PLEASE HELP!!
What two rational expressions sum to 3x-4/x^2+x-12 ? enter your answer so that each rational expression is in simplified form
Answers
The rational expression [tex]\frac{3x - 4}{x^2 + x - 12}[/tex] can be written as the sum of two partial fractions as [tex]\frac{3x}{(x+4)(x - 3)} - \frac{4}{(x+4)(x-3)}[/tex].
What is a partial fraction?For the decomposition of a rational equation, partial fractions are used. Each component of an algebraic expression that is divided into a sum of two or more rational expressions is referred to as a partial fraction.
Given, A rational expression [tex]\frac{3x - 4}{x^2 + x - 12}[/tex].
Now, x² + x - 12 can be written as
x² + x - 12.
= x² + 4x - 3x - 12.
= x(x + 4) - 3(x + 4).
= (x + 4)(x - 3).
Therefore, [tex]\frac{3x - 4}{x^2 + x - 12} = \frac{3x - 4}{(x + 4)(x - 3)}}[/tex].
[tex]\frac{3x - 4}{x^2 + x - 12} = \frac{3x}{(x+4)(x - 3)} - \frac{4}{(x+4)(x-3)}[/tex].
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Related Questions
Can someone help me please?and if you don’t know the answer don’t answer.
Answers
Answer:
a=3, b=3, c=5, d=2
Step-by-step explanation:
prime factorization of 600: [tex]2^{3}[/tex] × 3 × [tex]5^{2}[/tex]
The stock market drops 18 points.
Answers
or stocks, one point equals one dollar. So when you hear that a stock has lost or gained X number of points, it is the same as saying the stock has lost or gained X number of dollars.
Using points to describe share price gains, or declines, is generally done to describe short-term results, such as for the day or week.
Although one point always equals one dollar, the percentage value of a one-point movement can be different for two companies. Points refer only to the dollar amount that has changed, not the percentage. Two stocks can lose the same number of points but very different percentages.
Ok last one,
Find the x-intercept of the following equation. Simplify your answer.
4x + 13y = 6
x-intercept =
Answers
Answer:
x-intercept = 6/4 = 3/2 = 1.50000
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*x+13*y-(6)=0
Step 1: Equation of a Straight Line
Solve 4x+13y-6 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 4x+13y-6 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 6/13 so this line "cuts" the y axis at y= 0.46154
y-intercept = 6/13 = 0.46154
Calculate the X-Intercept :
When y = 0 the value of x is 3/2 Our line therefore "cuts" the x axis at x= 1.50000
x-intercept = 6/4 = 3/2 = 1.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.462 and for x=2.000, the value of y is -0.154. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.154 - 0.462 = -0.615 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -0.615/2.000 = -0.308
Geometric figure: Straight Line
Slope = -0.615/2.000 = -0.308
x-intercept = 6/4 = 3/2 = 1.50000
y-intercept = 6/13 = 0.46154
*PLEASE ANSWER IT'S CONFUSING!!!* *ILL GIVE BRAINLIEST*!!!!!
Riley and Layla are interested in forming a partnership but are concerned about the associated taxes. If the partnership agreement is set such that 80% of earnings go to Riley and 20% go to Layla, which of the following correctly describes how taxes will be paid on the earnings?(1 point)
a.) The partnership itself will pay the tax on each portion of earnings after they have been distributed to Riley and Layla.
b.) Riley and Layla will each pay personal income tax on half of the partnership's total earnings regardless of how the earnings are distributed.
c.) Riley and Layla will each pay personal income tax on the portion of earnings that is theirs.
d.) The partnership itself will pay the tax on total earnings before the earnings are distributed to Riley and Layla.
Answers
Answer:
c
Step-by-step explanation:
Answer:
c.) Riley and Layla will each pay personal income tax on the portion of earnings that is theirs.
Step-by-step explanation:
Take away -7x from {2y-2x}
Answers
Answer:
loading, please wait...
Step-by-step explanation:
Answer:
2y + 5x
Step-by-step explanation:
{ 2y - 2x } - ( - 7x )
= 2y - 2x + 7x
= 2y + 5x
HELP PLEASE QUICK I BEG I SUCK AT MATH
Answers
Answer:
y = 3/8x + 3
Step-by-step explanation:
Parallel lines have the same slope. In given equation, y = 3/8x + 5, the slope, m = 3/8. Therefore, the other line must also have the same slope.
Using the slope, m = 3/8, and the given point, (16, 9), substitute these values into the slope-intercept form:
y = mx + b
9 = 3/8(16) + b
9 = 6 + b
9 - 6 = 6 - 6 + b
3 = b (this is the y-intercept).
