Determine what must be multiplied so that the expression below will have a common denominator. Use the backslash / to type in a fraction.
Answers
Answer:
Multiply the first fraction by [tex]\frac{x+4}{x+4}[/tex]
Multiply the second fraction by [tex]\frac{x-4}{x-4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}[/tex]
Required
Make the denominator equal
[tex]\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}[/tex]
Factorize the denominator
[tex]\frac{4}{x^2 - 4^2} + \frac{3}{x^2 + 4x + 4x+ 16}[/tex]
[tex]\frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)}[/tex]
Multiply the first fraction by [tex]\frac{x+4}{x+4}[/tex]
Multiply the second fraction by [tex]\frac{x-4}{x-4}[/tex]
[tex]\frac{x+4}{x+4} * \frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)} * \frac{x-4}{x-4}[/tex]
[tex]\frac{4(x + 4)}{(x - 4)(x + 4)(x + 4)} + \frac{3(x - 4)}{(x+ 4)(x + 4)(x - 4))}[/tex]
[tex]\frac{4(x + 4)}{(x^2 - 16)(x + 4)} + \frac{3(x - 4)}{(x^2 - 16)(x + 4))}[/tex]
The expression now have the same denominator
Related Questions
what is 3/4r+2r+1/2r
Answers
Hope this helps you!!
Three swimmers competed in a race.
Karen finished 4.367 seconds ahead of Mary.
Brenda finished in 35.04 seconds.
Brenda finished 2.45 seconds behind Mary.
What was Karen’s finish time?
Answers
Answer:
33.123
Step-by-step explanation:
Brenda is at 35.04 seconds which is 2.45 seconds behind Mary so Mary is at 37.49 seconds.
Karen is ahead of Mary by 4.367 seconds which means she is at 33.123
the national debt is $22,000,000,000,000 and the population is 280,000,000. what is the amount of debt per person?
Answers
Answer:
78571.43 dollars
Step-by-step explanation:
brainliest appreciated
I WILL GIVE BRAINLIEST TO WHOEVER HELPS ME!!
Answers
Answer:
it changes by -4 pounds each month
Step-by-step explanation:
20 pounds in 5 months
20/5 is 4 pounds per month
the elephant loses 4 pounds a month
pls help rn if possible
Answers
Answer:
I would type these in Math-Way, then select Solve the system of equations (or inequalities, I forget which one). (4, -1, 0) would be the answer.
Is everything correct and how do you do the last part?
Answers
Answer:
5 terms
Step-by-step explanation:
Yes, that's correct. For the last part, set b₊₁ less than or equal to the error.
1 / (5ⁿ⁺¹ (n+1)!) ≤ 0.000005
5ⁿ⁺¹ (n+1)! ≥ 200,000
Use trial and error to find the value of n (notice that n starts at 0).
n = 0, 5ⁿ⁺¹ (n+1)! = 5
n = 1, 5ⁿ⁺¹ (n+1)! = 50
n = 2, 5ⁿ⁺¹ (n+1)! = 750
n = 3, 5ⁿ⁺¹ (n+1)! = 15,000
n = 4, 5ⁿ⁺¹ (n+1)! = 375,000
n = 4 is the fifth term. So it takes 5 terms.
Convert 10 feet into yards. Round your answer to the nearest hundredth.
Answers
Answer:
3.33 Yards
Step-by-step explanation:
divide 10 by 3
Can someone explain how to solve these? I have 10 questions I need to answer for problems like this & I can't go on until I solve it, so I just need the answer for this one and how to solve it. I need it finished fast because I need to bring up a low grade. Any help would be appreciated.
Answers
please help me
find dy/dx using implicit differentiation
e^((x+y)/4) +tan(ln(x/y)) = e^sqrt(y)
Answers
Step-by-step explanation:
Taking log both sides :
[tex]( \frac{x + y}{4} ) + \tan( ln( \frac{x}{y} ) ) = \sqrt{y} [/tex]
Differentiate both sides w.r.t x :
[tex] \frac{1}{4} + \frac{1}{4} \frac{dy}{dy} + {sec}^{2} ( ln\frac{x}{y} ) + \frac{y}{x} + \frac{1}{y} - \frac{x}{ {y}^{2} } = \frac{1}{2 \sqrt{y} } \frac{dy}{dx} [/tex]
Rearranging :
[tex]( \frac{4 - 2 \sqrt{y} }{8 \sqrt{y} }) (\frac{1}{4} + {sec}^{2} ( ln\frac{x}{y} ) + \frac{y}{x} + \frac{1}{y} - \frac{x}{ {y}^{2} }) = \frac{dy}{dx} [/tex]
(You can rearrange it further)
PLEASE HELP!!! ILL GIVE BRAINLIEST THIS IS WORTH 30 POINTS PLEASE (ignore where it says 10 points it’s how much the question adds up to in the grade book)
Answers
Answer:
4.472136 or 4.5 is the distance.
