Answer:
8/(x + 2) - 4/(x + 6)
Step-by-step explanation:
4x + 40 = Ax + 6A + Bx + 2B
Equating coefficients of x
4 = A + B (1)
Equating constant terms:
40 = 6A + 2B (2)
Multiply equation (1) by -2:
-8 = -2A - 2B .. (3)
Add (2) and (3):
32 = 4A
A = 32/4
A = 8.
4 = 8 + B
B = 4 - 8
B = -4.
The decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].
What is partial fraction?The partial fraction is the result of writing a rational expression as the sum of two or more fractions.
According to the given question.
We have a partial fraction
[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A}{(x+2)} +\frac{B}{(x+6)}[/tex]
We have to decompose the above partial fraction in terms of x.
The above partial fraction can be written as
[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A(x+6)+B(x+2)}{(x+2)(x+6)}[/tex]
⇒[tex]4x+40 = A(x+6)+B(x+2)[/tex]
⇒[tex]4x + 40 = Ax + 6A + Bx + 2B[/tex]
⇒[tex]4x + 40 = x(A+B) +6A + 2B...(i)[/tex]
On comparing the coefficient of x and the constant terms.
[tex]A+B = 4..(ii)[/tex]
⇒[tex]A = 4 - B[/tex]
and, [tex]6A+2B = 40..(iii)[/tex]
⇒[tex]2(3A+B) = 40[/tex]
Substitute the value of A in (iii)
⇒[tex]2(3A+B) = 40[/tex]
⇒[tex]3A+B = 20[/tex]
⇒[tex]3(4-B)+B = 20[/tex]
⇒[tex]12 - 3B +B = 20[/tex]
⇒[tex]12 - 2B = 20[/tex]
⇒[tex]-2B = 8[/tex]
⇒[tex]B = -4[/tex]
So, [tex]A = 4-(-4) = 8[/tex]
Substitute the value of A and B in the given partial fraction.
⇒[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex]
Hence, the decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].
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Circle A has a radius of 9.0 cm. The shortest distance between B and C on the circle is 8.5 cm. What is the approximate area of the shaded portion of circle A?
30.0 cm²
38.25 cm²
56.5 cm²
254.5 cm²
Answer:
38.25 cm²
Step-by-step explanation:
We use the formula for the length of an arc to find the central angle of the sector of the circle.
Then we use the formula for the area of a sector of a circle to find the area.
Length of arc of circle of radius r:
[tex] s = \dfrac{n}{360^\circ}2 \pi r[/tex]
s = arc length
n = measure of the central angle of the sector
[tex] s = \dfrac{n}{360^\circ}2 \pi r[/tex]
[tex] 8.5~cm = \dfrac{n}{360^\circ}2 \pi \times 9.0~cm[/tex]
[tex] n = 54.1^\circ [/tex]
Area of sector of circle of radius r:
[tex] A = \dfrac{n}{360^\circ} \pi r^2[/tex]
A = area of sector of circle
n = measure of the central angle of the sector
[tex] A = \dfrac{54.1^\circ}{360^\circ} \pi (9.0~cm)^2[/tex]
[tex] A= 38.25~cm^2 [/tex]
Find the GCF for the set of numbers.
18, 36, and 60
Step-by-step explanation:
Factors of 36 are {1,2,3,4,6,9,12,18,36}
.
Factors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60}
Common factors are }1,2,3,4,6,12} .
greatest Common Factor is 12 .
line d has a slope of 7/3. line e is perpendicular to line d. what is the slope of line e?
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
Here we have the number:-
[tex]\boxed{\frac{7}{3}}[/tex]
Flop it over:-
[tex]\boxed{\frac{3}{7} }\longleftarrow\sf{the~numerator~and~denominator~switch~places}[/tex]
Change its sign:-
[tex]\boxed{-\frac{3}{7}}[/tex]
Hence, the slope of line e is:-
[tex]\bigstar{\boxed{\pmb{Slope=-\frac{3}{7}}}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
this is due today! please help and i will give 50 points
Answer:
D) 154 ft²
Step-by-step explanation:
Formula
Area of a rectangle = width x length
We only need to calculate the area of the walls.
There are two pairs of walls with the following dimensions:
5 ft x 7 ft6 ft x 7 ftTherefore, area to paint = 2(5 x 7) + 2(6 x 7)
= 70 + 84
= 154 ft²
Bottom cube 's LSA need to be counted
H=7ftL=6B=5LSA:
2H(L+B)2(7)(5+6)14(11)154ft²It is now 11:15 A.M. What time will it be in three quarters of an hour?
A) noon
B) 11:45 A.M.
C) 11:45 P.M.
D) midnigh
Answer:
Ur mom
Step-by-step explanation:
Ur mom JK here's the answer 11:45 A.M. because 15 + 15 + 15 = 45 15 is a quarter so yeah Bois is 11:45 A.M Good luck
Convert km into cm
10 points available
The ratio of the measures of the three angles in a triangle is 15:8:13. Find the measure of the three angles.