Now that we have our slope, m = 3/8, and the y-intercept, b = 3:
The equation of the line parallel to y = 3/8x + 5 is:
y = 3/8x + 3
What is the rate of change over the interval [-1,2] for f(x)= 4x +1
Answers
Answer:
4
Step-by-step explanation:
To find the average rate of change, we have to plug in the difference between the intervals with this equation: f(b) - (fa) / x₂ - x₁
Let f(a) = f(-1) = 4(-1) + 1
f(b) = f(2) = 4(2) + 1
x₂ = 2
x₁ = -1
[4(2) + 1 - (4(-1) + 1)] / [2 - (-1)]
[8 + 1 + 4 - 1] / [3]
12 / 3 = 4
Write the inverse, converse and contrapositive of the given conditional statement.
"If it is a leap year, then it is a year with 366 days.."
CONVERSE:
INVERSE:
CONTRAPOSITIVE:
Answers
Answer:
converse: if a year has 366 days then it is a leap year
inverse: if it is not a leap year then it is not a year with 366 days
contrapositive: if a year does not have 366 days then it is not a leap year
4a) The vertices of a triangle are P(-7, -4) Q(-7, -8) and R(3, -3). What are the
coordinates of P' after a reflection over y=x? Please type your answer as
coordinates (x,y) with no spaces.
Answers
Answer:
P' (-4 , -7)
Step-by-step explanation:
reflection over y=x, (x,y) -> (y,x)
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Answers
Hello.
Have a beautiful and joyful day ahead.
Answer:
Step-by-step explanation:
was there a actual question ?
have a good day
which list contians three multiples of 3
Answers
Answer:
Without any answers, I can't give you information. But if the numbers in the list would be able to be divided by 3, resulting in a whole number - no fractions or decimals - then it's considered a multiple of 3.
Step-by-step explanation:
Help solve this pleASE
Answers
Answer:
i have no idea 5
Step-by-step explanation:
i need help too please help
What is the domain and range of the following function
Answers
Answer:
DOMAIN: (INFINITY, -INFINITY)
RANGE: (-infinity, INFINITY)
Step-by-step explanation:
hm good luck cus I'm a savage
Answer:
domain: (–∞,∞) or all real numbers
range: (–∞,∞) or all real numbers
Step-by-step explanation:
domain is left to right (x-axis). looking at the graph, as you go from left to right, the x-values are infinitely getting more negative and positive.
range is bottom to top (y-axis). as you go from bottom to top, the y-values are infinitely getting more negative and positive.
please show your work thanks.
Answers
Answer:
I don't know how 2 answer
Step-by-step explanation:
It doesn't show the fraction
Solve for x..:…
willl give brainliest
Answers
Answer:
x = 6
Step-by-step explanation:
(6x + 2) and 38 are vertically opposite angles and are congruent, then
6x + 2 = 38 ( subtract 2 from both sides )
6x = 36 ( divide both sides by 6 )
x = 6
What is the base of the expression 11^12
A.3
B.11
C.12
D.21
Answers
Answer:
21
Step-by-step explanation:
cus i got it right on my test
Explain why:
2⁴ = 16.
Answers
Answer:
Well, 2 to the 4th power is just: 2 x 2 x 2 x 2 which when multiplied, you get 16.
Step-by-step explanation:
Say you multiply the first two 2's, you get 4, then you multiply the last two 2's,
You're left with 4x4 which is equal to 16.
Two similar cups are 3cm and 5cm deep,if the longer cup has 625cm of water.what is the volume of the smaller one
Answers
Answer:
81
Step-by-step explanation:
the 5 cm deep cup is 625 which is 5^4
that means that the 3cm deep cup should be 81 which is 3^4
7. Which of the following is the LCM of 24, 48, and 80? A. 220 C. 260 B. 240 D. 280
8. What are the first 3 common multiples of 3, 4, and 6? A. 12, 24, 30 C. 12, 24, 36 B. 12, 24, 32 D. 12, 24, 42
9. Which of these multiples is the LCM of 12, 16, and 24? A. 24 C. 54 B. 48 D. 60
10.Alfred Jun visits the library once every 2 days. Jayson visits it once every 3 days while Justine Louie once every 4 days. They all meet one day in the library. After how many days will they meet in the library again? A. 12 C. 20 B. 16 D. 24
Answers
[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]
7.) LCM of 24, 48, 80
24 = 2 × 2 × 2 × 3 48 = 2× 2 × 2 × 2 × 380 = 2 × 2× 2 × 2 × 5so, LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240
8.) first three Common multiples of 3, 4, and 6
LCM = 12
first three common multiples of given numbers is first three multiples of their LCM, that is
