Answers
The only factoring you need to do is already done for you:
x² + x - 12 = (x + 4) (x - 3)
What you're asked to do is decompose
(3x - 4) / (x² + x - 12)
into partial fractions, i.e. find a and b such that
(3x - 4) / (x² + x - 12) = a / (x + 4) + b / (x - 3)
Multiply both sides by x² + x - 12 :
3x - 4 = a (x - 3) + b (x + 4)
3x - 4 = (a + b) x + (-3a + 4b)
So we have
a + b = 3
-3a + 4b = -4
and solving this system gives
a = 16/7 and b = 5/7
so you should submit the numbers in bold:
(3x - 4) / (x² + x - 12) = 16 / (7 (x + 4)) + 5 / (7 (x - 3))
Related Questions
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 sxs 3?
es)
A)
-2
B)
-3
D)
-6
Answers
Answer: -3
Step-by-step explanation: just multiply
The best estimate of the average rate of change for the function graphed over the interval 1 ≤ x ≤ 3 is 3.
What is Average Rate of Change of a Function?Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.
The interval given is 1 ≤ x ≤ 3.
The graph of the function is given below.
It can be clearly seen that,
The y value corresponding to x = 1 is y = f(1) = 2.
So one point on the graph is (1, 2).
The y value corresponding to x = 3 is y = f(3) = 8.
So the other point on the graph is (3, 8).
Average rate of change over 1 ≤ x ≤ 3 = [f(3) - f(1)] / [3 - 1]
= [8 - 2] / [2]
= 6/2
= 3
Hence the best estimate for the average rate of change of function over the interval 1 ≤ x ≤ 3 is 3.
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Which equation best represents the line?
Oy = 3x + 3
Oy=-x-8
O y = -x + 3
2
x+
Oy = 3x +
2
Answers
Answer:
Y=(1/2)x + 3
Step-by-step explanation:
The equation of the line is y = (1/2)x + 3.
We have,
The equation of a line is written as:
y = mx + c
Where m is the slope and c is the y-intercept.
Now,
From the line,
We have the following coordinates:
(2, 4) and (4, 5)
Now,
Slope.
m = (5 - 4) / (4 - 2) = 1/2
And,
(2, 4) = (x, y)
Substituting.
y = mx + c
4 = (1/2) x 2 + c
4 = 1 + c
c = 4 - 1
c = 3
Now,
y = (1/2)x + 3
Thus,
The equation of the line is y = (1/2)x + 3.
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1. (03.01) Factor completely. 10x4y2 + 4x3y – 3x2y2. (1 point) THANK YOU
Answers
Now the way you wrote it out was semi-confusing, however after looking at it for a second I believe I figured out the actual way it was intended to be written out as.
So,
10x4y^2+4x3y-3x2y^2
40xy^2+12xy-6xy^2
40xy^2-6xy^2+12xy
34xy^2+12xy
2xy(17y+6)
Hope this helps.
Answer:
x²y (10x²y + 4x - 3y)
Step-by-step explanation:
Factorise xy out first.
10[tex]x^{4}[/tex]y² + 4x³y - 3x²y² = xy (10x³y + 4x² - 3xy)
Then factorise another x out.
xy (10x³y + 4x² - 3xy) = x²y (10x²y + 4x - 3y)
Find the sum. (w+8) + 2(w +9)
Answers
Final answer: 3w + 17
I’ll mark you brainlist
Answers
Answer:
negative
Step-by-step explanation:
Answer:
Negative
Step-by-step explanation:
The line is going down, which means that it is decreasing...which makes it negative.
Hope this helps! :)
Patty has 817 marbles. She gave away 529 of her marbles. How many marbles doe she have left? 312 marbles, 298 marbles, or 288 marbles.
Answers
Answer:
288 because you just subtract 529 from 817
Step-by-step explanation:
Please help!!! Express the function graphed on the axes below as a piecewise function
Answers
9514 1404 393
Answer:
[tex]f(x)=\left\{\begin{array}{rl}-x-1,&\text{for $-6\le x<2$}}\\-\dfrac{1}{2}x-4,&\text{for $2<x<6$}\end{array}\right.[/tex]
Step-by-step explanation:
The upper piece of the graph is defined on the interval -6 ≤ x < 2. It has a slope of -1 and a y-intercept of -1, so its equation is y = -x-1.
The lower piece of the graph is defined on the interval 2 < x < 6. It has a slope of -1/2 and would cross the y-axis at -4 if it were extended. Its equation is ...
y = -1/2x -4
The two pieces together give the function ...
[tex]f(x)=\left\{\begin{array}{rl}-x-1,&\text{for $-6\le x<2$}}\\-\dfrac{1}{2}x-4,&\text{for $2<x<6$}\end{array}\right.[/tex]
Will mark brainliest who ever answers first !!!
