Answers
Answer:
[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}= \frac{(x+3)}{x}[/tex]
[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2} = \frac{3x + 1}{x^2}[/tex]
[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}=-\frac{5}{2x}[/tex]
[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x} = \frac{-(x-3)^2}{25}[/tex]
[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}= x +1[/tex]
[tex]\frac{9x^2 + 3x}{6x^2} = \frac{3x + 1}{2x}[/tex]
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x} = 3x[/tex]
Step-by-step explanation:
Required
Simplify
Solving (1):
[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}[/tex]
Factorize the numerator and the denominator
[tex]\frac{x^2(x + 2) -9(x+2)}{x(x^2-x-6)}[/tex]
Factor out x+2 at the numerator
[tex]\frac{(x^2 -9)(x+2)}{x(x^2-x-6)}[/tex]
Express x^2 - 9 as difference of two squares
[tex]\frac{(x^2 -3^2)(x+2)}{x(x^2-x-6)}[/tex]
[tex]\frac{(x -3)(x+3)(x+2)}{x(x^2-x-6)}[/tex]
Expand the denominator
[tex]\frac{(x -3)(x+3)(x+2)}{x(x^2-3x+2x-6)}[/tex]
Factorize
[tex]\frac{(x -3)(x+3)(x+2)}{x(x(x-3)+2(x-3))}[/tex]
[tex]\frac{(x -3)(x+3)(x+2)}{x(x+2)(x-3)}[/tex]
Cancel out same factors
[tex]\frac{(x+3)}{x}[/tex]
Hence:
[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}= \frac{(x+3)}{x}[/tex]
Solving (2):
[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2}[/tex]
Expand the numerator and factorize the denominator
[tex]\frac{3x^2 - 6x + x - 2}{x^2(x- 2)}[/tex]
Factorize the numerator
[tex]\frac{3x(x - 2) + 1(x - 2)}{x^2(x- 2)}[/tex]
Factor out x - 2
[tex]\frac{(3x + 1)(x - 2)}{x^2(x- 2)}[/tex]
Cancel out x - 2
[tex]\frac{3x + 1}{x^2}[/tex]
Hence:
[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2} = \frac{3x + 1}{x^2}[/tex]
Solving (3):
[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}[/tex]
Express x^2 - 9 as difference of two squares
[tex]\frac{6 - 2x}{x^2 - 3^2} * \frac{15 + 5x}{4x}[/tex]
Factorize all:
[tex]\frac{2(3 - x)}{(x- 3)(x+3)} * \frac{5(3 + x)}{2(2x)}[/tex]
Cancel out x + 3 and 3 + x
[tex]\frac{2(3 - x)}{(x- 3)} * \frac{5}{2(2x)}[/tex]
[tex]\frac{3 - x}{x- 3} * \frac{5}{2x}[/tex]
Express [tex]3 - x[/tex] as [tex]-(x - 3)[/tex]
[tex]\frac{-(x-3)}{x- 3} * \frac{5}{2x}\\[/tex]
[tex]-1 * \frac{5}{2x}[/tex]
[tex]-\frac{5}{2x}[/tex]
Hence:
[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}=-\frac{5}{2x}[/tex]
Solving (4):
[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x}[/tex]
Expand x^2 - 6x + 9 and factorize 5x - 15
[tex]\frac{x^2 -3x -3x+ 9}{5(x - 3)} / \frac{5}{3-x}[/tex]
Factorize
[tex]\frac{x(x -3) -3(x-3)}{5(x - 3)} / \frac{5}{3-x}[/tex]
[tex]\frac{(x -3)(x-3)}{5(x - 3)} / \frac{5}{3-x}[/tex]
Cancel out x - 3
[tex]\frac{(x -3)}{5} / \frac{5}{3-x}[/tex]
Change / to *
[tex]\frac{(x -3)}{5} * \frac{3-x}{5}[/tex]
Express [tex]3 - x[/tex] as [tex]-(x - 3)[/tex]
[tex]\frac{(x -3)}{5} * \frac{-(x-3)}{5}[/tex]
[tex]\frac{-(x-3)(x -3)}{5*5}[/tex]
[tex]\frac{-(x-3)^2}{25}[/tex]
Hence:
[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x} = \frac{-(x-3)^2}{25}[/tex]
Solving (5):
[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}[/tex]
Factorize the numerator and expand the denominator
[tex]\frac{x^2(x - 1) -1(x - 1)}{x^2 - x-x+1}[/tex]
Factor out x - 1 at the numerator and factorize the denominator
[tex]\frac{(x^2 - 1)(x - 1)}{x(x -1)- 1(x-1)}[/tex]