12 24 369. LCM of 12, 16 and 24
12 = 2 × 2 × 316 = 2 × 2 × 2 × 224 = 2 × 2 × 2 × 3LCM = 2 × 2 × 2 ×2 × 3 = 48
10. The day when the three of them will meet is LCM of the number of days they visit the library every week.
that is LCM of 2 , 3 and 4
that is 12
Answer:
7. 240
8. 12, 24, and 36
9. 48
10. 12
Step-by-step explanation:
7. Do the multiple of 24, 48, and 80. Then find the LEAST common number that all three numbers have in common. (Answer: 240)
8. Do the multiple of 3, 4, and 6. Then find 3 LEAST common numbers that all three numbers have in common. (Answer: 12, 24, and 36)
9. Do the multiple of 12, 16, and 24. Then find the LEAST common number that all three numbers have in common. (Answer: 48)
10. Do the multiple of 2, 3, and 4. Then find the LEAST common number that all three numbers have in common. (Answer: 12)
STEPS ON HOW TO SOLVE:
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3, 4, and 6. Write this prime number(2) on the left of the given numbers(3, 4, and 6), separated as per the ladder arrangement.
Step 2: If any of the given numbers (3, 4, 6) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 3, 4, and 6 is the product of all prime numbers on the left, i.e. LCM (3, 4, 6) by division method = 2 × 2 × 3 = 12.
5^n=0.2 need to find value of n
Answers
Answer:
Below
Step-by-step explanation:
5^n = 0.2
First write the number in exponential form with the base of 5 :
5^n = 5^-1
Because the bases are the same, we can set the exponents as equal :
x = -1
Hope this helps! Best of luck <3
What is the length of segment HK?
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's take length of HK = n
By using trigonometry,
[tex] \sin(30) = \dfrac{22}{n} [/tex][tex] \dfrac{1}{2} = \dfrac{22}{n} [/tex][tex]n = 44[/tex]Hence, value of HK = 44 cm
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sin30=\dfrac{JK}{HK}[/tex]
[tex]\\ \rm\Rrightarrow sin30=\dfrac{22}{HK}[/tex]
[tex]\\ \rm\Rrightarrow HK=\dfrac{22}{sin30}[/tex]
[tex]\\ \rm\Rrightarrow HK=44[/tex]
What is 93.195 written in expanded form?
Answers
Standard Form:
93.195
Expanded forms can be written like a sentence or stacked for readability as they are here.
Expanded Notation Form:
93.195 =
90
+ 3
+ 0.1
+ 0.09
+ 0.005
Expanded Factors Form:
93.195 =
9 × 10
+ 3 × 1
+ 1 × 0.1
+ 9 × 0.01
+ 5 × 0.001
Expanded Exponential Form:
93.195 =
9 × 101
+ 3 × 100
+ 1 × 10-1
+ 9 × 10-2
+ 5 × 10-3
Word Form:
93.195 =
ninety-three and one hundred ninety-five thousandths
How to check 20p+75=35p+30
Answers
[tex]20p+75=35p+30[/tex]
Step 1: Subtract [tex]20p[/tex] from both [tex]p[/tex] sides
[tex]\:\:\:\:20p+75=35p+30\\-20\:\:\:\:\:\:\:\:\:\:\:\:-20[/tex]
20 - 20 = 0, so it is canceled out. 35 - 20 = 15, don't forget the [tex]p[/tex]!
[tex]75=15p+30[/tex]
Step 2: Subtract 30 from both sides
[tex]\:\:\:\:75=15p+30\\-30\:\:\:\:\:\:\:\:\:\:\:\:-30[/tex]
30 - 30 = 0, so it is canceled out. 75 - 30 = 45.
[tex]45=15p[/tex]
Step 3: Divide both sides by 15
[tex]\frac{45}{15} =\frac{15p}{15}[/tex]
15 ÷ 15 cancels out. 45 ÷ 15 = 3.
[tex]20p+75=35p+30\quad :\quad \boxed {\bold {p=3}}[/tex]
Answer:
20p+75=35p+30
Step-by-step explanation:
A line contains the points(−26, −37) and(−32, −61).
What is the slope of the line in simplified form?
