Answers
Answer:
C
Step-by-step explanation:
We want to simplify the rational expression:
[tex]\displaystyle \frac{n^4-11n^2+30}{n^4-7n^2+10}[/tex]
First, we can factor both the numerator and the denominator. This yields:
[tex]\displaystyle =\frac{(n^2-6)(n^2-5)}{(n^2-2)(n^2-5)}[/tex]
Cancel like terms:
[tex]\displaystyle =\frac{(n^2-6)}{(n^2-2)}[/tex]
However, since we canceled a term from our expression, we must place restrictions in order to stay true to the original expression.
Rational expressions are undefined whenever the denominator equals 0. The denominator is (before canceling):
[tex](n^2-2)(n^2-5)=0[/tex]
Solve for n. By the zero product property:
[tex]n^2-2=0\text{ and } n^2-5=0[/tex]
Therefore:
[tex]n^2=2\text{ and } n^2=5[/tex]
By taking the square root of both sides (since we are taking an even root, it is required to have plus/minus):
[tex]n=\pm\sqrt{2}\text{ and } n=\pm\sqrt5[/tex]
Therefore, our fully simplified expression is:
[tex]\displaystyle \frac{n^2-6}{n^2-2}\, ,n\neq \pm\sqrt5, \pm\sqrt2[/tex]
Hence, our answer is C!
Related Questions
What is two over nine times by forty-five
Answers
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
2/9 × 45 = 10
16-2=15-1 true or false
Answers
Answer:
True because when you do 16-2 is 14 and 15-1 is 14
16-2=14
15-1=14
14=14
The two numbers that multiply to 11 and add to -12 are
Answers
Answer:
-11 and -1
Step-by-step explanation:
These are the two numbers that multiply to 11 and add to -12.
Answer: 11x1 is 11. 11- 13 = -12
Step-by-step explanation:
Need this QUICK!! Evaluate without using a calculator (x2y-3)0+x1/3-(4x)1/2 when x = 64 and y = 27.Show work
Answers
Answer:
-11
Step-by-step explanation:
Given the expression
(x²y-3)⁰+x^1/3-(4x)^1/2 when x = 64 and y = 27.Show work
Note that anything raise to power of zero is 1, hence (x²y-3)⁰ = 1
x^1/3
= 64^1/3
= ∛64
= 4
(4x)^1/2
= (4* 64)^1/2
= 4^1/2 * 64^1/2
= 2 * 8
= 16
Substitute;
(x²y-3)⁰+x^1/3-(4x)^1/2
= 1 + 4 - 16
= 5 - 16
= -11
Hence the required value is -11
1.A house worth $250,000 has an coinsurance clause of 90 percent. The owners insure the property for $191,250. They then have a fire that causes $80,000 in damage. How much money will they receive from insurance?
2.A house worth $180,000 has a coinsurance clause of 75 percent. The owners insure the property for $101,250. They then have a loss that results in a $50,000 claim. How much money will they receive from insurance?
Answers
1. Multiply the value of the house by the percent:
250,000 x 0.9 = 225,000
Divide the amount the owner insured by the clause amount:
191,250/225,000 = 0.85
Multiply that by the amount of damage:
0.85 x 80,000 = 68,000
They will receive $68,000
2. Follow the same steps as above:
180,000 x 0.75 = 135,000
101,250 / 135,000 = 0.75
0.75 x 50,000 = 37,500
They will receive $37,500
Answer:
1. They will receive $72,000 in insurance.
2. They will receive $37,500 in insurance.
Step-by-step explanation:
1.Given that the coinsurance is 90 percent.
For the fire that caused a $80,000 in damage, 90 percent of $80,000 will be received in insurance.
90 percent of $80,000 will be received in insurance
90 percent of $80,000 = 0.9 * 80000
= 72,000
Therefore, they will receive $72,000 in insurance
2. The coinsurance is 75 percent, given that they have a loss that results in a $50,000 claim.
they will received 75 percent of $50,000
75 percent of $50,000 = 0.75 * 50000
= 37.500
Therefore, they will receive $37,500
B = 4x + 30 C = 2/3 * x + 20 A = x + 30
Anyone know the answer to this?
Answers
Answer:
all the ways to answer
Step-by-step explanation:
B:
Factor:
2(2x+15)
Evaluate:
4x+30
C:
Factor:
2(x+30)/3
Evaluate:
2(x+30)/3
A:
DIFFERENTIATE W.R.T. X:
1
Evaluate:
x+30
hope that helps.
if correct please mark as brainliest
thank you
HAVE A NICE DAY
19NBoli
The expression (x^-8) (x^3) is equivalent to the expression x^n. what is the value of n?