(2, -4) is the midpoint.
Step-by-step explanation:
Answer:
4.47 units(2, -4)Step-by-step explanation:
Given points
A(1, -2) and B(3, -6)Distance AB is
AB = √((3 -1)^2 + (-6 + 2)^2) = √(4+16) = √20 = 4.47Midpoint is
M = ((1+3)/2, (-2- 6)/2) = (2, -4)A green grocer has 180 mangoes to sell. She has to arrange them in piles of 9, 10 or 12mangoes.
In which ways would she arrange the mangoes without any remaining?
Answers
Answer:
in piles of 9,10 &12
Step-by-step explanation:
this is because if you divide 180 by each number there is no remainder hence the green grocer can arrange in any way.
It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.
Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:
9 mangoes piles: 180/ 9 = 20 piles (9 x 20 = 180 with no remainders)
10 mangoes piles: 180/10 = 18 piles (10 x 18 = 180 with no remainders)
12 mangoes piles: 180/12 = 15 piles (12 x 15 = 180 with no remainders)
Hence, It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.
Learn more about division in
brainly.com/question/369266
#SPJ2
A local road rises 15 feet for every 309 feet of highway . What is the slope of the highway
Answers
is 1.36 a rational number or irrational number
Answers
Answer:
No an irrational number
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction of two integers . -1.36 can be expresed as -136/100
Answer:
Rational!
Step-by-step explanation:
Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. So, any terminating decimal is a rational number. Any decimal number that is repeating can be written in the form a/b with b not equal to zero so it is a rational number.
I hope this helps you understand what a rational number is! Have a wonderful day!
Which of the following relationships does NOT represent y as a function of x ?
a) y^3 = x
b) y = 1/x
c) y = x^2
d) y^2 = x
Answers
Step-by-step explanation:
A constant regarding force of 10 Newton is exerted to a body of mass 20 kg moving initially with a speed of 10 meter per second how long does the body take to stop
Simultaneous Equations
2x+3y=3750, 4x+y=4250
The answer is x=900 and y=650
I just need the steps
Answers
Answer:
It's long but you use Substitution!
Step-by-step explanation:
Let's solve your system by substitution.
2x+3y=3750;4x+y=4250
Rewrite equations:
4x+y=4250;2x+3y=3750
Step: Solve 4x+y=4250 for y:
4x+y = 4250
4x+y+−4x = 4250+−4x (Add -4x to both sides)
y = −4x+4250
Step: Substitute −4x+4250 for y in 2x+3y = 3750:
2x+3y=3750
2x+3(−4x+4250)=3750
−10x+12750=3750 (Simplify both sides of the equation)
−10x+12750+−12750=3750+−12750 (Add -12750 to both sides)
−10x =−9000
−10x = −9000 (Divide both sides by -10)
−10 −10
x=900
Step: Substitute 900 for x in y = −4x+4250:
y=−4x+4250
y=(−4)(900)+4250
y=650 (Simplify both sides of the equation)
Answer:
x=900 and y=650
The perimeter of a rectangular solar panel is 540 cm. The ratio of the length to the width is 3 : 2. What are the length and width?
Answers
Total number of parts = 3 + 2 = 5 parts
[tex]each \: part \: = \frac{(540 \div 5)}{2} \: m[/tex]
[tex] \\ each \: part \: = \frac{108}{2} m \: \\ \\ each \: part \: = 54 \: m[/tex]
Then , the length of this triangle :
[tex]54 \times 3 \: m[/tex]
[tex] = 162 \: m[/tex]
Then , the width of this triangle will be :
[tex]54 \times 2 \: m[/tex]
[tex]108 \: m[/tex]
∴ The length of this rectangle is 162 m and the width of this rectangle is 108 m .
2c + y = 7 solve for y
Answers
Answer:
y = 7 - 2c
Step-by-step explanation:
Step 1:
2c + y = 7 Equation
Step 2:
y = 7 - 2c Subtract 2c on both sides
Answer:
y = 7 - 2c
Hope This Helps :)
Answer:
y = 7 - 2c
Step-by-step explanation:
2c + y = 7
=> y = 7 - 2c
−18x+21>−15 OR 20x−13≥27
Answers
Answer:
I dont know what is your question, but I solved this.
Step-by-step explanation:
-18x>-15-21
-18x>-36
x<2
20x>=27+13
20x>=40
x>2
Find the equation of the line
passing through the points. (5, 2) and (10, 6).??
