x-3)

(x+3)(x+2)/(x+3)(x-3)

Ans: (x+2)/(x-3)

nlexa [21]3 years ago

6 0

$\frac{x-2}{x+3} + \frac{10x}{ x^{2} -9}= \\ = \frac{x-2}{x+3}+ \frac{10x}{(x-3)(x+3)}=$
Restrictions are: x ≠ - 3, x ≠ 3.
$= \frac{(x+2)(x-3)+10x}{(x+3)(x-3)}= \\ \frac{ x^{2} -3x+2x-6+10x}{(x+3)(x-3)}= \\ = \frac{ x^{2} +9x-6}{(x+3)(x-3)}$

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You have the numbers 1-24 written on slips of paper. if you choose one slip at random, what is the probability that you will sel

zysi [14]

First find the numbers that are divisible by 3.
3, 6, 9, 12, 15, 18, 21, 24
There are 8 numbers divisible by 3 so there are 16 that are not divisible by 3.
P(not div by 3) = 16/24 = 2/3

3 0

2 years ago

PLEASE HELPPPPPP what is a semicirles permitier if the diameter is 4

trapecia [35]

The straight edge of the semicircle is 4 units, as this is this the diameter.

The circumference of the full circle is

C = pi*d = pi*4 = 4pi

which is the distance around the full circle (aka circle's perimeter)

So half of this is 4pi/2 = 2pi

Add this onto the straight edge length to get 4+2pi as the exact distance around the entire semicircle. This includes both straight and curved portions.

If you use the approximation pi = 3.14, then 4+2*pi = 4+2*3.14 = 10.28 is the approximate answer. To get a more accurate answer, use more decimal digits in pi.

---------------------------------------------------------

In summary,

exact answer in terms of pi is 4+2pi units

approximate answer is roughly 10.28 units (using pi = 3.14)

6 0

3 years ago

Last year at a certain high school, there were 125 boys on the honor roll and 80 girls on the honor roll. This year, the number

Elodia [21]

Answer:

6.8% decrease

Step-by-step explanation:

a drop of 8% means that only 92% of 125 boys remained on honor roll from last year; .92 x 125 = 115

a drop of 5% means that only 95% of 80 girls remained on honor roll from last year; .95 x 80 = 76

total number of students on honor roll last year = 125 + 80 = 205

total number of students on honor roll this year = 115 + 76 = 191

percent of change = (191 - 205) ÷ 205 = -14/205 = -.068

-.068, which represents a 6.8% decrease

3 0

2 years ago

Solve the inequalities 3x2 – 11x > 20

Bas_tet [7]

Answer:

x=-10

Step-by-step explanation:

3x · 3x=9x-11x>20

-2x>20

÷-2 -2

___________-

x=-10

Hope this helps ∞

5 0

2 years ago

AABC has vertices at A(12, 8), B(4,8), and C(4, 14).

borishaifa [10]

Answer:

Triangle ABC and triangle MNO are congruent. A Rotation is a single rigid transformation that maps the two congruent triangles.

Step-by-step explanation:

ΔABC has vertices at A(12, 8), B(4,8), and C(4, 14).

length of AB = √[(12-4)² + (8-8)²] = 8

length of AC = √[(12-4)² + (8-14)²] = 10

length of CB = √[(4-4)² + (8-14)²] = 6

ΔMNO has vertices at M(4, 16), N(4,8), and O(-2,8).

length of MN = √[(4-4)² + (16-8)²] = 8

length of MO = √[(4+2)² + (16-8)²] = 10

length of NO = √[(4+2)² + (8-8)²] = 6

Therefore:

AB ≅ MN

AC ≅ MO

CB ≅ NO

and ΔABC ≅ ΔMNO by SSS postulate.

In the picture attached, both triangles are shown. It can be seen that counterclockwise rotation of ΔABC around vertex B would map ΔABC into the ΔMNO.

3 0

3 years ago