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
A line passes through the points (-3,0) and (2,5). Find its equation in general
form.
Answers
1. Ryan is washing windows on a skyscraper. He lowers himself six times,
going down an equal distance each time. In all, Ryan lowers himself 48 ft.
What integer represents the change in Ryan's position each time he lowers
himself? *
Answers
Answer:
Ryan went down a total of 8 times
Step-by-step explanation:
He goes down 6 times 48/6 = 8
A city has a population of 320,000 people. Suppose that each year the population grows by 7%. What will the population be
after 15 years?
Use the calculator provided and round your answer to the nearest whole number.
Answers
Population will increase by 105%
100+105=205
320,000. 100%
x. 205%
x=320,000 • 205% divided by 100%
x=656,000 people
Barak spent $20 at the mall. This represents 16% of the money he earned working at the pizza parlor last week. How much money did Barak earn at the pizza parlor last week?
Answers
Answer: Amount of Money Barak earned last week =$125
Step-by-step explanation:
Amount of money Barak spent= $20
Amount of money spent = 16% of Money earned (X)can be represented as
16% x X =20
0.16 x X =20
X = Money earned last week = 20/ 0.16= $125
PLEASE HELP
show work for problem
Answers
Answer:
[tex]tan(x)-1 =30/45[/tex]
Step-by-step explanation:
put that in your calculater
Please answer this below Question # 15
Answers
Answer:
[tex]c. \: 5x - 2y = 10 \\ \: \: \: \: \: 10x - 4y = 20 \\ [/tex]
Which statement about 7/3 is true
A. 7/3 = 7 x 3/1
B. 7/3 = 7 x 3/3
C. 7/3 = 7 c 1/7
D. 7/3 = 7 x 1/3
Answers
Answer:
D, the rest are not true about the statement 7/3
Answer:
D. 7/3 = 7 x 1/3
Step-by-step explanation:
[tex]7 * \frac{1}{3} = \frac{7}{1} * \frac{1}{3} = \frac{7}{3}[/tex]
The perimeter of a regular hexagon is 78 cm .What will be the length of each side?
Answers
Answer:
13 cm
Step-by-step explanation:
78/6=13
Answer:
13cm
Step-by-step explanation:
regular means the sides are equala hexagon has 6sides78/6=13Pig E Bank brags a 4% interest rate compounded annually. If Mr. Ant wants to invest $5,000
on his first born child's birthday and surprise him with the account on the child's 40th
birthday. Write and solve an equation to determine the amount in the account when his
child turns 40.
Answers
hii! i just wanted to say hope you're having a fantastic day and hope that things are going well (: stay strong and stay safe!
if your heat beats 75times per minute how many time does it beat in 5 hours
Answers
Answer:
This is your answer . IfI'm right so,
Please mark me as brainliest. thanks!!!
Find the measure of A in Triangle ABC.
Since we are given
information here, we
can use the following equation to solve for m angle A.
Answers
Answer:
First part= SSS
Second part=0.2
Third part=78
Answer:
A.
On edge.
Step-by-step explanation:
DONT ANSWER IF YOU DONT KNOWWWWWW . Click All that apply:)
Answers
Answer:
1.Location
2.shape
3.orientation
Step-by-step explanation:
Answer: Orientation
Step-by-step explanation:
Basically how the shape looks like on a graph for example a right side up triangle would look different from a upside down triangle
Can someone tell me a proportion to convert 5 pounds to ounces asap. pls someone reply quick
Answers
Answer:
5 pounds = 80 ounces
Hope it helps!!!
List five examples of materials and equipment that can be used for math activities.
Answers
Answer:
compass
protecter
scale
pencil
Hence, the fives examples are explained.
What is the mathematics?
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes
(1) Ruler
(2) Set-squares
(3) Compass
(4) Divider
(5) Protactor
Hence, the fives examples are explained.
To know more about the maths
https://brainly.com/question/12789483
#SPJ5
A football field measures at 100 yards with 2 end zones. There are 2 end zones. Each end-zone is 10 yards long. What is the total length of the football field in feet?
Answers
Answer:
360 feet.
Step-by-step explanation:
If there are 2 end zones each measuring 10 yards long then that means that both together measure 20 yards long. We add this to the 100 yards of the field and we get a total length of 120 yards. Now we can simply turn this into feet, we know that ...
1 yard = 3 feet
120 yards = x feet
120 * 3 = x
360 feet = x
Finally, we can see that the length of the football field is 360 feet.
i need the answer for this question
Answers
Answer:
z=-13.9
Hope this helped!!
Answer: z= 4.1
Step-by-step explanation:
Find the distance between the two numbers on a number line. Write your answer as a fraction in simplest form.
3/4,1/8
Answers
Answer:
From 3 to 4,1 is 1,9 and from 4,1 to 8 it is 4,9 I think. I am sorry if I'm wrong I haven't done this is a while?
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
q/19 < 4
pls be correct if you type it !!!!
Answers
Answer:
q<76
Step-by-step explanation:
hope this is the answer you were looking for!
Find the value of the marked angles in each of the following ( see image ).
Please show workings.
The only given angles are 62° and 85°.
The angle to look for is marked by “))”
Answers
Answer:
(180-62)
118
180-118=62
180-85=95
180-(62+95)
180-157
23
Answer:
23°Step-by-step explanation:
The inscribed is the cyclic quadrilateral.
The opposite angles are supplementary in cyclic quadrilaterals.
The angle opposite to 85° is:
180° - 85° = 95°The missing angle of the triangle is:
180° - (62° + 95°) = 23°Please help if possible :)
Answers
Answer:
4.5
Step-by-step explanation:
any value of XYZ divided by the corresponding value from RST = 4.5 the scale factor
I WILL GIVE BRAINLEST!!! 20 POINTS!!!
If tomatoes cost 5.30 per pound and i have 9.7 pounds how much would i pay?
Answers
Given f(x) = 4x - 1 and g(x) = x2, choose
the expression for (fºg)(x).
Click on the correct answer.
Answers
Step-by-step explanation:
step 1. f°g(x) = f(x^2)
step 2. f(x^2) = 4(x^2) - 1
step 3. answer: 4x^2 - 1
help with this too!!
Answers
Answer:
a
Step-by-step explanation:
Bella can run a mile in 9.54 minutes. Linda can run a mile in 8.22 minutes. How much faster can Linda run than Bella? Justify your reasoning.
Answers
Answer:1.16 times
Step-by-step explanation:
Given
Bella can run a mile in 9.54 minutes
Linda can run a mile in 8.22 minutes
We know, [tex]\text{distance=speed}\times\text{ time}[/tex]
Speed of Bella, for running a mile is
[tex]\Rightarrow v_b=\dfrac{1}{\frac{9.54}{60}}=\dfrac{60}{9.54}\\\\\Rightarrow v_b=6.29\ mph[/tex]
Speed of Linda, for running a mile is
[tex]\Rightarrow v_l=\dfrac{1}{\frac{8.22}{60}}=\dfrac{60}{8.22}\\\\\Rightarrow v_l=7.29\ mph[/tex]
So, Linda is faster than Bella, as her speed is more compared to Linda.
Linda is [tex]\frac{9.54}{8.22}=1.16[/tex] times faster than bella
If the measure of arc RT = 80 degrees and the measure of arc US = 40 degrees, what is the m<2?
Answers
360-120=240
240/2=120
So answer is 120
Grade 10 math help please show work
Answers
Answer:
∅ = 1.91°
Step-by-step explanation:
sin ∅ = 10/300 = 0.0333
∅ = 1.91°
HELP ME PLZZ I NEED HELP WITH THIS
Answers
Answer:
25 + 11 hope this helps
Step-by-step explanation:
answer is the third one
In order for a rhombus to be proven using either its sides or angels, it must first be proven to be a
Answers
Answer:
It must be proven to be a quadrilateral
Step-by-step explanation:
The question is straightforward, and it requires a direct answer.
A rhombus has four sides and as such it means it is a type of quadrilateral.
So, before a shape is proven to be a rhombus, it has to first be proven to be a quadrilateral.
Write a rational number between -3 and -4.
Answers
Answer:
-3.25
Step-by-step explanation:
Answer:
-3.25
Step-by-step explanation:
sorry I'm wrong.....im not that good at math