Answers
Solution given to both questions below, they reveal the given answers.
The steps are self-explanatory, let me know if anything is unclear.
Question 24[tex]\cfrac{2}{(x-2)(x-3)} +\cfrac{2}{(x-1)(3-x)}+\cfrac{1}{(1-x)(2-x)} =[/tex][tex]\cfrac{2}{(x-2)(x-3)} -\cfrac{2}{(x-1)(x-3)}+\cfrac{1}{(x-1)(x-2)} =[/tex][tex]\cfrac{2(x-1)}{(x-1)(x-2)(x-3)} -\cfrac{2(x-2)}{(x-1)(x-2)(x-3)}+\cfrac{x-3}{(x-1)(x-2)(x-3)} =[/tex][tex]\cfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)} =[/tex][tex]\cfrac{x-1}{(x-1)(x-2)(x-3)} =[/tex][tex]\cfrac{1}{(x-2)(x-3)}[/tex]Question 25[tex](4x - 1)(x + 2) = 2 + 7x[/tex][tex]4x^2+8x-x-2=2+7x[/tex][tex]4x^2+7x-2=2+7x[/tex][tex]4x^2=4[/tex][tex]x^2=1[/tex][tex]x=\sqrt{1}[/tex][tex]x=\pm1[/tex]Answer:
[tex]\textsf{24.} \quad \dfrac{1}{(x-2)(x-3)}[/tex]
[tex]\textsf{25.} \quad x=1, \quad x=-1[/tex]
Step-by-step explanation:
Question 24Given expression:
[tex]\dfrac{2}{(x-2)(x-3)}+\dfrac{2}{(x-1)(3-x)}+\dfrac{1}{(1-x)(2-x)}[/tex]
When adding rationals with different denominators, make the denominators the same by finding the least common denominator.
Create a common denominator by:
[tex]\textsf{Multiplying the first fraction by $\dfrac{x-1}{x-1}$}.[/tex]
[tex]\textsf{Multiplying the second fraction by $\dfrac{-(x-2)}{-(x-2)}$}.[/tex]
[tex]\textsf{Multiplying the third fraction by $\dfrac{x-3}{x-3}$}.[/tex]
[tex]\implies \dfrac{2}{(x-2)(x-3)} \cdot \dfrac{x-1}{x-1}+\dfrac{2}{(x-1)(3-x)}\cdot \dfrac{-(x-2)}{-(x-2)}+\dfrac{1}{(1-x)(2-x)}\cdot \dfrac{x-3}{x-3}[/tex]
[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{-(x-1)(x-2)(3-x)}+\dfrac{x-3}{(1-x)(2-x)(x-3)}[/tex]
[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(-3-(-x))}+\dfrac{x-3}{(-(-1+x))(-(-2+x))(x-3)}[/tex]
[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(x-3)}+\dfrac{x-3}{(x-1)(x-2)(x-3)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{d}+\dfrac{b}{d}+\dfrac{c}{d}=\dfrac{a+b+c}{d}:[/tex]
[tex]\implies \dfrac{2(x-1)-2(x-2)+(x-3)}{(x-1)(x-2)(x-3)}[/tex]
Expand the numerator:
[tex]\implies \dfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)}[/tex]
[tex]\implies \dfrac{x-1}{(x-1)(x-2)(x-3)}[/tex]
Cancel the common factor (x - 1):
[tex]\implies \dfrac{1}{(x-2)(x-3)}[/tex]
Question 25Given equation:
[tex](4x-1)(x+2)=2+7x[/tex]
Expand the left side:
[tex]\implies 4x^2+7x-2=2+7x[/tex]
Subtract 7x from both sides:
[tex]\implies 4x^2+7x-2-7x=2+7x-7x[/tex]
[tex]\implies 4x^2-2=2[/tex]
Add 2 to both sides:
[tex]\implies 4x^2-2+2=2+2[/tex]
[tex]\implies 4x^2=4[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x^2}{4}=\dfrac{4}{4}[/tex]
[tex]\implies x^2=1[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]
[tex]\implies x= \pm 1[/tex]
Therefore, the solutions are:
[tex]x=1, \quad x=-1[/tex]
Related Questions
I need to write an solve an inequality that describes the width of the lot in terms of w
Answers
Given:
The length of the rectangle is 50 yards. The perimeter is less than 180 yards.
Required:
Write the solution inequality in terms of width w.
Explanation:
Let the width of the rectangle is w.
The perimeter of the rectangle is given by the formula:
[tex]P=2(length+width)[/tex][tex]\begin{gathered} 2(50+w)<180 \\ 50+w<90 \\ w<90-50 \\ w<40 \end{gathered}[/tex]Final Answer:
The first option is the correct answer.
Paula completely covered a square wall using 52.5 ft2 of wallpaper without any overlap. Which measurement is closest to the side
length of this wall in feet?
O 9 ft
O 7ft
O 22 ft
O 44 ft
Answers
Explanation:
We can make an equation!
Area= b^2
We know the area is 52.5 ft^2.
52.5=b^2.
To get rid of an exponent, you can square root it! And when you do something to one side, you must do it to the other as well.
The square root of 52.5 is 7.25.
This is the closest to 7. Therefore, the answer is 7 ft!!
i hope this helped! <3
Shiloh is starting a new workout regimen. Her trainer recommends that she increase the number squats she does by 35% every week. If in the second week Shiloh is doing 108 squats, how many squats did she do during her first week?
Middle School Math
Answers
The number of squats she did in the first week is 81 squats.
What is a Percentage Increase?This refers to the amount of value that a thing is incremented by, in a percentage, which is over 100.
Calculations and ParametersGiven that she had a percentage increase by 35%
And started doing 108 squats
To find the number of squats she did during the first week would be:
100-35= 75%
75/100 * 108= 81 squats.
Read more about percentage increase here:
https://brainly.com/question/11360390
#SPJ1
A bag of fertilizer that weighs 18 3/4 pounds can cover 5000 square feet. how many pounds of fertilizer will be needed to cover 27,000 square feet? how many bags of fertilizer are needed?
Answers
We know how many pounds are needed to cover 5000 ft^2, and we need to find how many are needed to cover 27000ft^2. To find this value, divide 27000 by 5000 and multiply the result by the weight.
27000/5000 x 18.75
5.4 x 18.75
101.25
So, we need 101 1/4 pounds of fertilizer. How many bags is that?
101.25/18.75
5.4
We'll say that since the 0.4 of a bag will still need to be used, that you need 6 bags to cover 27000ft^2.
What is the slope of the line that passes through the points (10, 4) and
(7, 3)? Write your answer in simplest form.
Answers
================================================
Work Shown:
[tex](x_1,y_1) = (10,4) \text{ and } (x_2,y_2) = (7,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 4}{7 - 10}\\\\m = \frac{-1}{-3}\\\\m = \frac{1}{3}\\\\[/tex]
-----------------
Extra info:
A slope of 1/3 means "go up 1, then to the right 3"
Think of it like this
slope = rise/run = 1/3
rise = 1 = go up 1
run = 3 = go to the right 3
The distance of a golf ball from the hole can be represented by the right side of a parabola with vertex (-1,8). The ball reaches the hole 1 second after it is hit. What is the equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit?
Answers
The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is
y = (-2m/s²)t² + (-2m/s)t + 6m.
Given:
Let's assume that the hole is at y = 0m, with x seconds as the time.
The vertex of the parabola can be written as (-1s, 8m) where the time variable, x, is supposed to be in seconds, while the distance variable, y, is supposed to be in meters.
The ball reaches the hole at x = 1s, so we have point (1s, 0m)
The vertex of the parabola y = ax² + bx + c is known to be at
x = -b/2a,
So, -1 = -b/2a
We have the following equations,
8m = a(-1s)² + b(-1s) + c
0m = a*(1s)² + b(1s) + c
-1s = -b/2a
b = 2a × 1s
Substituting the value of b in the equations and simplifying them,
8m = a×1s² - 1s×2a×1s + c
⇒ 8m = a( 1s² - 2s²) + c = -a×1s² + c.
0m = a×1s² + 1s×2a×1s + c
⇒ 0m = a(1s² + 2s²) + c = a×3s² + c
Deriving the value of c from the second equation we put it in the first equation,
c = - a×3s²
The first equation is as,
8m = -a×1s² - a×3s² = -a×4s²
a = 8m/-4s² = -2m/s²
From the value of a we can calculate the values of b and c.
c = -a×3s² = -(-2m/s²)×3s²= 6m.
b = 1s×2a = 1s×(-2m/s²) = -2m/s.
Then the equation is:
y = (-2m/s²)t² + (-2m/s)t + 6m
To know more about equation of the parabola in vertex form visit:
https://brainly.com/question/20333425
#SPJ10
What is the percentage change from 5 to 2?
Answers
Answer:
the percentage change is a 60% change.
Step-by-step explanation:
A change from 5 to 2 represents a negative change (decrease) of -60%
Use the formula found below on this webpage to find the percent change by replacing the given values:
Percent change = New - Old
|Old|
× 100%
Percent change = 2 - 5
|5|
× 100% =
-3
5
× 100 = -60% (decrease)
Where: 5 is the old value and 2 is the new value. In this case we have a negative change (decrease) of -60 percent because the new value is smaller than the old value.
Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per
gigabyte. She wants to keep her bill under $70 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Mei Mei can
use while staying within her budget.
Answers
The flat cost of the plan = is $46 per month
Cost per gigabyte = $5 per gigabyte
Number of gigabytes = g
The maximum amount Mei Mei wants to spend on the bill = is $70 per month,
So, for each month,
$46 + $5(g) < $70
⇒ $5(g) < $70 - $46
⇒ $5(g) < $24
⇒ g < $24/$5
⇒ g < 4.8
The number of gigabytes to be used per month should be less than or equal to 4.8.
What is Inequality?Inequalities are algebraic expressions that show how one term is less than, less than or equal to, greater than, or greater than or equal to another rather than how both sides of an equation are equal to each other.The collection of all real numbers that satisfy the inequality is its solution. As a result, x can have any value that resolves the inequality.The values indicated by the symbols < (greater than) and > (less than) are not included in the answer.An inequality with terms of the type of ab, where a and b are real positive numbers or variable expressions, is referred to as a "power inequality." They frequently show up in exercises from mathematics Olympiads.To learn more about Inequality, refer to:
https://brainly.com/question/28823603
#SPJ13
Inequality: 5g+46<70
Answer: g<4.8
3. Ross wrote a check for $124 and received a notice 4.
from the bank stating he was $51 overdrawn. His
account now shows a negative balance. How much
money did he have in his account before writing the
check?
SC
1
3
Answers
Answer:
$73
Step-by-step explanation:
A recipe calls for 4 apples to serve 6 people. If Jack is planning to serve a crowd of 33 people, how many apples should he use?
Answers
Answer:
22 apples
Step-by-step explanation:
33/6=5.5*4=22
Pls give brainliest
Answer:
I believe the answer would be 22 apples
Wukong and Nice are playing a soccer match and the probabilities of them scoring are 7/8 and 5/6 respectively. What is the probability that at least one of them will score a goal if they each play the ball once?
Answers
Answer:
Step-by-step explanation:
2038
Here are six numbers
-4, -2, -1, 5, 6, 8
Arrange the numbers into two pairs with the same total
Answers
Answer: (8,-4), (6,-2), (5,-1)
Please please help me with this I’ll give brainly
Answers
Hello!
The ratio between pig and other animals
==> looks like [tex]\text{number of pigs}: \text{ number of other animals}[/tex]
Since there are 8 pigs and 11 other kind of animals
⇒ the ratio is ⇒ 8: 11
Hope that helps!
Alayna is hanging a picture frame in the center of a wall that is 8 feet wide. If the picture frame is 21 1 over 4
inches wide, how far will each side of the picture frame be from the edge of the wall (in inches)? First, estimate the amount and then find the exact measurement. In two or more complete sentences, explain how you solved the problem. You may include a diagram in your explanation if you wish.
Answers
8 feet is known to equal 96 inches.
48 inches are divided in half,
and because the image is hung in the middle of the wall,
the subject of the image is that,
11 inches on each side, as well.
This is,
37 inches of wall on each side of 48-11.
How do you figure out a rectangle's area?A rectangle is a closed figure with four equal and opposite sides. Consequently, the length, which is also known as the height, and the width of a rectangle can be used to define it (sometimes called breadth).
The formula for a rectangle's surface area is as follows:
A=lxw
A=l×w
where:
A is the surface area of the rectangle;
L specifies the length of the rectangle.
Usually, it refers to the longest side of the rectangle.
W is the rectangle's width which is rectangle's shortest side.
to learn more about area of rectangle visit:
https://brainly.com/question/2607596
#SPJ9
Which expressions are equivalent to 211? Select all that apply.
What do the answer?
Answers
Answer:
A,B,C
Step-by-step explanation:
We would like to estimate the proportion of uf students who owns a scooter to within 1% of the truth, with 95% confidence. We believe around 20% of students do. How many students should be sampled?.
Answers
It is determined that 188 students should be sampled to use the confidence interval for a proportion.