Please help
Answers
I believe the answer is x=-2
Skye ran rlaps today at soccer practice. Nadine ran five fewer laps than Skye. If Nadine ran eight laps at practice, which of the following equations could be used to find how many laps Skye ran?
r-5= 8
r+5 = 8
r=8-5
-5r=8
Answers
Answer:
A. r - 5 = 8
Step-by-step explanation:
If Nadine ran 5 fewer laps than Skye, and Nadine ran eight laps, "r" equals 13.please answer the question. Anderson deposits $700 into a savings account that pays a simple interest of 2% per year. Which of the following would be the total amount in her savings account at the end of 10 years?
Answers
Answer:
840
Step-by-step explanation:
2% of 700 is 14. Multiply 14 by 10 years, and then add that result (140) to the original amount
SCHOOL LUNCH In 2015, Ed spent $800 buying lunches. In 2017, he spent $300 buying lunches. What was the rate of change from 2015 to
2017? Plz help asap plz
Answers
Explanation:I took the test
The rate of change from 2015 to 2017 is -$250 per year.
Given that,
In 2015, Ed spent $800In 2017, Ed spent $300We need to find the rate of change.According to the scenario, computation of the given data are as follows,
Total change = $300 - $800
= -$500
Total years from 2015 to 2017 = 2 years
So rate of change = -$500 [tex]\div[/tex] 2
= - $250
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please show work
8) 3n+1 +8n2 – 8n – 7
9. given the function: f(x) =3x-7, find f(-2)
Answers
Answer:
D and A
Step-by-step explanation:
8. 1+8n^2-5n-7
8n^2-5n-6
9. -6-7
-13
How do I find x in these equations
Answers
Answers:
Problem 9) x = 1Problem 10) x = 3Problem 11) x = 12Problem 12) x = 12==============================================
Explanation:
For problems 9 through 12, we'll use the same set of steps. Recall that any parallelogram has the property that the adjacent angles are supplementary. This means close by angles add to 180. Each of the four diagrams show pairs of adjacent angles.
------------------
In problem 9, we have the following steps
(79x-1) + (102) = 180
79x + 101 = 180
79x = 180-101
79x = 79
x = 79/79
x = 1
------------------
Problem 10 is the same idea
(85) + (30x+5) = 180
30x+90 = 180
30x = 180-90
30x = 90
x = 90/30
x = 3
------------------
Problem 11
(55)+(9x+17) = 180
9x+72 = 180
9x = 180-72
9x = 108
x = 108/9
x = 12
------------------
Problem 12
(3x+12)+(132) = 180
3x+144 = 180
3x = 180-144
3x = 36
x = 36/3
x = 12
Answer:
9. X = 1
10. X = 3
11. X = 12
12. X = 12
Step-by-step explanation:
9.
1) 79x - 1 + 102 = 180
2) 79x + 101 = 180
3) Subtract 101 from both sides
4) 79x = 79
5) x = 1
10.
1) 85 + 30x + 5 = 180
2) 30x + 90 = 180
3) Subtract 90 from both sides
4) 30x = 90
5) x = 3
11.
1) 55 + 9x + 17 = 180
2) 9x + 72 = 180
3) Subtract 72 from both sides
3) 9x = 108
4) X = 12
12.
1) 3x + 12 + 132 = 180
2) 3x + 144 = 180
3) Subtract 144 from both sides
4) 3x = 36
5) x = 12
All answers have been checked by plugging the X back into the equation.
Please help me with this! I will appreciate the help :)
Answers
Answer:
D
Step-by-step explanation:
I'm pretty sure it's D
Help me out plssss!!!!
Answers
Answer: m=6.2t, 148.8 miles
Step-by-step explanation:
to figure out the equation we do 93/15=6.2 and we make it into a equation which is m=6.2t. since we know the butterfly travels 6.2 per hour we do 6.2 x 24 = 148.8
sorry if it's wrong
what is the value of X with f (x) =4
Answers
Answer:
I can find all the x-values in the domain of the function f(x)=4:
Domain = (−∞, ∞), {x | x∈R}
Here’s the range if you need it:
Range: {4}
Hope this helps! :)
The answer is Range: {4} or, x is a member of the real numbers and that it can be anything from negative infinity to positive infinity.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
Here, we have,
f (x) =4
now,
we can find all the x-values in the domain of the function f(x)=4:
Domain = (−∞, ∞), {x | x∈R}
Here’s the range if you need it:
Range: {4}
There are x’s in the equation.
It’s actually all numbers are x’s because anything you put into the function f(x)=4, y will always equal 4.
So the value of x in f(x)=4 is all numbers.
To be more specific, all real numbers.
That’s why I put (−∞, ∞), {x | x∈R} because x is a member of the real numbers and that it can be anything from negative infinity to positive infinity.
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Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32 ounces. The number of pints he canned is represented by p, and the number of quarts he canned is represented by q. Which equation models the scenario if Chin canned a total of 1,280 ounces? 1280 plus 16 p equals 32 q 1280 plus 32 q equals 16 p 32 q minus 16 p equals 1280 16 p plus 32 q equals 1280
Answers
Answer:
16 p plus 32 q equals 1280
16p + 32q = 1,280
Step-by-step explanation:
A pint = 16 ounces
A quart = 32 ounces
p = number of pints he canned
q = number of quarts he canned
if Chin canned a total of 1,280 ounces?
Total ounces canned = 1,280
Equation:
p × 16 ounces + q × 32 ounces = 1,280
16p + 32q = 1,280
The options:
1280 plus 16 p equals 32 q
1,280 + 16p = 32q
1280 plus 32 q equals 16 p
1,280 + 32q = 16p
32 q minus 16 p equals 1280
32q - 16p = 1,280
16 p plus 32 q equals 1280
16p + 32q = 1,280
The correct answer is
16 p plus 32 q equals 1280
16p + 32q = 1,280
Answer:
16p+32q=1280
Step-by-step explanation:
edge
rewrite as difference of squares (2x+5)(2x-5)
Answers
I got u homie wherever in the world u r
Jake has 3 1/2 hours before bedtime. He must spend 2 hours doing homework. The rest of his time will be spent doing puzzles. It takes jake 1/2 hour to complete each puzzle. Which equation models the number of puzzles, p, jake can complete before bedtime?
Answers
Explanation: p is number of puzzles
Answer:
3 1/2 puzzles
Step-by-step explanation:
Plz help meeeeeeeeee
Answers
Answer:
Part 4
4 | a. When Peter wrote: I = 275(.8)(12), he wrote the rate of 8% as 0.80 instead of 0.08.
4 | b. The correct interest is $264.
Part 5
5 | a. Isabella multiplied 3000*0.04*6 incorrectly, she probably forgot that she multiplied 3000 into the expression.
5 | b. The correct interest is $720.
Evaluate the expression when a=3
2a=
Answers
Answer:
6 is ur answer hope it help u
lol :)
☃️✌
Merry christmas~
I need these answers please please please I need it ASAP
Answers
Answer:
1:101
2:15
3:11
4:56
Source:trust me bro
1. Stacy's mom is baking treats for Stacy's birthday party. She has 9 eggs to
use for this purpose. A batch of cookies requires one egg and a batch of
brownies requires 2 eggs. How many of each treat can Stacy's mom
bake?
Part A: List three possible combinations of cookies and brownies Stacy's
mom could make for the party.
Part B: Write an inequality to represent the situation.
Part C: Graph the inequality and shade the area where the solutions are.
Answers
here is the graph
i learned this in math lol lol
Use the expression to complete the statements. (0.5)10 (0.5)10 is the . (0.5) is the of (0.5)10. 10 is the of (0.5)10. A power is another way to write .
Answers
Question:
Use the expression to complete the statements.
[tex](0.5)^{10\\[/tex]
________ is the power .
(0.5) is the ________
A ______ is another way to write
Answer:
0.5 is the base
10 is the power
[tex](0.5)^{10\\ = (\frac{1}{2})^{10}[/tex] -- another way to write
Step-by-step explanation:
Given
[tex](0.5)^{10\\[/tex]
Required
Fill ion the gaps
[tex](0.5)^{10\\[/tex] is pronounced as; 0.5 raise to the power of 10
From the above statement, we can deduce the following:
0.5 is the base
10 is the power
Lastly, another way to write [tex](0.5)^{10\\[/tex]
Express 0.5 as a fraction
[tex](\frac{5}{10})^{10}[/tex]
Simplify the fraction
[tex](\frac{5/5}{10/5})^{10}[/tex]
[tex](\frac{1}{2})^{10}[/tex]
Hence:
[tex](0.5)^{10\\ = (\frac{1}{2})^{10}[/tex]
Last year 858 people attended the Middleton County Fair. This year 1,635 people attended. What was the percent increase from last year to this year? (Round to the nearest percent)
Answers
Answer:
91%
Step-by-step explanation:
The first step is to calculate the increase
= 1635-858
= 777
Therefore the percent increase can be calculated as follows
= 777/858 × 100
= 0.905× 100
= 90.5 %
= 91%
Hence the percentage increase is 91%
i need help quick! (number 7, NOT 8!)
Answers
Answer:
(-6, 18)
Step-by-step explanation:
Help with the his question
Answers
Answer:
The variable is b books and the equation is gonna be 12b + 16 = 120
Step-by-step explanation:
A recipe for a batch of muffins calls for cup of sugar, cup of flour, and cup of milk. How many total cups of sugar, flour, and milk will be needed for three batches of muffins?
Answers
Answer:
9 total cups. 3 cups of sugar. 3 cups of flour, 3 cups of milk
Step-by-step explanation:
Fiona can make 8 cards in 12 hour. She divides to find the number of cards she can make per hour, but she makes a mistake. Three of these reasons explain why her answer must be wrong. Which does NOT?
Answers
Answer:
2/3 card per hour
Step-by-step explanation:
The correct calculation is given below
The number of cards she can make per hour is :
12 hours = 8 cards
1 hour = x cards
Cross Multiply
12 hours × x cards = 8 cards × 1 hour
x cards = 8 cards × 1 hour/12 hours
x cards = 2/3 card
She can make 2/3 card per hour
Answer:
a
not C B D A
Step-by-step explanation:
Help me pls ASAP thank you
Answers
Answer:
3rd option
Step-by-step explanation:
The input(x) does not repeat