Answers
Given:
The expression is
[tex]\dfrac{2}{a-2}-\dfrac{8}{a^2-4}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{2}{a-2}-\dfrac{8}{a^2-4}[/tex]
It can be written as
[tex]=\dfrac{2}{a-2}-\dfrac{8}{a^2-2^2}[/tex]
[tex]=\dfrac{2}{a-2}-\dfrac{8}{(a-2)(a+2)}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
Taking LCM, we get
[tex]=\dfrac{2(a+2)-8}{(a-2)(a+2)}[/tex]
[tex]=\dfrac{2a+4-8}{(a-2)(a+2)}[/tex]
[tex]=\dfrac{2a-4}{(a-2)(a+2)}[/tex]
[tex]=\dfrac{2(a-2)}{(a-2)(a+2)}[/tex]
Cancel out the common factors.
[tex]=\dfrac{2}{a+2}[/tex]
Therefore, the simplified form of the given expression is [tex]\dfrac{2}{a+2}[/tex].
Related Questions
What is the value of q in the solution to this system of equations?
2m-5q=8
4m+2q=64
A.4
B.6
C.9
D.14
Answers
Answer:
4
Step-by-step explanation:
M,q 14,4
The value of q in the system of equations 2m-5q=8 and 4m+2q=64 is 4 thus option (A) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given system of equations,
2m-5q=8
4m+2q=64
Multiply by 2 into the equation 2m - 5q = 8
4m - 10q = 16
Subtract 4m - 10q = 16 by 4m+2q=64
-10 - 2q = 16 - 64
-12q = -48
q = 4
Hence"The value of q in the system of equations 2m-5q=8 and 4m+2q=64 is 4".
For more about the equation,
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An item is regularly priced at $19. It is now priced at a discount of 65% off the regular price. Use the a calculator or something to find the price now. THX!
Answers
Answer:
6.65
Step-by-step explanation:
65%of19 is 12.35
19-12.35=6.65 so the item is now priced at $6.65
In Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at $220 before tax.
How much sales tax does Yuki pay for her handbag purchase?
Answers
Answer:
$18.15
Step-by-step explanation:
Yuki is paying tax of 4.6% + 3.65% = 8.25%
Converting to decimal form, that is 8.25/100 = 0.0825
Multiply that by the original sale price. 0.0825 x $220 = $18.15 exactly for tax.
The question asks for the tax, NOT for the total she will pay. Please don't get them mixed up.
With word problems, alwasy double check that you are answering what is actually asked. :)
3/2x3/4= -1/5
uh i need help
Answers
Answer:
I'm not smart but I think there's no solution
What does 43/12 is equivalent too?
Answers
Hi there!
Fractions can be equivalent to a lot other fractions...
Explanation:
43/12x2 would be 86/24 so that would be equivalent.
Let do another one..
43/12 when doing this, you can decide to divide or not but this is in the simplest form already so we can just multiply 43 and 12 with anything we want so let do... 5.
So 43 multiply by 5 would be..215 and 12x5 would be 60. So another equivalent fractions that’s the same as 43/12 or we can say 86/24 is 215/60.
I also added how I got the equivalent fractions just in case you don’t understand still...
please help mee with thisss
Answers
Answer: 200.96
Step-by-step explanation:
3.14 times 8^2 = 200.96
Answer:
200.96 inches²
Step-by-step explanation:
The area of a circle is pi x r². In this case it would be: 3.14 x 8² (64). This is also: 200.96.
Hope it helps!
What is a reflection of a geometric shape
Answers
Answer:
A reflection of a geometric shape is the mirror image of the shape.
Hope this helps, thank you !!
HELLP ILL GIVE ALL MY POINTS IF SOMEONE HELPS The ratio of bows to headbands of Monique’s hair accessories is 8:4.
Select all true statements.
For every 8 hair accessories, 4 are bows.
For every 8 bows, there are 4 headbands.
For every 8 headbands, there are 4 bows.
For every 8 hair accessories, 4 are headbands.
For every 12 hair accessories, 4 are headbands.