Answers
n = -5
_______
(x^a)(x^b) = x^(a + b)
________________
(x^-8) (x^3) = x^(-8 + 3) = x^(3 – 8) = x^(-5)
HURRY PLEASE!!!!
What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome??
Answers
The limitations of using the Fundamental Counting Principle when determining the probability of an outcome is that it is not simple and it does not apply to non-uniform probability distribution
What is probability?Probability is the likelihood or chance of an event happening or not.
Probability values helps in decision-making in day-to-day activities.
The Fundamental Counting Principle in probability is a way to determine the number of outcomes in a probability problem. It states that if there are p ways to do one thing and q ways to do another, the number of way to do both things is p × q.
However, this principle is limited for non-uniform probability distribution and for larger samples space.
Therefore, the limitations of using the Fundamental Counting Principle when determining the probability of an outcome is that it is not simple and it does not apply to non-uniform probability distribution.
Learn more about probability at: https://brainly.com/question/24756209
#SPJ2
Write 0.000673 in scientific notation
Answers
Answer:
6.17
Step-by-step explanation:
Answer:
6.73 × 10-^4
Step-by-step explanation:
Ted and Meg have each drawn a line on the scatter plot shown below
Which line best represents the line of best fit?
Line P, because it is closest to most data points
Line P, because it shows a positive association
Line R, because it is closest to most data points
Line R, because it shows a negative association
Answers
Answer:
Line P, because it is closest to most data points
Step-by-step explanation:
hope that helps.
please mark as brainliest if correct
thank you
19NBoli
P.S i am learning about this topic in my school
Answer:
line P is the best fit, since the data points are closest to it, so the first answer.
Once I get it wrong, I can’t redo the same question again and I have to go onto the next question. I only have 5 questions but if I get 1 wrong I have to keep on answering questions til I get 5 questions right. So far I got 3 out of 5 questions correct. So can someone please help me? I’ve been trying to get 5 questions correct all day.I would greatly appreciate it.
Answers
Answer:
29.25
or 29.3 if rounded to 10s place.
Step-by-step explanation:
Answer:
[tex]\Huge\boxed{29.3}[/tex]
Step-by-step explanation:
Hello There!
Remember The Trigonometric Ratios
Sin = opposite divided by hypotenuse
Cos = adjacent divided by hypotenuse
Tan = opposite divided by adjacent
We need to find the measure of angle X given the opposite side length and hypotenuse
Opposite and hypotenuse correspond with sine so we are going to use sine to solve for x
We create an equation: [tex]sin(x)=\frac{43}{88} \\[/tex]
[tex]\frac{43}{88} =.4886363636\\sin(x)=.4886363636[/tex]
Now we want to get rid of the sin
To do so we take the inverse of sin (which would be arcsin) and apply it to each side
[tex]arcsin^-^1(sinX)=x\\arcsin^-^1(.4886363636)=29.25099306[/tex]
finally we round to the nearest tenth
we're left with x = 29.3
A runner covers a distance of 1200m with an average speed of 4m/s. How long does it take to run this distance? Then calculate the time in min.
Be the first answer for Brainliest, please I need help.
Answers
Answer:
5mins
Step-by-step explanation:
well i did 1200 divided y 4 then divided that answer by 60
What prime factor is common to 35, 84 and 21?
Answers
Answer:
7 is the prime factor that is common to all three numbers.
7x5 = 35
7x12 = 84
7x3 = 21
Let me know if this helps!
35/7=5
84/7=12
21/7=3
5, 12, and 3 don’t have any common factors so 7 is the prime factor.
Estimate 15% tip from $15.00
Answers
Answer:
17.25
Step-by-step explanation:
search it up
HELP ASAP
in rectangle ABCD the diagonals intersect each other at point O and mABD=30 degrees. find BC if AC=16
Answers
This is my answer.I hope this is useful.
............
I need help with this math problem ASAP plsssss helppp. The problem is attached below
Answers
Answer:
234.67 in³
Step-by-step explanation:
volume of full sphere = 4/3(π)(r³) = 4/3(3.14)(5³) = 523.33 in³
volume of half sphere = 523.33/2 = 261.67 in³
volume of cube = LWH = 3³ = 27 in³
261.67 - 27 = 234.67 in³
Solve the simultaneous equation:
6x+4y=34
3x-y=14
Answers
Answer:
x=5, y=1. (5, 1).
Step-by-step explanation:
6x+4y=34
3x-y=14
---------------
y=3x-14
6x+4(3x-14)=34
6x+12x-56=34
18x=34+56
18x=90
x=90/18
x=5
3(5)-y=14
15-y=14
y=15-14
y=1
The design for a mural is 16 in. Wide and 9 in. High. What are the dimensions of the largest possible complete mural that can be painted on a wall 24 ft wide by 14 ft high?