Answer: 75, 40, 65
Step-by-step explanation:
Let the angles measure 15x, 8x, and 13x.
Since the sum of the angles of a triangle is 180 degrees,
15x+8x+13x=180, meaning that x=5.
So, the angles are 15(5)=75 degrees, 8(5)=40 degrees, and 13(5)=65 degrees.
Find the side labeled x.
Answer:
4√3
Step-by-step explanation:
Hello!
This is a 30° 60° 90° because it has a 90° angle, a 30° angle, and the missing angle is 60° (sum of angles in a triangle is 180°). This triangle has special properties.
In a 30°-60°-90° triangle, the leg opposite 30° is always half the hypotenuse.
This means that the hypotenuse would be 2 times 4, or 8.
The leg opposite to 60° in a right triangle of this sort is the length of a leg multiplied by √3.
So the measure of x is 4√3.
An image is attached for your reference.
The value of side labeled x using Trigonometric ratio is [tex]{4}{\sqrt 3}[/tex].unit.
Given:
Angle = 30
Perpendicular or opposite side= 4
Using Trigonometric ratio
tan 30 = Opposite side / Adjacent side
Substituting Opposite side= 4 and Adjacent side = 4 in above ratio
So, tan 30 = 4 / x
As, the value of tan 30 = [tex]\dfrac{1}{\sqrt 3}[/tex] then
tan 30 = 4 / x
[tex]\dfrac{1}{\sqrt 3}[/tex] = [tex]\dfrac{4}{x}[/tex]
solving for x
x = [tex]{4}{\sqrt 3}[/tex]
Thus, the value of x is [tex]{4}{\sqrt 3}[/tex].
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Can someone help me pls
Answer:
The angle of KLM is 50°
Step-by-step explanation:
Used protractor
Answer:
∠ KLM ≈ 33.7°
Step-by-step explanation:
using Pythagoras' identity in right triangle JKM
KM² = JK² + JM² = 7² + 4.5² = 49 + 20.25 = 69.25 ( take square root of both sides )
KM = [tex]\sqrt{69.25}[/tex] ≈ 8.322 cm
using the sine ratio in right triangle KLM
sin KLM = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{KM}{LM}[/tex] = [tex]\frac{8.322}{15}[/tex] , then
∠ KLM = [tex]sin^{-1}[/tex] ( [tex]\frac{8.322}{15}[/tex] ) ≈ 33.7° ( to 3 significant figures )
Mr. Wilson bought a bag of birdseed and put half of it in his bird feeder. He split the other half equally among his 4 pet birds. How much of the bag did each pet bird get?
Answer:
each pet bird got 1/8 of the bag of birdseed
Step-by-step explanation:
the easiest way to do this is to divide the bag into eighths. if you divide the bag into eighths, 4/8 of the bag, being half, goes into the bird feeder. the other 4/8 of the bag is divided among Mr. Wilson's four pet birds, leaving each bird to get 1/4 of the bag when split evenly.
hope this helps
3.) Jan wants a bunch of balloons for her birthday party. She chooses 10 red, 12 blue, 8 green and 9 yellow balloons. Her mom says she can only have 60% of them. Jan doesn't care what colors she has. How many balloons does she end up with?
Answer:
Lets break this down
The question asks for “How many balloons does she end up with”?
A important fact is that Jan doesn’t care what color she has.
So using this we can disregard the colors.
She is only allowed to have 60 percent of all the balloons she choosed.
So lets add them.
10 + 12 +8 + 9 = 39
She chose 39 balloons in total.
Since she doesn’t care about the color we can jsut find 60 percent of 39.
In order to find this we just multiply 60% of 39.
Percentage means out of a hundred so 60 percent is 60 out of a hundred or in this age 60/100.
Now 60/100 is basically 0.6
So we multiply 39 by 0.6
23.4 is the answer.
Now you can’t have .4 of a balloon so we jsut round down for any decimal in this case.
23.4 is 23 now.
So 23 balloons is the amount of balloons Jan ends up with
The leg lengths of a right triangle are 14 in and 26 in. What is the length of the missing side?
Answer:
29.5
Step-by-step explanation:
14sq + 26sq = 872
sq root of 872 is 29.5
Make a story problem about conversion of measurements.
Make a story problem about conversion of measurements.
ANSWERCairo wants to join the basketball team, so he tried out and filled up a form. But he realized that the form wanted to get his height in "cm or centimeters", the problem is that he only knows his height in "feet" which is 6'5.
Since he didn't know how to convert centimeters to feet, he asked his friend Tyga and Tyga easily converted his height into cm. Cairo then filled up the form again and wrote "195.58 cm" in his official height--the equivalent of 6'5 in centimeter measurement.
What is the answer to u/5+6=2 with work shown?
A ________ is a set of points that extends infinitely in both directions.
Answer:
line
Step-by-step explanation:
A line is a set of points that extends infinitely in both directions.