Express x^2 - 1 as difference of two squares and factor out x - 1 at the denominator
[tex]\frac{(x +1)(x-1)(x - 1)}{(x -1)(x-1)}[/tex]
[tex]x +1[/tex]
Hence:
[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}= x +1[/tex]
Solving (6):
[tex]\frac{9x^2 + 3x}{6x^2}[/tex]
Factorize:
[tex]\frac{3x(3x + 1)}{3x(2x)}[/tex]
Divide by 3x
[tex]\frac{3x + 1}{2x}[/tex]
Hence:
[tex]\frac{9x^2 + 3x}{6x^2} = \frac{3x + 1}{2x}[/tex]
Solving (7):
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x}[/tex]
Change / to *
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} * \frac{x}{x-1}[/tex]
Expand
[tex]\frac{x^2-2x-x+2}{4x} * \frac{12x^2}{x^2 - 2x} * \frac{x}{x-1}[/tex]
Factorize
[tex]\frac{x(x-2)-1(x-2)}{4x} * \frac{12x^2}{x(x - 2)} * \frac{x}{x-1}[/tex]
[tex]\frac{(x-1)(x-2)}{4x} * \frac{12x^2}{x(x - 2)} * \frac{x}{x-1}[/tex]
Cancel out x - 2 and x - 1
[tex]\frac{1}{4x} * \frac{12x^2}{x} * \frac{x}{1}[/tex]
Cancel out x
[tex]\frac{1}{4x} * \frac{12x^2}{1} * \frac{1}{1}[/tex]
[tex]\frac{12x^2}{4x}[/tex]
[tex]3x[/tex]
Hence:
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x} = 3x[/tex]
Related Questions
Sam owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007?
Answers
Answer:
370 stores
Step-by-step explanation:
Given data
initial number of stores P= 200
r= 8%
t= 1999-2007= 8 years
Let us apply the compound interest expression to find the final amount of stores
A= P(1+r)^t
A= 200(1+0.08)^8
A= 200(1.08)^8
A= 200*1.85
A=370
Hence the number of stores in 2007 is 370 stores
Find the length of the third side.if necessary, round to the nearest tenth 24 18
Answers
Answer:
30
Step-by-step explanation:
\text{Legs: 18, 24}\hspace{20px}\text{Hypotenuse: ?}
Legs: 18, 24Hypotenuse: ?
a^{2}+b^{2}=
a
2
+b
2
=
\,\,c^{2}
c
2
The Pythagorean Theorem
18^{2}+24^{2}=
18
2
+24
2
=
\,\,c^{2}
c
2
Plug in. c is the hypotenuse.
324+576=
324+576=
\,\,c^{2}
c
2
Square the numbers.
900=
900=
\,\,c^{2}
c
2
Add.
\sqrt{900}=
900
=
\,\,\sqrt{c^{2}}
c
2
Square root both sides.
30=
30=
\,\,c
c
The hypotenuse.
I generally need help
Answers
Answer:
24 units²
Step-by-step explanation:
4(12)/2=24
Point s and point t are located at -6, 13 and 8, 13 on the coordinate plane what is the distance between the two points
Answers
Answer:
[tex]14[/tex] units
Step-by-step explanation:
Since both points have the same y-coordinate, we can calculate the distance between them by taking the absolute difference of their x-coordinates. Therefore, the distance between them is [tex]|-6-8|=|-14|=14[/tex] units. Hope this helps!
Mrs. Safar purchases a bedroom set for $1600. Five percent sales tax is added to the purchase price and she must also pay a $60 delivery fee. If Mrs. Safar pays for the total cost of the bedroom set in 12 equal payments, how much is each payment? MAFS.7.EE.2.3
Answers
1600+5%(80)+60=$1740:12=145
9.
The equation a = 640s gives the relationship between s square miles and a acres. Pam owns 7.5 square miles of farmland. How many acres does she own?
4,800 acres
11.72 acres
1.17 acres
480 acres
Answers
[tex]a = 640s[/tex]
[tex]a = 640(7.5)[/tex]
[tex]a = 4800 \: [/tex]
She owns 4800 acres.
Answer:
4,800 acres
Step-by-step explanation:
Which expression is equal to 4(2+3)
Question 1 options:
A.4+5
B.8+12
C.2+12
D. 8+3
Answers
Answer:
B, 8+12
Step-by-step explanation:
2 + 3 is 5, 4 × 5 = 20
Therefore the only option which equals 20 is B.
