Answers
Answer:
Question:
[tex]\textsf{factor : \ } x^4+\dfrac{1}{x^2}[/tex]
Rewrite the expression using the exponent rule [tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]
[tex]\implies x^4+\dfrac{1}{x^2}=\dfrac{x^6}{x^2}+\dfrac{1}{x^2}[/tex]
Factor out common term [tex]\dfrac{1}{x^2}[/tex] :
[tex]\implies \dfrac{1}{x^2}(x^6+1)}[/tex]
Factor [tex](x^6+1)[/tex]:
Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] to get cubic exponents:
[tex]\implies x^6+1 = (x^2)^3+1^3[/tex]
Apply the sum of cubes formula: [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
where [tex]a=x^2[/tex] and [tex]b=1[/tex]:
[tex]\implies (x^2)^3+1^3=(x^2+1)((x^2)^2-x^2 \cdot 1+1^2)[/tex]
[tex]\implies (x^2+1)(x^4-x^2+1)[/tex]
Therefore,
[tex]\implies \dfrac{1}{x^2}(x^6+1)}=\dfrac{1}{x^2}(x^2+1)(x^4-x^2+1)[/tex]
Simplify by dividing the 2nd parentheses by [tex]x^2[/tex]:
[tex]\implies (x^2+1)\left(\dfrac{x^4-x^2+1}{x^2}\right)[/tex]
[tex]\implies (x^2+1)\left(x^2-1+\dfrac{1}{x^2}\right)[/tex]
Factor out [tex]x[/tex] from first parentheses:
[tex]\implies x\left(x+\dfrac{1}{x}\right)\left(x^2-1+\dfrac{1}{x^2}\right)[/tex]
Related Questions
The height of a golfball hit off a 128-foot hill is modeled by the function h(t) = −16t2 + 32t + 128, where h is height in feet and t is time in seconds. Find the time the golf ball takes to reach the ground.
Answers
The time taken for the golf ball to reach the ground is 1 s.
Motion of the golf ballThe path of motion of the golf ball can be described as parabolic because it is projectile.
When the golf ball reaches the ground, the final velocity will be zero.
Velocity of the golf ball is change in height with time.
v = dh/dt
h(t) = -16t² + 32t + 128
dh/dt = -32t + 32
0 = -32t + 32
32t = 32
t = 1 s
Thus, the time taken for the golf ball to reach the ground is 1 s.
Learn more about time of motion here: https://brainly.com/question/2364404
Answer:
6 seconds, the other dude is a dimwit
Step-by-step explanation:
What is the value of a?
Answers
Answer:
97
Step-by-step explanation:
(a - 48) + a = a + 49
2a - 48 = a + 49
a = 97
We can do this because the angles of a triangle all add up to 180 and 2 angles of a line add up to 180.
There are 140 boys and 120 girls in a school. find the ratio of
i, boys to girls
ii, boys to the total number of students
iii, girls to the total number of students
i want process with answer
giving answer with process
making him/heras a brainlists
Answers
Answer:
i. 7:6
ii. 7:13
iii. 6:13
Step-by-step explanation:
boys to girls = 140:120 so we can simplify by 20 to get 7:6
boys to total = 140:(120+140) = 140:260 we can simplify again to get 7:13.
girls to total = 120:(120+140) = 120:260 we can also simplify to get 6:13
What formula can we use to find the surface area of a rectangular prism? Question 4 options: SA = 2lw 2lh 2wh SA = 2lwh SA = πr2 SA = lw lh wh.
Answers
Check the picture below.
Which table represents the function y = 3x – 1?
Answers
Answer:
The fourth table
Step-by-step explanation:
3(0)-1=-1
3(1)-1=2
3(2)-1=5
Hope this helps :)
math related xxxxxxxxxx
Answers
Answer:
x = 9
PQ = 19
QR = 19
RP = 10
Step-by-step explanation:
if 3x - 8 = 2x+1
then,
3x -2x = 1+8
x = 9
for pq,
2x+1
2x + 1 = 2*9+1
=>18 +1 = 19
for qr,
3x-8 = 3*9-8
=>27-8 =19
for rp,
x+1=9+1
=> 10
Please help people!!! :D
Answers
Answer:
The answer is C
Step-by-step explanation:
Since the line above the letters is an arrow that means the two points have to create a line like that. Therefore, the answer is DB.
Answer:
DB
Step-by-step explanation:
Why others rejected?
E C
E and C are in cent res or at midpoint near area s .The correct name should be A FE B is rejected as points are not on one line
Mr. Salam bought a 2½-pound wheel of cheese. His family ate ¼ of the wheel. How much cheese did they eat?
Answers
Answer:
5/16 of a pound
Step-by-step explanation:
2½ x ¼ = 5/4 × 1/4 = 5/16
Draw a number line to represent the inequality
y < 3
Answers
Answer:
< means y is smaller than 3, it's not equal, so it's open dots.
(number line see the attach image.)
help, please ????? ???????????
Answers
Exponential
Exponential
Linear
Linear
Non
Brainliest pls!!!
HELPPPPPP :((( i am marking brainliest!
Answers
a) trapezoid
b) isosceles triangle
c) equilateral triangle
d) kite
Help please I will give brainliest fast please 15 points
Answers
Answer: 40/11 hours
Step-by-step explanation:
Since y represents the amount of time the car goes at 35 miles per hour, and it is given that the car spends no time at 35 miles per hour, y = 0.
We can plug y into the equation given to find x, which would be the time travelled at 55 miles per hour, or the total time in this case.
55x + 35*0 = 200
55x = 200
x = 200/55
x = 40/11 hours
what does b=. pls help
Answers
Answer:
Step-by-step explanation:
b=-13
can anyone help me please ?
Answers
In descending order of b powers means the term whose b has the greatest power comes first, followed by the nxt and the one with the lowest power be the last in that order
From is the powers of b in the expression are 3,6,4
Arranging this in descending (biggest to smallest)
= 6,4,3
Hence the expression in descending order of the powers of b is
4a2b6 -5b4 + 3ab3
1. In ∆MNO, what is the included side of <M and <O?
2. In ∆ABC, what is the included angle of sides AB and AC?
Answers
Answers:
Segment MOAngle A====================================================
Explanation:
The included side between two angles is simply the segment with the endpoints mentioned. So we involve endpoints M and O to form segment MO. This is the same as saying segment OM. The order doesn't matter.The angle between two sides involves the shared letter. For sides AB and AC, that shared common letter is A. Therefore, angle A is the included angle between the sides. We can refer to it as angle BAC or angle CAB, but angle A should suffice as a name assuming there aren't any other letters as part of the diagram.Laura goes to a bank and opens a new account . She deposits $5,500. • The bank pays 1.6% interest compounded annually on this account • Laura makes no additional deposits or withdrawals. Which amount is the closest to the account balance at the end of 4 years? O A.$5,852.00
B. $5,860.53
C.$5,940.00
D.$5,954.31 $
Answers
Answer:
B
Step-by-step explanation:
formula= principal (1+(rate÷100))^number of years
5500(1+(1.6÷100))^4
5500 (1+0.016)^4
5500(1.016)^4
5500 (1.06555245)
5,860.53
$5,860.53
A student has an average score of 90 on four tests. If the student scored 88, 96 and 92 on the first three tests. What was the students score on the fourth tests
Answers
Answer:
84
Step-by-step explanation:
(92 + 96 + 88 + x) ÷ 4 = 90
92 + 96 + 88 + x/4 = 90
276 + x/4 = 90
(276 + x) × 4/4 = 90 × 4
276 + x = 360
x = 360 - 276
x = 84
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY
find all the zeros of the equation y=x^4+3x^3+x^2-12x-20
Answers
Answer:
x = 2, -2
explanation:
[tex]\sf y=x^4+3x^3+x^2-12x-20[/tex]
Find a factor for this equation:
-5 < x < 5
-------------
f(-3) = 25
f(-2) = 0
f(-1) = -9
f(0) = -20
f(1) = -27
f(2) = 0
f(3) = 115
Hence found that ( x -2) and ( x + 2) are the factor of the following equation.
Divide both by the following equation:
[tex]\sf \rightarrow \dfrac{x^4+3x^3+x^2-12x-20}{\left(x-2\right)\left(x+2\right)}[/tex]
[tex]\sf \rightarrow \dfrac{\left(x-2\right)\left(x+2\right)\left(x^2+3x+5\right)}{\left(x-2\right)\left(x+2\right)}[/tex]
[tex]\sf \rightarrow x^2+3x+5[/tex]
Using quadratic formula: [tex]\sf x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]
[tex]\sf \hookrightarrow x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}[/tex]
[tex]\hookrightarrow x=-\dfrac{3}{2}+i\dfrac{\sqrt{11}}{2},\:x=-\dfrac{3}{2}-i\dfrac{\sqrt{11}}{2}[/tex]
Thus the zero's of the function are:
x = 2, -2
Answer:
[tex]x=2, x=-2[/tex]; [tex]\frac{-3\pm i\sqrt{11}}{2} \in \mathbb{C}[/tex]
Step-by-step explanation:
Zeroes are found by setting the RHS = 0.
Since the quantity [tex]x^4+3x^3+x^2-12x-20[/tex] is a 4th degree polynomial there isn't a formula that gives us the solution, so we're stuck having to divide: to do so we make THE LIST: you list the divisors of the constant term without its sign (20: 1,2,4,5,10,20), the divisor of the lead coefficient (1), and you divide the first by the second in any possible way, adding a plus or minus:
[tex]\pm1, \pm2, \pm4, \pm5,\pm10,\pm20[/tex]. At this point you just have to check, replacing each one in the equation until you find two values that work (why two? You need to lower the degree of the polynomial by two, if you found only one you'd be stuck with a third degree equation which doesn't have an "easy" solving formula).
After some adding and multiplying you find that both 2 and -2 make the expression to zero. At this point you have two options
First is to divide the given expression by[tex](x-2)(x-2)=(x^2-4)[/tex] or, as I did in the image, notice that you will end up with a 2nd degree polynomial, whose coefficient you find by multiplying and confronting with the original equation.
Either way, you will end up with
[tex](x+2)(x-2)(x^2+3x+5)=0[/tex]
First two factors will give [tex]x=-2; x=2[/tex] respectively, while the third term has no real solutions (it still offers a pair of solutions in [tex]\mathbb{C}[/tex] which I'll add for the sake of completeness, but you're most likely required to look for real solutions only).
Helpppp!!!!!! Pleaseeeee!!!!!!!!!
Answers
Answer:
56 meters
Step-by-step explanation:
5+5+5+11+7+16+7 = 56
Answer:
Should be 56 m
Step-by-step explanation:
5+7+16+7+11+5+5 = 56 m
I need help asap!!!!!!!
Answers
Answer:
Step-by-step explanation:
Hurry please!
What is the slope of a line perpendicular to the line whose equation is x – 3y = 27.
Fully simplify your answer.
Answers
Answer:
So a line perpendicular to this equation would be any line with a slope of -3/4 (the negative reciprocal of the slope)
Step-by-step explanation:
First convert the original equation into y = form to find the slope.
Subtract 4x on both sides leaving -3y = -27 - 4x
This leaves y = (-27 - 4x)/(-3)
You can divide both -27 and -4x by -3 individually to get 9 and 4/3 respectively
This makes your equation y = 9 + (4/3)x
Whenever an equation is in y = mx + b form, the 'm' represents the slope. In this case the slope is 4/3.
The prices of consumer goods do not always exactly follow the CPI. The following chart shows several consumer items, along with their respective prices in 1983 and today. Item Price in 1983 ($) Current Price ($) Shower curtain 8. 85 15. 66 Floor rug 71. 25 119. 75 T-shirt 13. 95 23. 99 Oscillating fan 22. 75 37. 50 Using the prices shown on this chart, which of the following is a reasonable estimate of the current CPI? a. 164 b. 170 c. 185 d. 199.