Answers
Assuming this is a liner function, you must first find the slope through the point slope formula [(y2-y1)/(x2-x1)]. When you plug in the corresponding values [(6-2)/(10-5)], your slope value should be 4/5.
After this, apply the slope to the x-values to find the intercept. For example, 10 x 4/5 is 8. To get to 6, you must subtract 2. This means your intercept value is -2
Therefore, your equation is y=(4/5)x-2
PLEASE HELP!!! ILL GIVE BRAINLIEST THIS IS WORTH 10 POINTS PLEASE (ignore where it says 8&2 points it’s how much the question adds up to in the grade book)
Answers
Answer:
Since the points X , Y and Z are collinear:
For the diagram, you just have to draw a line and mark the end-points of the line as X and Z and mark the mid-point of the line as Y
Since we are given that XY = YZ,
We will replace with the provided values:
XY = YZ
4(x + 5) = 2(x + 11)
4x + 20 = 2x + 22
2x = 2
x = 1
Since x = 1 and XY = YZ,
We can say that:
XZ = XY + YZ
XZ = XY + XY or XZ = 2XY
Now, replacing the variables for the value of XZ
XZ = 2XY
XZ = 2(4x + 20)
XZ = 2(4 + 20) (Since x = 1)
XZ = 48 units
Retailers will buy 45 Wi-Fi routers from a wholesaler if the price is $10 each but only 20 if the price is $85. The wholesaler will supply 56 routers at $46 each and 70 at $50 each. Assuming that the supply and demand functions are linear, find the market equilibrium point.
Answers
The Fenwick family filled their new in-ground swimming pool with 75,700 liters of water. One gallon of water is about 3.785 liters. About how many gallons of water are in the pool?
gallons
Answers
Answer:
20,000 gallons
Step-by-step explanation:
75,700 ÷ 3.785 = 20,000 gallons that are in the pool.
Answer:
20,000
Step-by-step explanation:
hoped this helped :D
5) Boat World charges an initial price of $20 plus $12.50 per hour for canoe rentals, which is
represented by the expression 20 + 12.5h.
• Complete each statement to describe the terms.
Answers
Answer:
The variable "h" represents: The number of hours
The constant 20 represents: the initial rental price
The variable term 12.5h represents: the hourly rental amount
Step-by-step explanation:
Find the distance between the points (-4,0) and (2,1). If necessary,round to the nearest 10th.
Answers
Answer:
square root of 37
Step-by-step explanation:
you would use the formula (X2-X1) squared + (Y2-Y1) squared
Some students are planning to sell gourmet popcorn at a school fundraiser. They plan to offer cheese popcorn and peanut butter popcorn. The table shows the cost of the ingredients for each type of popcorn and the price at which the students plan to sell the popcorn.
The students want to make and sell 100 containers of popcorn. They can spend at most $50 for the ingredients for each type of popcorn and the price at which the students plan to sell the popcorn.
Answers
Answer : 5 Step-by-step explanation:
There are 18 girls in Mr. Brimley's math class. If 40% of the students are girls, what is the best estimation for the number of boys in the class?
A. 20
B. 30
C. 40
D. 50
Answers
Answer:Its B I got It right on my test
Step-by-step explanation:
What is the factored form of 5x − 625x4?
Answers
Answer:
I think it's 5 I think
Step-by-step explanation:
hopefully I helped
Answer:
I think it's 5
Step-by-step explanation:
round 649,418 to the nearest hundred
Answers
Answer:
649,400
Step-by-step explanation:
Answer:
649,420
Step-by-step explanation:
I think of a number.
I multiply this number by 8, then subtract 66
The result is twice the number that I was thinking of.
What is the number I was thinking of?
Answers
6x=66(put the x’s on one side)
x=11 (simplify)
Answer:
11
Step-by-step explanation:
Set up:
8x - 66 = 2x -> Subtract 2x from either side
8x - 2x = 66 -> Simplify
6x = 66 -> Divide either side by 6
x = 66/6 = 11
The number is 11
Step by step of how to find f(g(x)) and g(f(x))
Answers
Answers:
[tex]f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}[/tex]
===============================================
Work Shown:
[tex]f(x) = \sqrt[3]{x}\\\\\\f(g(x)) = \sqrt[3]{g(x)}\\\\\\f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\[/tex]
The idea is to replace every x with g(x). Then you'll plug in the definition of g(x).
---------------------------------
Similarly,
[tex]g(x) = \frac{x+1}{x^3}\\\\\\g(f(x)) = \frac{f(x)+1}{(f(x))^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{(\sqrt[3]{x})^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\\\\\\[/tex]