Solve for x. 3 - √x = 0
Answers
Answer:
x = 9
Step-by-step explanation:
3 - √x = 0
Subtract 3 from both sides of the equation
3 - 3 - √x = 0 - 3
-√x = -3
Divide both sides by -1
-√x / -1 = -3 / -1
√x = 3
Take the square of both sides
(√x) ² = 3²
X = 9
Solve for G
6G = -72
(show your work)
Answers
Answer:
-12
Step-by-step explanation:
6G = -72
G = -72 / 6
G = -12
The spinner below is spun. Find the probability,
P(D greater than 1)
What is the numerator for the probability?
What is the denominator for the probability?
Answers
Answer:
5 - numerator
6 - denominator
please help me please do them all its just thrree
Answers
10+50m+20, 30+50m
8a+a^2+3a, 11a+a^2
Step-by-step explanation:
hope this helps. I worked out then posted.
Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x^3 + 2.
include the average rate of change in your answer.
Answers
Step-by-step explanation:
step 1. we will denote the average rate of change as r.
step 2. r = (f(5) - f(3))/(5 - 3)
step 3. r = (375 - 81)/2
step 4. r = 294/2
step 5. r = 147.
step 6. note: this is just like finding m. m = (y2 - y1)/(x2 - x1)
umm pls help me ik how to do it but not sure on this specific one
Answers
9514 1404 393
Answer:
-8, +9
Step-by-step explanation:
You need factors of (6)(-12) = -72 that have a sum of +1.
From your knowledge of multiplication tables, you know that 72 = 8·9. Then -72 = (-8)(9), and those two factors have a sum of +1.
6x^2 +x -12
= 6x^2 +9x -8x -12
= 3x(2x +3) -4(2x +3)
= (3x -4)(2x +3)
Just want answers pls/brainliest if correct !
Answers
Answer:
If AB is 16, then AD is 8.
If AB = 12 and CB = 10, then the height of the triangle is 8.
Step-by-step explanation:
AD = [tex]\frac{AB}{2}[/tex], so AD is equal to 8.
Use the Pythagorean Theorem, [tex]\sqrt{10^{2} - 6^{2}}[/tex] equals 8, so the height of the triangle is equal to 8.
What is 4x^2+14x+6=9x^2-6x+1 answer
Answers
Answer:
20x+5=5x^2
Step-by-step explanation:
For this type of albreic question you want to simplify
4x^2+14x+6=9x^2-6x+1
first you take the common integers(That might not be the right word)
4x^2+14x+6=9x^2-6x+1
+6x -1 -4x^2
20x+5=5x^2
You cannot simplify any further
A sphere has a radius of 1 inch. What is the volume of the sphere, in cubic inches?
Answers
Answer:
V≈ 4.19in³
Step-by-step explanation:
V=4/3 π r³= 4/3 ·π· 1³ ≈4.18879in³
8/9i+12=2/9i+34 (solve for a)
Answers
Answer: I=33, O and when you said solve for a I don’t see a, I see i and that all...if you know what I mean
Step-by-step explanation: hope this help
Susanna's family traveled 5 7 of the distance to her grandmother's house on Saturday. They traveled 1 2 of the remaining distance on Sunday. What fraction of the total distance to her grandmother's house was traveled on Sunday?
Answers
Answer:
1/7
Step-by-step explanation:
Please write these fractions as 5/7 and 1/2. 5 7 and 1 2 are incomplete and confusing.
On Saturday the distance traveled was 5/7 of the total distance.
2/7 of that total was left for Sunday. Half of 2/7 is 1/7.
1/7 of the total distance was traveled on Sunday.
In the figure above, PQRS is a circle. If PQT and SRT
are straight lines, find the value of x.
Answers
Given:
PQRS is a circle, PQT and SRT are straight lines.
To find:
The value of x.
Solution:
Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.
We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.
[tex]m\angle SPQ+m\angle QRS=180^\circ[/tex]
[tex]81^\circ+m\angle QRS=180^\circ[/tex]
[tex]m\angle QRS=180^\circ-81^\circ[/tex]
[tex]m\angle QRS=99^\circ[/tex]
Now, SRT is a straight line.
[tex]m\angle QRT+m\angle QRS=180^\circ[/tex] (Linear pair)
[tex]m\angle QRT+99^\circ=180^\circ[/tex]
[tex]m\angle QRT=180^\circ-99^\circ[/tex]
[tex]m\angle QRT=81^\circ[/tex] ...(i)
According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.
Using exterior angle theorem in triangle QRT, we get
[tex]m\angle PQR=m\angle QRT+m\angle QTR[/tex]
[tex]x=81^\circ+22^\circ[/tex]
[tex]x=103^\circ[/tex]
Therefore, the value of x is 103 degrees.
Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?
Answers
Out of the 96 customers at Jamie's boutique, 28 wore a size medium.
What is the probability that a randomly selected customer wore a size medium?
Answers
Answer:
7/24
Step-by-step explanation:
The probability would be 28/96, but we can simplify this fraction:
Divide 2 on both sides:
14/48
Divide 2 again:
7/24
So 7/24 is your answer! :) I hope I helped!
find the inequality of 3x-2÷4+3≥12
Answers
Answer:
x + 5 = ,3
Step-by-step explanation:
x+5-5= +3-5
x= -2
Which scenario could be represented by the value −8 ? Select each correct answer. A puppy gains 8 pounds. The temperature is 8 degrees below 0. The elevation of a hot air balloon is 8 meters. A student's class average decreases by 8 points.
plzz help ill give brainliest
Answers
Answer:
- The temperature is 8 degrees below 0
- A student's class average decreases by 8 points.
Answer:
The temp is 8 degrees below 0, a student's class average decreases by 8 points
Step-by-step explanation:
a puppy gaining 8 pounds is positive
the temp is 8 degrees below 0 which is negative
the elevation of a hot air balloon is 8 meters above the ground
A student's class average decreases by 8 points = negative
The value -8 is negative and it doesn't say you have to only select one answer
I need help it's due by 7
Answers
Answer:
Step-by-step explanation:
w=204.8
Answer:
204.8
Step-by-step explanation:
8x25.6=204.8
DOuble Check:
204.8 divided by 25.6=8
HELP! WILL GIVE BRAINLY!!! Find the volume of a cylinder with height = 10ft and the diameter of the base circle is 12ft.
Answers
Answer:
About 1,130.4 Cubic Feet
(My previous answer was a mistake. It has now been corrected)
Step-by-step explanation:
The Volume of a cylinder = Height * Pi * Radius^2
The radius is half the diameter, so 12 ÷ 2 = 6
Pi rounded to the hundredth place is 3.14.
Volume = 10 * 3.14 * 6^2 = 1,130.4
Therefore the Volume is about 1,130.4 cubic feet.
Answer:
Exact Volume = 360pi cubic feet
Approximate Volume = 1130.4 cubic feet
The approximate volume is found when you use pi = 3.14; use more decimal digits of pi to get a more accurate value.
===========================================================
Explanation:
The volume of a cylinder is found by the formula
V = pi*r^2*h
where,
pi = 3.14 approximatelyr = radius = 6 ft, since the radius is half the diameter.h = height = 10 ftSo,
V = pi*r^2*h
V = pi*6^2*10
V = pi*36*10
V = pi*360
V = 360pi ........... exact volume in terms of pi
V = 360*3.14
V = 1130.4 ......... approximate volume if you use pi = 3.14
The units of the volume are in "cubic feet" which we can abbreviate to "ft^3". Think of a 1 ft by 1 ft by 1 ft cube. The volume would be 1*1*1 = 1 cubic foot. So basically having a volume of roughly 1130 cubic feet means we need this many cubic blocks to form the cylinder (some of the blocks will be cut up to be able to fit).
What are all t possible names for these?? Help plz
Answers
Answer:
13.....square
14....parallelogram
15....rhombus
16....trapezium
17...kite
18....rectangle
Answer:
#13 is a square, #14 is a rectangle, #15 is a rhombus, #16 is a trapezoid, #17 is a qaudrilateral, and #18 is a rectangle also.
Hope this helps :)
What is the value of so that −10and 10are both solutions of 2−=70
Answers
Answer:I think 7
Step-by-step explanation:
Simplify The Following: -4h + 22 + 6h -7
Answers
Answer:
2h + 15
Step-by-step explanation:
-4h + 22 + 6h -7
2h + 22 - 7
2h + 15
The equation  is written in point-slope form. What is the equation written in slope-intercept form?    
Answers
Answer:y+6 = 1/3 (x, -9)
Step-by-step explanation:The equation y+6 = 1/3 (x, -9) is written in point-slope form. What is the equation written in slope-intercept form? The point-slope form of a line that has a slope of -2 and passes through point (5, -2) is shown below. ... The equation y - 2/3 = -2 (x - 1/4) is written in point-slope form.
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?
A. -1/3
B. 3
C. 5
D. 6
E. -9
Answers
Answer:
C. 5
Step-by-step explanation:
plato
Answer:
C. 5
Hope this helps!
Step-by-step explanation:
