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alisha [4.7K]
3 years ago
7

12) Add the fractions, and simplify if possible. (y+7)/(y^2-y-12) - 2/(y^2-9)

Mathematics
1 answer:
Tanzania [10]3 years ago
5 0

Simplified form of \frac{(y+7)}{(y^2-y-12)}-\frac{2}{(y^2-9)} is \frac{y^2+2y-13}{(y-4)(y-3)(y+3)}

Step-by-step explanation:

Add and simplify the fractions:

\frac{(y+7)}{(y^2-y-12)}-\frac{2}{(y^2-9)}

For Solving, First factor out the denominators:

Factoring: y^2-y-12

y^2-y-12\\=y^2-4y+3y-12\\=y(y-4)+3(y-4)\\=(y-4)(y-3)

Factoring: y^2-9

y^2-9\\=(y)^2-(3)^2\\=(y-3)(y+3)

Putting factors in the denominators:

\frac{(y+7)}{(y-4)(y-3)}-\frac{2}{(y+3)(y-3)}

Now taking LCM of (y-4)(y-3) and (y+3)(y-3): (y-4)(y-3)(y+3)

\frac{(y+7)*(y-3)-2((y-4))}{(y-4)(y-3)(y+3)}\\=\frac{y^2-3y+7y-21-2y+8}{(y-4)(y-3)(y+3)}\\=\frac{y^2+2y-13}{(y-4)(y-3)(y+3)}

So, Simplified form of \frac{(y+7)}{(y^2-y-12)}-\frac{2}{(y^2-9)} is \frac{y^2+2y-13}{(y-4)(y-3)(y+3)}

Keywords: Adding the fractions

Learn more about Adding the fractions at:

  • brainly.com/question/2456302
  • brainly.com/question/1648978
  • brainly.com/question/1757979

#learnwithBrainly

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In 2009 the number of vehicle sales in the United States was 10,002 thousand and in 2013 it was 17,884 thousand.a. [3 pts] Deter
anygoal [31]

Answer:

1970.5 thousand

Step-by-step explanation:

Given

Vehicle sales in 2009 = 10,002 thousand

Vehicle sales in 2013 = 17,884 thousand

Required

Determine the average rate of change;

From the given parameters, it can be seen that the number of vehicles is a function of year

Let x represent the years and y represent the number of vehicles;

Such that;

x_1 = 2009;\ y_1 = 10,002

x_2 = 2013;\ y_2 = 17,884

The rate of change is calculate as follows;

m = \frac{y_1 - y_2}{x_1 - x_2}

m = \frac{10002 - 17884}{2009 - 2013}

m = \frac{-7882}{-4}

m = \frac{-7882}{-4}

m = 1970.5

Hence, the average rate of change is 1970.5 thousand

6 0
3 years ago
Evelyn took out a car loan for $16125 that has 0% APR for the first 14 months and will be paid off with monthly payments over 6
never [62]
72 months=6 years
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14 months 0% so evelyn be charged interest after 14 months

72-14=58 months evelyn be charged interest?
5 0
3 years ago
Read 2 more answers
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klio [65]

Answer:

y = -1/4x -2

Step-by-step explanation:

the perpendicular slope would be -1/4

2 = -1/4 (-16) + b

b = -2

the equation should be y = -1/4x -2

None of the answers you typed could be correct.

5 0
3 years ago
Urgent help required with right triangle trig
mixas84 [53]

To find the area of a square with it's diagonal, there's actually a formula = (1/2)d², but here's how to do it if you don't have the formula:


The diagonal <em>c</em> separates the square into two of the same triangles. Therefore, we can apply Pythagorean Theorem


a²+b²=c² ← Since this is a square, a=b is a must

a²+a²=c² ← Combine like terms, and plug 26 in for c

2a²= 26² ← 26²=676, then divide 2 on both sides

a²= 676/2

a²=338 ← We can just stop here! Since <em>a </em>is a side of the square, therefore the area of a square = a²


Answer: 338 units²


6 0
3 years ago
1) -24, -4, 16, 36, ...<br> Find a23
viktelen [127]

We're given the Arithmetic Progression <em>-24, -4, 16, 36 ...</em> .

We know that a term in an AP is generally represented as:

\bf a_n\ =\ a\ +\ (n\ -\ 1)d

where,

  • a = the first term in the sequence
  • n = the number of the term/number of terms
  • d = difference between two terms

We need to find \sf a_2_3.

From the given progression, we have:

  • a = -24
  • n = 23
  • d = (-24 - (-4) = -20

Using these in the formula,

\sf a_2_3\ =\ a\ +\ (n\ -\ 1)d\\\\\\a_2_3\ =\ -24\ +\ (23\ -\ 1)\ \times\ (-20)\\\\\\a_2_3\ =\ -24\ +\ 22\ \times (-20)\\\\\\a_2_3\ =\ -24\ -\ 440\\\\\\\bf a_2_3\ =\ -464

Therefore, the 23rd term in the AP is -464.

Hope it helps. :)

7 0
3 years ago
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