Answers
Answer:
Its a
Step-by-step explanation:
Answer:
B and D I think
Explaination:
its bows to hair so its 8:4
and add head bands to bows thats 12
12:4
( all to headbands)
Hope it make sense
WHAT IS INSIDE QRS
HELP ME NOW PLS
Answers
Answer:
(-3,3)
Step-by-step explanation:
Point (-3,3) is inside QRS
I hope this helps!! Let me know if you need anymore help
A streetlamp has a 20 ft shadow that makes a 40° angle with the ground. which expression represents the height of the street lamp in feet ?
Answers
Answer:
20 sin 40° ≈ 12.86 ftStep-by-step explanation:
Let the height of the street lamp be x
Opposite angle is 40° and the shadow, the hypotenuse of the formed triangle is 20 ft.
sin 40° = x/20x = 20sin 40°x ≈ 12.86 ftIn 42 minutes, Mr. Goo can run 6 miles. How long does it take him to run 1 mile?
Answers
Answer:
7 min
Step-by-step explanation:
Answer:
7 Minutes
Step-by-step explanation:
If you divide 42 by 6, you get 7.
What two numbers are located 3/4 unit from 1/10 on a number line?
Answers
Answer:
-13/20 and 17/20Step-by-step explanation:
The numbers are either side from 1/10
To the left:
1/10 - 3/4 = 2/20 - 15/20 = -13/20To the right:
1/10 + 3/4 = 2/20 + 15/20 = 17/20What is the area of a parallelogram that has a base of 12 inches and a height of 8 inches?
Question 1 options:
96 square inches
1.5 square inches
20 square inches
Answers
Answer:
96 square inches
Step-by-step explanation:
Given in a parallelogram
base (b) = 12 inches
height (h) = 8 inches
Now
Area of parallelogram
= b * h
= 12 * 8
= 96 square inches
Hope it will help :)
Answer:
96
Step-by-step explanation:
Area= base x height
= 12 x 8
= 96
Since Area of parallelogram is base into height
Please do number 14 for me. (Show work)
Answers
Answer:
A
Step-by-step explanation:
3x+h=180
h=180-3x
x+15+x+15+180-3x=180
-x+210=180
-x= -30
x=30
Now that we know that x=30 we can easily figure out the values of the other angles
HDZ= 45
HZD= 45
x=3
what is the measure of CBF?
Answers
Answer:
∠CBF=136°
Step-by-step explanation:
The angles along a straight line always add up to 180:
∠CBF+∠FBA=180
∠CBF+44=180
∠CBF=136°
Identify the initial amount a and the rate of decay r (as a percent) of the exponential function y = 8(1 – 0.15). Evaluate the function
when t = 3. Round your answer to the nearest tenth.
Answers
Answer:
Initial amount = 8
Decay rate = 15%
Step-by-step explanation:
Given the exponential function :
y = 8(1 – 0.15)
The general form of an exponential Decay function is :
A = P(1 - r)^t
Where
A = final amout ; P = initial amount ; r = days cay rate ; t = time
Hence, comparing with the equation given :
P = 8 = initial amount
r = 0.15 = 0.15 * 100% = 15% = Decay rate
The average cost for a gallon of gasoline in 2006 was $2.45. In 2007, the average cost of a gallon of gasoline was $3.29. What is the approximate percent of change in the cost of a gallon of gasoline?
A. 25%
B. 35%
C. 75%
D. 135%
Answers
Answer:B
Step-by-step explanation:
2.45(0.35)= 0.8575+2.45= 3.30
Wezi has sixty-three $5-bills. He takes the $5-bills to the bank to exchange them for $20-bills. How many $20-bills does Wezi get? Is there money left over? Explain.
Answers
Answer: 15
Step-by-step explanation:
From the question, we are informed that Wezi has sixty-three $5-bills. The total amount that he has will be:
= 63 × $5
= $315
We are further told that he takes the $5-bills to the bank to exchange them for $20-bills. Based on this, the number of $20-bills that Wezi get will be:
= $315 / $20
= 15 3/4
Therefore, he will get 15 $20 bills
The circumference of a circle is 36 pi feet. What is the length of the radius of this circle?
a, 9 ft
b, 18 ft
c, 36 ft
d, 72 ft
the answer is b, I just did the quiz on edge2021
Answers
Answer: The answer is 18ft (B)
Step-by-step explanation: Got it correct on Egde 2021. Hope this helps!
Answer:
Answer i can confirm is B
Step-by-step explanation:
I took the quiz on edge
o curso de inglês de Carolina teve duração de 4 semestres e 2 meses . quantos tempo durou esse curso de Carolina ?
a 26 meses
b: 24 meses
c : 22 meses
d: 20 meses
Answers
Answer:
a 26 meses gracias por los puntos
Xavier claims that the number of text messages he sends is proportional to the amount he owes on his monthly phone bill. He has listed the number of text messages sent and the amount he owed for a few months: January: 300 text messages sent; $15.00 owed February: 314 text messages sent; $15.70 owed March: 486 text messages sent; $24.30 owed April: 205 text messages sent; $10.25 owed Which of the following methods would help Xavier prove his claim? Select all that apply.
Answers
Answer:
Xavier could plot data points based on the number of text messages sent in each month and the amount owed to create a straight line on the graph starting at (0, 0.05).
Xavier could create a table listing the number of text messages sent in each of the months listed and the amount he owed for those months to test for equivalent ratios.
Step-by-step explanation:
what is area of a quadrilateral
Answers
Answer:
So, area of quadrilateral ABCD = (½ × AC × BE) + (½ × AC × DF) We can calculate the area of different types of quadrilaterals by using the given formula. For the quadrilateral ABCD, if we use centimeter as the unit of measurement, the unit of measure for the area will be cm2 .
I hope it's helpful!
Answer:
Step-by-step explanation:
R u asking for formula ?
If so then,
1/2 x (h1+h1 )d
which is half the sum of height 1 and 2 multipied by daigonal
Find the common difference for the given sequence.
1.05, 1.1, 1.15, 1.2, ...
0.5
0.05
0.005
Answers
Find the product of ^
Answers
Answer:
D
Step-by-step explanation:
Bob's Pet Shop sold the following pets last month:
5 cats
9 dogs
7 birds
What is the ratio of birds to total pets in the simplest form?
Answers
1 : 3
Fully factorise 20x + 16.
.
2
-2
✓
2
TT
0
Enter your answer
Answers
Answer:
4(5x+4) is the answer
Step-by-step explanation:
..............
find the inverse f(x)=x-11
Answers
Answer:
f(x)=x+1/11
Step-by-step explanation:
These two lines would be perpendicular.
Answer:
[tex]f^-^1(x) = x+11[/tex]
Step-by-step explanation:
- Write as an equation.
y = x - 11
- Interchange the variables.
x = y - 11
- Solve for y
y = x + 11
- Replace the y with [tex]f^-^1(x)[/tex] to show the final answer.
[tex]f^-^1(x) = x+11[/tex]
hope this helps :)
what is the value of x ? round your answer to the nearest tenth .
Answers
Answer:
39 maybe i don't know
Step-by-step explanation:
A camera shop's daily profit is given by P = 3x2 – 3x + 10, where x is the total number of
cameras sold in the day. If they only had profit of $70 today, how many cameras did they
sell?
Answers
Answer:
5 cameras they sell
Step-by-step explanation:
P = 3x² – 3x + 10 p = 70
3x² – 3x + 10 = 70
3x² – 3x - 60 = 0
x² - x -20 = 0
(x + 4) (x - 5) = 0
x can't be negative, x = 5
The no of cameras sold if A camera shop's daily profit is given by P = 3x² – 3x + 10, where x is the total number of cameras sold in the day. If they only had a profit of $70 today is 5.
What is equation?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in, 3x + 5 Equals 15, instances. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Given:
The equation, P = 3x² - 3x + 10,
If P = 70 then,
70 = 3x² - 3x + 10
x = 5 and -4 but the number of cameras can not be negative
Therefore, The no of cameras sold if A camera shop's daily profit is given by P = 3x2 – 3x + 10, where x is the total number of cameras sold in the day. If they only had a profit of $70 today is 5.
To know more about equation:
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find area of the triangle 15ft 10ft 10ft
Answers
Answer:
75
Step-by-step explanation:
i'm going to assume that the base is 10, the formula for a triangle is base x height divided by 1/2 (or 2)
15height x 10base = 150 now divided by 2, 150/2 = 75