What is mean by the term confidence interval?A confidence interval is indeed the mean of the estimate plus and minus its variation.We get the very next confidence interval of percentages in a sample of n people surveyed with a success probability of π and a confidence level of.π ± z√π(1-π)/n
In which case,
z is indeed the z-score with the p-value of 1+α/2
The error margin is as follows:
M = z√π(1-π)/n
In this case:
z does have a p-value of at 95% confidence, so z = 1.96.Thus p = 0.2, a 20% estimate.Taking into account, this same sample size is n. M = 0.02.Then:
M = z√π(1-π)/n
0.02 = 1.96√0.02(1-0.02)/n
√n = 13.72
n = 188.23
To summarize:
A total of 188 students must be sampled to estimate the proportion of of students who owns a scooter.
To know more about the confidence interval, here
https://brainly.com/question/20309162
#SPJ4
-3p-4<6. I rlly need help guys
Answers
Answer:
p > -10/3
Step-by-step explanation:
-4<6+3p
-10<3p
p>-10/3
:]
Answer: p > 10/-3
Step-by-step explanation:
1) Remove the whole numbers next to the variable
Add 10 on both sides.
-3p < 10
2) Set x by itself
Divide -3 on both sides. Dividing -3 will flip the operator sign. (Dividing/Multiplying negative number flips the sign)
p > 10/-3
Gino has a debit card. The account pays no interest. He keeps track of his purchases and deposits in this debit card register. Find the missing entries a through f.
SARL
778.19
8/4 Baseball Bat
42.19
8/5 Gas
8/7 Deposit
8/7 Gas
8/7
Dinner at Spooner's
On the Beach
8/11 Books for Fall Semester
a. 92.19
b. 51.00
C. $400.00
d. 25.00
e. 71.12
f. 491.51
**
**
92 19
ST 00
25 00
71 12
491 ST
400 00
a.
b.
C.
d.
e.
Answers
The missing entries are (a) $686, (b) $635, (c) $1035, (d) $1010, (e) $938.88 and (f) $447.37.
What is Debit Card?Debit card is a card owned by a person for which the money used for transaction will be withdrawn or added into the account of the holder immediately.
Given is a table showing the transactions of Gino with his debit card.
He has an initial deposit amount of $778.19.
New balance in the account will be the difference of previous balance and the payment amount.
He paid $92.19 for baseball bat.
a = $778.19 - 92.19 = $686
He paid $51.00 for gas.
b = $686 - $51 = $635
He deposited $400.
c = $635 + $400 = $1035
He paid $25 for gas.
d = $1035 - $25 = $1010
He paid $71.12 for dinner at Spooner's on the beach.
e = $1010 - $71.12 = $938.88
He paid $491.51 for the books for all semester.
f = $938.88 - $491.51 = $447.37
Hence the missing entries are found.
Learn more about Debit Card here :
https://brainly.com/question/27934503
#SPJ2
Kaitlin has a bookcase with books. There are 50 shelves in the bookcase. Each shelf has the same number of 5 books. How many books does each shelf have?
Answers
You do 50 shelves times 5 books on each shelf to get 250 books total.
Identify the slope and y intercept
Answers
Step-by-step explanation:
the y-intercept (b) is the easiest :
it is the y-value, when x = 0 : -3
the slope (m) is the ratio (y coordinate difference / x coordinate difference) when going from 1 point to another.
so, we need to identify 2 points in the line.
one we have already with b : (0, -3)
another is the x-axis intercept, which is clearly (4, 0)
the difference is not important, but we need to use the same for both (x and y).
I prefer to go from left to right, so from (0, -3) to (4, 0) :
x changes by +4 (from 0 to 4)
y changes by +3 (from -3 to 0)
the slope is +3/+4 = 3/4
In parallelogram ABCD, AB = 3 cm and the diagonals AC and BD are 5.8 cm and 4.2 cm respectively. If the diagonals AC and BD intersect at O, then the perimeter of ∆AOB is
Answers
In parallelogram ABCD, AB = 3 cm and the diagonals AC and BD are 5.8 cm and 4.2 cm respectively. If the diagonals AC and BD intersect at O, then the perimeter of ∆AOB is 8 cm
How to find the perimeterperimeter of a triangle = length 1 + length 2 + length 3
assuming
length 1 = AB = 3 cm
length 2 = 5.8 / 2
length 3 = 4.2 / 2
Reason for length 2 and length 3 is when the diagonal of a parallelogram intersect they bisect each other. bisect means divide each other into two equal parts
substituting the values
perimeter of the triangle = 3 + 5.8 / 2 + 4.2 / 2
= 3 + 2.9 + 2.1
= 8 cm
The perimeter of the triangle formed is 8 cm
read more on perimeter of a triangle here: https://brainly.com/question/24382052
#SPJ1
9. Find the area of the shaded region.
22 cm
10 cm
7cm
Answers
Using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².
What is the formula for the area of a rectangle and triangle?Area of rectangle = length x widthArea of triangle = 1/2 x base x heightIn the given shaded region there is one rectangle and one triangle.
First, find the area of the shaded rectangle.
Here, length = 22 cm and width = 10 cm.So, Area of rectangle = length x width = 22 x 10Area of rectangle = 220 square cm.Now find the area of the shaded triangle.
Here, base = 10 cm and height = 7 cm.So, the Area of the triangle is:
Area = 1/2 × 10 × 7= 35cm²Therefore, the total area of the shaded region is:
Area of shaded region = Area of rectangle + Area of triangle= 220 + 35Area of shaded region = 255 square cm.Therefore, using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².
To know more about the area:
brainly.com/question/19298480
#SPJ13
PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
Answers
2.divide both sides by 3 and you will get the answer x=32
50% of $99.97
Two answers
Answers
Answer:
Step-by-step explanation:
you would cut 99 in half and make your way down until nothing left which gives you 48.985 or
49.99$ rounded
what is the answer to 7.25x348
Answers
Answer:2,523
Step-by-step explanation:
The varsity baseball team has won 15 out of their last
16 games. The junior varsity team has won 6 out of their
last 10 games. What is the probability that both teams
win their next game?
If you could give me step by step explanation that would be great.
Answers
Answer:
Step-by-step explanation:
5) The lengths of the fours sides of a quadrilateral are consecutive integers. If the perimeter is 94 meters, find the value
of the shortest of the four side lengths.
Answers
The shortest side is 22 meters in the mentioned quadrilateral.
Let us assume the length of first side be x. So, the other three sides of length will be (x + 1), (x + 2) and (x + 3). The perimeter is sum of all sides of the quadrilateral.
Keep the values in the formula of perimeter -
94 = x + x + 1 + x + 2 + x + 3
Performing addition on Right Hand Side of the equation
94 = 4x + 6
Shifting 6 to other side of the equation
4x = 94 - 6
Performing subtraction on Right Hand Side of the equation
4x = 88
Shifting 4 to Right Hand Side of the equation
x = 88 ÷ 4
Performing division
x = 22
Thus, the shortest side of quadrilateral is 22 meters long.
Learn more about quadrilateral -
https://brainly.com/question/23935806
#SPJ9
a community assesses a random sample of its residents by telephone questionnaire. obesity is strongly associated with diagnosed diabetes. this study design is best described as which one of the following: a. experimental b. cohort c. cross-sectional d. case-control
Answers
The study design is best described as a case-control study.
A community uses a telephone survey to rate a representative sample of its citizens.
Diabetes is significantly correlated with obesity.
Non-experimental or observational study designs include cohort designs. In a cohort study, the participants don't already have the desired result. They are chosen based on the person's exposure status.
A case-control study is a sort of observational research in which two existent groups with outcomes that differ from one another are found and compared on the basis of a purported causal factor.
An example of an observational study design is the cross-sectional study design. In a cross-sectional study, the researcher simultaneously assesses the participants' exposures and outcomes.
Therefore, the study is a case-control study.
Learn more about case-control study here:
brainly.com/question/28024581
#SPJ4
If I rotated Block C by 90 degrees clockwise where would it be?
Answers
After the 90° rotation, Block C will resemble this in some ways (see the image below).
What is rotation?The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a specific area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point. As an example of rotation in the real world, we know that the earth revolves around its own axis. A group of people walking in a circle while holding hands and rotating either clockwise or counterclockwise.So, rotate block C by 90°:
Block C will look somewhat like this (Refer to the image attached below) after the rotation of 90°.
Therefore, after the 90° rotation, Block C will resemble this in some ways (see the image below).
Know more about rotation here:
https://brainly.com/question/98217
#SPJ3
300 divided by 2(0.5 +4.5)^2
Answers
Answer: 6
Step-by-step explanation:
1. add (0.5 + 4.5) which equals 5, so now you have 2 x 5^2.
2. evaluate the power (5^2) which equals 25 and you end up with 2 x 25 which equals 50.
3. now you have 300 divided by 50.
300 divided by 50 is 6.
The value of the expression 300 divided by 2(0.5 +4.5)²is 6
What is Simplification ?Simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.
Given an expression, 300 divided by 2(0.5 +4.5)²
300/2(0.5 +4.5)²
= 300/2x5²
= 300/2x25
= 300/50
= 6
Hence, The value of the expression 300 divided by 2(0.5 +4.5)²is 6
For more references on simplification, click;
https://brainly.com/question/2804192
#SPJ2