Compare using < , > , or =-1.75 and -1 3/4
Answer:
1.75 = 1 3/4
Step-by-step explanation:
1 3/4 = 1.75
Answer:
=
Step-by-step explanation:
-1.75 is the same as -1 3/4
The enrollment at Allenton High School is expected to decrease by 5% each year.
There are currently 720 students at the high school. The following function can be used to approximate the
number of students who will be enrolled at Allenton High School in tyears from now.
ald) = 720(1 – 0.05)
A. In how many years will the high school have approximately 450 students?
Round your solution to the nearest hundredth of a year. Show your work.
Answer:
around 8 or 9 years
Step-by-step explanation:
1. Find the common ratio of the geometric sequence
6, 30, 150, 750, ....
Answer:
Each number multiplies by 5
Step-by-step explanation:
6x5 = 30
30 x 5 = 150
150 x 5 = 750 etc.
A field is shaped like the diagram below.
It is a rectangle with semicircles at two ends. There is a running track around the perimeter of the field.
(a)
100 m
64 m
What is the circumference of the track?
Step-by-step explanation:
must be at least 100m, and the rectangle width, also known as twice the circle radius, must be less than or equal to 60m. That would make for a relatively normal-shaped track
The perimeter of the track is 464 m
What is a perimeter?The length around an object is called its perimeter.
Given that, a rectangle with semicircles at two ends. there is a running track around the perimeter of the field.
The dimension of the rectangle are 100 m and 64 m
The distance between the outer an dthe inner track is 10 m,
The diameter of the outer semicircles is 64+10+10 = 84 m
Therefore, is radius = 42 m
The perimeter of the outer semicircle = 2×π×radius
= 2×3.14×42
= 264 m
The length of the two straight lines = 100 + 100 = 200 m
Therefore, total perimeter of the whole track = 200+264 =464 m
Hence, the perimeter of the track is 464 m
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The figure for this question is:
Which of the following is an expression
A. 7x = 4
B. 7 = x = 4
C. 7 - x
D. 7n - 3 = 32
Answer:
c 7-x
Step-by-step explanation:
Express the cubed root of a cubed root of the cubed root of 2 with a rational index.
Answer:
[tex]2^{\frac{1}{27} }[/tex]
Step-by-step explanation:
→ Write in number format
∛∛∛2
→ Rewrite
[tex]2^{\frac{1}{3} } *2^{\frac{1}{3} } *2^{\frac{1}{3} }[/tex]
→ Simplify
[tex]2^{\frac{1}{27} }[/tex]
Answer:
2^(1/27).
Step-by-step explanation:
That would be [(2)^1/3)^1/3]^1/3
= 2^1/3*1/3*1/3)
= 2^(1/27)
(100 POINTS AND BRAINLIEST) 1 Question - Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work.
Question 2 - (05.03)Lisa has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area of the polygon. Be sure to show all your work and explain your answer. (Picture is for question 2)
Answer:
I don't know I'm trying my best and I'm late
Step-by-step explanation:
It’s a 4 digit number. The tens are double the ones. The thousands are double the tens. The sum of the digit is 19
URGENT
what is the slope of line AB
Answer:
2,3
Step-by-step explanation:
you count up 2,then count over three
solve pls brainliest
Answer:
63
Step-by-step explanation:
Multiply each side by 9
4y=252
Divide by 4
y=63
Answer:
y= 63
Step-by-step explanation:
The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount. The half-life of the radioactive gas radon is approximately 2.8 days. The initial amount of radon used in an experiment is 74 grams. If N represents the number of grams of radon remaining t days after the start of the experiment,
Answer:
N = 74(1/2)^(t/2.8)
Step-by-step explanation:
The exponential function expressing a half-life relation can be written ...
amount = (initial amount) × (1/2)^(t/(half-life))
For the numbers given in this problem, this is ...
N = 74(1/2)^(t/2.8)
__
Some folks like to express these relations in the form ...
N = 74e^(-kt)
In this form, the value of k is ...
k = ln(2)/(half-life) ≈ 0.693147/2.8 ≈ 0.24755
N = 74e^(-0.24755t)
[tex]\sqrt{180}=a\sqrt{b}[/tex]
please help
the measures of the angles in a triangle are in a ratio 1:5:6. find the measures of the angles
Answer:
The required angles are 15, 75 and 90
Step-by-step explanation:
1x + 5x+ 6x = 180
or 12x = 180
180 ÷ 12 = 15
hence,
15, 75, 90.
A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is23ft ft?
Answer:
Step-by-step explanation:
Simply put, it is similar to finding the area of a circle.
Therefore, a=pi*r^2
a=pi*23^2
a=529pi
a=1661.9 ft^2
How many different triangles can you make if you are
given these three measurements for angles?
Answer:
1
Step-by-step explanation:
If you're given 3 side lengths and 3 measurements of the angles , there's only one triangle that you may draw. You also can draw distinctive triangles given 3 aspect lengths or aspect lengths and the blanketed distinctive measure.
Answer:
1
Step-by-step explanation:
if you are given 3 measurements you are kind of stuck making that one triangle, no matter which way you shape it you have to have those three angles so you can't make more than that one triangle