Question 1 options:
4
-4
14
−14
Answers
Step-by-step explanation:
The slope of the line = (y₂ - y₁) ÷ (x₂ - x₁)
= (-37 - (-61)) ÷ (-26 - (-32))
= 24 ÷ 6
= 4
I need help please and thank you
Answers
your
Step-by-step explanation:
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WHOEVER GETS THIS RIGHT WILL HAVE 60+ POINTS (MATH) NO BAD ANSWERS ORELSE REPORTING
Answers
9514 1404 393
Answer:
a. 2x +y = 10; 2x +3y = 22
b. 6 minutes
Step-by-step explanation:
a) The problem statement tells you that ...
x = minutes around the block
y = minutes around the park
2x +y = 10 . . . . twice around the block and once around the park: 10 min
2x +3y = 22 . . . twice around the block and 3 times around the park: 22 min
__
b) Subtracting the first equation from the second gives ...
(2x +3y) -(2x +y) = (22) -(10)
2y = 12 . . . . . . . . simplify
y = 6 . . . . . . . . . divide by 2
It takes you 6 minutes to jog around the park.
Answer:
Part A) The system of equations is
[tex]2x+y=10[/tex]
[tex]2x+3y=22[/tex]
Part B) The number of minutes it takes you to jog around the park is [tex]6[/tex] mins
Explanation:
Part A) Write a system of linear equations
Let [tex]x[/tex] ----> the number of minutes it takes you to jog around the block
Let [tex]y[/tex] ----> the number of minutes it takes you to jog around the park
we know that [tex]2x+y=10[/tex] ----> equation A
and [tex]2x+3y=22[/tex] ----> equation B
Part B) How long does it take you to jog around the park?
Multiply equation A by [tex]-1[/tex] both sides
[tex]-1(2x+y)=-10[/tex] ----> [tex]-2x-y=-10[/tex] ----> equation C
Adds equation B and equation C
[tex]2x+3y=22[/tex]
[tex]-2x-y=-10[/tex]
____________
[tex]3y-y=22-10[/tex]
[tex]2y=12[/tex]
[tex]y=6[/tex] minutes
Find the value of [tex]x[/tex]
[tex]2x+(6)=10[/tex]
[tex]2x=10-6[/tex]
[tex]x=4/2=2[/tex] minutes
Credit:
(This answer was originally made by calculista. All credit goes to them.)
In a piggy bank on his dresser, Tom has a total of $2.85 in pennies and quarters. If
the number of pennies is 5 more than three times the number of quarters, how
many pennies and quarters does he have in his piggy bank?
Answers
3Y+5=X
0.01X+0.25Y=2.85
X=35 Y=10
35 Pennies and 10 Quarters
Number of pennies in piggy bank will be 35.
Number of quarters in piggy bank will be 10.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Total cost in piggy bank with pennies and quarters = $2.85
And, The number of pennies is 5 more than three times the number of quarters.
Let Number of quarters = x
And, Number of pennies = y
= 5 + 3x
Since, Total cost in piggy bank with pennies and quarters = $2.85
So, we can formulate;
0.25x + 0.01y = $2.85
Substitute the value of y as;
0.25x + 0.01(5 + 3x) = 2.85
0.25x + 0.05 + 0.03x = 2.85
0.28x + 0.05 = 2.85
x = 10
And, y = 5 + 3x = 5 + 3 × 10 = 35
Thus,
Number of pennies in piggy bank will be 35.
Number of quarters in piggy bank will be 10.
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Find the unit rate . Round to the nearest hundredth if necessary .
$420 for 15 tickets
A. $28 per ticket
B. $ 0.04 per ticket
C. $ 405 per ticket
D. $ 840 per 30 ticket
Answers
28x15 is $420
In a class, 4/7 of the total number of students are boys. If 2/5 of the boys or 8 boys are wearing spectacles, calculate the number of girls in the class.
Answers
Answer:
15
Step-by-step explanation:
let total num of boys be X.
then,2/5 of X = 8
2 ×x = 40
X = 20
Now, let the total num of students be y,then we get,
4/7 of y = 20
4 × y = 140
y = 35
similarly, total num of girls = total num of students - total num of boys
= 35 - 20
= 15 ans
Please help with this math problem! Will give brainliest! :)
Answers
Answer:
9
Step-by-step explanation:
All triangles (3 sided polygons) have angles added up to 180, so we can do the following:
(7x-1) + (7x+8) + (5x+2) = 180° - equation
7x-1 + 7x+8 + 5x+2 = 180° - "distribute"
19x - 1 + 8 + 2 = 180° - combine the x terms
19x + 9 = 180° - combine the integer terms
19x = 171 - subtract 9 form both sides
x = 9 - divide both sides by 19