Answers
The reasonable estimate of the current customer price index is 195. The option B is the correct option.
Customer price indexCustomer price index is the price index which measures the weight average of price of basket of customers goods or services.
It can be given as,
[tex]\rm CPI_t=\dfrac{C_t}{C_0}\times 100[/tex]
Here [tex]\rm C_t[/tex] is the cost of market basket in current period and [tex]\rm C_0[/tex] is the cost of market basket in the base period.
Cost of market basket in current period is
[tex]\rm C_t=15.66+119.75+23.99+37.50\\\\C_t=196.9[/tex]
Cost of market basket in 1983 is,
[tex]\rm C_0=8.85+71.25+13.95+22.7\\\\C_0=116.8[/tex]
Substitute all the values in the formula
[tex]\rm CPI_t=\dfrac{C_t}{C_0}\times 100\\\\\rm CPI_t=\dfrac{196.9}{116.8}\times 100\\\\\rm CPI_t=1.685\times 100 \\\\ CPI_t=168.5\\\\\rm CPI_t= 170 \ \rm approx[/tex]
Thus the value of current CPI is 168.5 which is near about the 170.
Hence, the reasonable estimate of the current customer price index is 195. The option B is the correct option.
Learn more about the customer price index here;
https://brainly.com/question/25495502
pls help asap. i hate these questions
Answers
Answer:
5. 8
6. 5
7. 7
8. 6
9. 3
10. 4
Step-by-step explanation:
The unknown number is the the larger number divided by 10.
Like in #5 : 80 ÷ 10 = 8
please help quickly!! will give branliest
Answers
Answer:
10
Step-by-step explanation:
hope this helped have a nice day
I NEED THE ANSWER PLEASE I DONT UNDERSTAND I JUST NEED THE ANSWER FOR 23,21,18
Answers
Step-by-step explanation:
follow the picture uploaded. everythinh has been solves systematically
find the value of x If necessary, you may learn what the markings on a figure indicate.
Answers
Answer:
x=36°
Step-by-step explanation:
Find the answer with the theorems related to isosceles triangle and the exterior angle theorem
2x – 20 < -14 please help i have to find the inequality and graph the solution
Answers
Answer:
x < 3
Step-by-step explanation:
Step 1: Add 20 to both sides.
[tex]2x-20+20 < -14+20[/tex] [tex]2x < 6[/tex]Step 2: Divide both sides by 2.
[tex]2x/2 < 6/2[/tex] [tex]x < 3[/tex]Ira can use the greatest common factor to rewrite 75+30 as
(5+
).
Answers
Answer:
Step-by-step explanation:
15(5+2) is the Answer
The greatest common factor to rewrite 75+30 as 15(5+2)
What is GCD?Greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
An expression is a combination of numbers, variables and operators.
The given expression is 75+30.
By using distributive law we can find this.
Let us find factors of 75 and 30.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 30 are 1, 3, 5, 9, 15, 45
Their GCF is 15.
To get 75, we will multiply 15 by 5.
To get 30, we will multiply 15 by 2.
By using distributive property
75+30 can be splitted to factors as
15(5+2)
Hence the greatest common factor to rewrite 75+30 as 15(5+2)
To learn more on GCD click:
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what is the measure of
Answers
Answer: B
Step-by-step explanation:
lan is going bowling. The shoe rental is $5.00 for
the evening. Each game costs $3.00. He only has
$20 in his pocket. How many games can he play?
Let y represent the number of games in this
inequality:
$5.00 + 3y <$20
Ay 25
BY
C.y = 5
D.y > 5
Answers
Answer:
choose the last answer D I did this quiz and i am foolproof it is correct
Step-by-step explanation:
Answer:
he can play 5 more games.
Step-by-step explanation:
he has $20 and he uses $5 for shoes so he has $15 left. each game costs $3 so 3x5 = 15