Answers
Answer:
Largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.
Step-by-step explanation:
Design of a mural is 16 in. wide and 9 in. high.
Dimensions of the wall are 24 ft by 14 ft.
If we enlarge the size of the design along the width the wall, scale factor to be used,
Scale factor = [tex]\frac{\text{Width of the wall}}{\text{Width of the design}}[/tex]
= [tex]\frac{24}{16}[/tex]
= [tex]\frac{3}{2}[/tex]
With the same scale factor, height of the design will be,
[tex]\frac{3}{2}=\frac{\text{Height of the wall used}}{\text{Height of the design}}[/tex]
[tex]\frac{3}{2}=\frac{\text{Height of the wall used}}{9}[/tex]
Width of the wall used = [tex]\frac{3\times 9}{2}[/tex]
= 13.5 ft
Therefore, largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.
what is -2g< 10 find g
Answers
Answer:
g>-5
Step-by-step explanation:
Andre wants to buy a bike that normally costs $125, but is on sale for 20% off.
How much is the discount? Andre will pay $100 after the discount
Answers
Answer:
The discount takes $25 dollars off
Step-by-step explanation:
So yes, he'll pay $100 after the discount is applied
Answer:
25 dollars
Step-by-step explanation:
125 - 100= 25
Translate triangle ABC 4 units right and 5 units down H E L P
Answers
SKIP # 14 SHOW ALL WORK PLEASE AND I WILL GIVE BRAINLY AND 77 points for it
Answers
Answers:
11. 48%
12. 25%
13. 36%
15. 93%
16. 99%
17. 0.16%
18. 160%
19. 85%
Work for 19:
The chart is incorrect because it calculates 40% of 34 instead of 40 percent of x (we got 85% for our answer but I'm using x as the unknown number) results in the number of 34.
Percentage of 40% of what number = 34?
40% of what number = 34 is equivalent to: 40% × ? = 34
--------------------------
40% × ? = 34
? =
34 ÷ 40% =
34 ÷ (40 ÷ 100) =
(100 × 34) ÷ 40 =
3,400 ÷ 40 =
85
Proof:
If 40% × 85 = 34 =>
Divide 34 by 85...
... And see if we get as a result: 40%
----------------------------------------------------------
20. 21 students
Step-by-step explanation:
I hope I helped, and I always appreciate brainliest!!! ;)
An initial investment of $1000 grows at an interest rate of 4% per year. How long will it take that investment to reach $1,500? Assume that you make no further deposits or withdrawals from the investment account. Round to the nearest tenth of a year.
Answers
Answer:
it would take 12.5 or 12 and a half years
Step-by-step explanation:
Last summer, Marrero was at Newgrange, a stone mound in Ireland that has a diameter of 250 feet. He found a walkway 62 feet long that leads to the center of the mound. Help Marrero find perpendicular distance x from the end of the walkway to either side of the mound.
Answers
Answer:
108 ftStep-by-step explanation:
The line connecting the center with the end of the walkway is radius and is the hypotenuse of the right triangle.
Horizontal leg is the distance x.
Vertical leg has the length:
(250)/2 - 62 = 63 ftUsing Pythagorean theorem to find the length of x:
x² = (250/2)² - 63²x² = 125² - 63²x² = 11656x = √11656x = 107.96 ≈ 108what's
[tex] \alpha + \beta [/tex]
if
[tex] \alpha = 1 \: and \: \beta = 2[/tex]
Answers
Answer:
3
Step-by-step explanation:
1+2 = 3
I hate these type of qn
lol
Please help me! This assignment is due today and i’m desperate so I made it a lot of points :) I need to know if this graph is a function or not, and the domain and range. Thanks to whoever helps!!
Answers
Answer:
this is a function
Step-by-step explanation:
there are no duplicates on the y axis so it is a function
How many 7-digit even numbers can be
formed using all of the digits 0, 1, 1, 2,
3, 4, 5?
Answers
Answer: The answer is 1320 hope this is right.
Step-by-step explanation:
Plz help really need this
Answers
Explanation:
W(2,0)
2 • 1.5 = 3
0 • 1.5 = 0
W’ = (3,0)
Answer:
Step-by-step explanation:
for T and T' it's going to be ( 2 , -1) you switched them the x, and y
W and W' is ( 0, 3) as the other person said
please answer it fast with details.
Answers
Answer:
estepra gerue
Step-by-step explanation:
Use special right triangle find the exact value of x.
X=?
Answers
Answer: 12
Step-by-step explanation: