If P = (-3,-2) and Q = (1, 6) are the endpoints of the diameter of a circle, find the equation of the circle.
(x +?)^2 + (y - ?)^2 = ?
Answers
Answer:
(x+1)²+(y-2)²= 20
Step-by-step explanation:
P = (-3,-2)
Q = (1, 6)
Center (h, k)
C = ((-3+1)/2 , (-2+6)/2)
C = (-2/2 , 4/2)
C = (-1 , 2)
Radius = Distance from the center to point Q
R = √((1-(-1))² + (6-(2))²)
R = √((2)² + (4)²)
R = √(4+ 16)
R = √20
Equation
(x-h)²+(y-k)²= R²
(x-(-1))²+(y-2)²= (√20)²
(x+1)²+(y-2)²= 20
Related Questions
2 ⋅ √ 2 + √ 8 - simplify
Answers
Answer:
[tex]4\sqrt2[/tex]
Step-by-step explanation:
[tex]2\sqrt{2} +\sqrt{8}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}[/tex]
Step-by-step explanation:
i sent the solution in the photo pls check it
the image of p(m,5-n) when reflected on line y=0 is p'(2m-3,2n-8) find the values of m and n
Answers
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)
If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:
2m - 3 = m
m = 3
Also:
-(5 - n) = 2n - 8
-5 + n = 2n - 8
n = 3
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
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The total cost, C, for running an advertisement in a local newspaper, The Free Press, is made up of an initial cost of $12 plus a charge of $5 per day. A rival newspaper, The Banner, is currently running a special on advertisements at $8 per day with no initial cost.
a) Write an equation representing the cost in The Free Press.
b) Write an equation representing the cost in The Banner.
c) For each newspaper, create a table of values.
d) Use Geometer’s Sketchpad to graph each cost on the same set of coordinate axes.
e) Which newspaper would you use for an ad that ran 1 day?
f) Which newspaper would you use for an ad that ran 12 days?
Answers
The equation representing the cost in The Free Press is 12 + 5d.
How to depict the equation?The equation representing the cost in The Free Press will be:
= 12 + (5 × d)
= 12 + 5d
The equation representing the cost in The Banner will be:
= 8 × d
= 8d
The table of value for Free Press will be:
1st day = 12
2nd day = 17
3rd day = 22
4th day = 27
5th day = 32
The table of value for the Banner will be:
1st day = 8
2nd day = 16
3rd day = 24
4th day = 32
5th day = 40
The newspaper that will be used to run the advertisement for the first day is Free Press since it's cheaper.
The newspaper that will be used to run the advertisement for twelve days will be:
Free press = 12 + 5d
= 12 + 5(12)
= 12 + 60 = 72
The banner = 8d = 8 × 12 = 96
Therefore, for 12 days, Free Press is cheaper.
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Which is an equation of the line through (0,0) and (2,-3)?
Answers
Answer:
y = -1.5x
How to build equation?
Given points: (0, 0), (2, -3)
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5[/tex]
Then find equation:
[tex]y-y_1 = m(x - x_1)[/tex]
[tex]y - 0 = -1.5(x -0)[/tex]
[tex]y = -1.5x[/tex]
Answer:
y = (-3/2)x
Step-by-step explanation:
I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:
[tex]m=\frac{-3-0}{2-0}=\frac{-3}{2}[/tex]
Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x
Find the answer
a
b
c
d
Answers
Answer: a
Step-by-step explanation:
[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x^{2}-1}}{\sqrt{x-1}}}=\sqrt{\frac{x^{2}-1}{x-1}}=\sqrt{\frac{(x-1)(x+1)}{x-1}}=\boxed{\sqrt{x+1}}[/tex]
Joe paid $14 for a board game. this is 70% of the original price. what was the original price?
Answers
Step-by-step explanation:
It is given that Joe paid 14.00 for a board game this is 70% of the original price what is the original price.
Let the original price of board game be
X.
x * 70/100 = 14
x * 7/10 = 14
Multiply both sides by 10.
7x = 140
Divide both sides by 7.
x = 20
Researchers conducted a study to find out if there is a difference in the use of ereaders by different age groups. randomly selected participants were divided into two age groupsin the to 29year-old group7% of the 628 surveyed use ereaders, while 11of the 2,309 participants 30 years old and older use ereaders(use subscripts let 1 16- to 29-year-old users , and 230 years old and
Answers
No, there is significant difference in the use of e readers by different age groups.
Given sample 1 ( 29 years old) [tex]n_{1}[/tex]=628, [tex]p_{1}[/tex]=7%, sample 2( 30 years old)[tex]n_{2}[/tex]=2309, [tex]p_{2}[/tex]=0.11.
We have to first form hypothesis one null hypothesis and other alternate hypothesis.
[tex]H_{0}:[/tex]π1-π2=0
[tex]H_{1}:[/tex]π1-π2≠0
α=0.05
Difference between proportions [tex]p_{1}-p_{2} =-0.04[/tex]
[tex]p_{d}=0.07-0.11=-0.04[/tex]
The pooled proportion needed to calculate standard error is:
[tex]p=(X_{1} -X_{2} )/(n_{1} +n_{2} )[/tex]
=(44+254)/(628+2309)
=0.10146
The estimated standard error of difference between means is computed using the formula:
[tex]S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }[/tex]
=[tex]\sqrt{0.101*0.899/628+0.101*0.899/2309}[/tex]
=[tex]\sqrt{0.000143+0.00003}[/tex]
=[tex]\sqrt{0.000173}[/tex]
=0.01315
Z= Pd-(π1-π2)/[tex]S_{p_{1} -p_{2} }[/tex]
=-0.04-0/0.013
=-3.0769
This test is a two tailed test so the p value for this test is calculated as (using z table)
p value:2 P(Z<-3.0769)
=2*0.002092
=0.004189
P value< significance level of 5%.
Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.
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Question is incomplete as it also includes:
Significance level of 5%.
PLEASE HELP!!! FINDING PROBABILITY MATH!!!
i need the answer to question 2, 3, and 4. question 1's answer is 9/28 & 32.1%.
Answers
The probability that a person wins the game is 32.1%
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
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hep me out with this question i will give you brainly!
Answers
Answer:
c because have great day
Find x and y.
x - y = 2
3x - y = 12
Answers
the answer is
X=5
y=3
hope you like it
Which three pairs of measurements are possible side lengths for the triangle?
A
B
60°
F
AB=4, BC= 4√3
OBC= 2√3, AC=2
AB=3, AC=3√3
BC=10, AC= 4√3
AB=7, AC=14
AB=11, BC=11√3
30°
C
Answers
Answer:
Options (1), (5), and (6)
Step-by-step explanation:
See attached image
Three pairs of measurements which are possible side lengths for the triangle are,
1. AB = 4, BC = 4√3
5 AB = 7, AC = 14.
6. AB = 11, BC = 11√3
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Now, We get;
The sides of this triangles has lengths in the ratio x : √3x : 2x
where 2x is the hypotenuse.
Now, When C = 30, the side AB is the small leg (=x).
When B = 90, the hypotenuse is AC ( =2x).
When A = 60, the larger leg is BC (=√3x).
1. AB = 4, BC = 4√3 :- Are possible legs.
5 AB = 7, AC = 14. :- AB = small leg, AC = hypotenuse.
6. AB = 11, BC = 11√3:- AB = small, BC = larger leg.
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pleeeaaseee helllppppp!!!!
Answers
Answer:
[tex]sin\theta=\dfrac{1}{2}[/tex]
=============
Given[tex]cos \theta=\dfrac{\sqrt{3} }{2}[/tex]To findThe value of [tex]sin\theta[/tex]SolutionUse identity [tex]sin^2\theta+cos^2\theta=1[/tex] :
[tex]sin^2\theta=1-cos^2\theta[/tex][tex]sin^2\theta=1-(\dfrac{\sqrt{3} }{2} )^2[/tex][tex]sin^2\theta=1-\dfrac{{3} }{4}[/tex][tex]sin^2\theta=\dfrac{{1} }{4}[/tex][tex]sin\theta=\sqrt{\dfrac{{1} }{4} }[/tex][tex]sin\theta={\dfrac{{1} }{2} }[/tex]Please help!!!!!!!!!!
Answers
Using the together rate, it is found that it will take 18 hours for Erick to build the garden box himself.
What is the together rate?The together rate is given by the sum of each separate rate.
In this problem, the rates are given as follows:
Eric's: 1/x.Drew's: 2/x.Together: 1/6.Hence:
[tex]\frac{1}{x} + \frac{2}{x} = \frac{1}{6}[/tex]
[tex]\frac{3}{x} = \frac{1}{6}[/tex]
x = 18.
Hence, it will take 18 hours for Erick to build the garden box himself.
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A projectile is fired from the ground with an upward speed of 245 m/s. What is the maximum height of the projectile?
Answers
The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The maximum height (H) of a projectile is given as:
H = u²/2g
Where u is the initial speed = 145 m/s, g is the acceleration due to gravity = 10 m/s²
H = 245²/ 2(10) = 3001.25 m
The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m
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An adult gerbil at Fish 'n' weighed 1/5 lb. A young gerbil weighed 1/4 of that amount. How many did the young gerbil weigh?
Answers
What is part of 1 minute and 5 seconds
Answers
The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.
Fraction of 5 seconds in 1 minute
The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is calculated as follows;
1 minute = 60 secs
Fraction = 5 / 60
Fraction = 1/12
Thus, the fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.
The complete question is below:
What is part of 1 minute is 5 seconds?
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Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with a horizontal line crossing the y axis at three that ends at the open point 2, 3, a closed point at 2, 1, and another horizontal line starting at the open point 2, -2.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x. .
Does not exist; does not exist
1; 1
-2; 3
3; -2
Answers
Limit of x approaches two from the left of f of x: 3. Limit of x approaches two from the right of f of x: - 1 (negative 1)
How to find the value of the function as x approaches infinity (+ve or -ve)?If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.
In order to find the limit as x approaches two from the left of f of x:
Lim x→2- f(x) = ?
According to the graph, when x approaches two from the left (x<2), the function approaches 3:
Lim x→2- f(x) = 3
IN order to find the limit as x approaches two from the right of f of x:
Lim x→2+ f(x) = ?
According to the graph, when x approaches two from the right (x>3), the function approaches -1:
Lim x→2+ f(x) = - 1
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A spinning wheel has the following numbers.
(There are 1-8 numbers in the wheel)
Cathy spins the wheel and tosses a coin simultaneously.
Find the following probabilities:
Getting a 7 and tails.
Getting a prime number and heads.
Getting a number greater than 5 and tails.
Answers
Answer:
[tex]\frac{1}{16}, \frac{1}{4}, \frac{3}{16}[/tex]
Step-by-step explanation:
Recall a probability: [tex]P=\frac{F}{T}[/tex] , where F is a number of favorable outcomes and T is a number of total outcomes.
The probability to get tail is [tex]\frac{1}{2}[/tex] as well as probability to get head.
The probability to choose number 7 of 8 numbers at total is equal to [tex]\frac{1}{8}[/tex].
Therefore, the probability to get number 7 and a tail is:
[tex]\frac{1}{8}\cdot \frac{1}{2}=\frac{1}{16}[/tex]
Prime numbers from 1 to 8 are: 2, 3, 5 and 7, so there are 4 numbers of 8 numbers in total, so the probability to get a prime number is [tex]\frac{4}{8}=\frac{1}{2}[/tex].
The second probability is equal to [tex]\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}[/tex].
The numbers greater than 5 are: 6,7,8, so there are 3 numbers of 8 in total, so the probability to get a number greater than 5 is [tex]\frac{3}{8}[/tex].
The third probability is equal to: [tex]\frac{3}{8}\cdot \frac{1}{2}=\frac{3}{16}[/tex].
A motor bike depreciated in value from 4500 to 3285. calculate the percentage depreciation
Answers
The percentage depreciation is 27 % .
What is percentage ?
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.Given ,
from 4500 to 3285 is depreciation value of a motor bike.
So,
= [tex]\frac{( 4500 - 3285 )} {4500} * 100[/tex]
= [tex]\frac{1215}{4500} * 100\\[/tex]
= [tex]\frac{121500}{4500}[/tex]
= 27 %
Therefore, The percentage depreciation is 27 % .
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Select all the correct answers.
A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.
Pick a card from a deck of standard playing cards four times, with red suits representing those who prefer watching a movie at a theater and black suits representing those who do not.
Spin a spinner with four equal sections three times, with one section representing each person.
Roll a six-sided die four times, with even numbers representing those who prefer watching a movie at a theater and odd numbers representing those who do not.
Generate a set of four numbers using a number generator, with numbers 0 to 5 representing those who prefer watching a movie at a theater and 6 to 9 representing those who do not.
Answers
An equivalent situation, in which the binomial distribution could be used, is given by:
Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the parameters are:
p = 0.5, n = 4;
The other situation that would represent a binomial distribution with the same parameters is given by:
Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.
The other situations have different values of p, hence they are not equivalent.
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Solve the following system of equations using elimination by eliminating the y variable
first.
5x + 2y = 3
2x + 3y = 10
Answers
The solution to the system of equations is x = -1 and y = 4
How to solve the system of equations?The system of equations is given as:
5x + 2y = 3
2x + 3y = 10
Multiply the first equation by 2 and the second by 5.
10x + 4y = 6
10x + 15y= 50
Subtract the above equations
10x - 10x + 4y - 15y = 6 - 50
This gives
-11y = -44
Divide by -11
y = 4
Substitute y = 4 in 5x + 2y = 3
5x + 2 * 4 = 3
This gives
5x + 8 = 3
Subtract 8 from both sides
5x = -5
Divide by 5
x = -1
Hence, the solution to the system of equations is x = -1 and y = 4
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Work out the
circumference of a circle with diameter 1.8 cm.
Take pi to be 3.142 and give your answer to 1 decimal place.
Answers
Step-by-step explanation:
the circumference of a circle is
2×pi×r
with r being the radius, which is always half of the diameter.
r = 1.8 / 2 = 0.9 cm
circumference :
2×pi×0.9 = 1.8×pi = 1.8 × 3.142 = 5.6556 cm ≈ 5.7 cm
Answer:
5.7cm
Step-by-step explanation:
circumference = π · d
(2πr)
{note: "d" is diameter; "r" is radius; "π" is pi}
we know our diameter (d) to be 1.8
let's plug this into our cicumference formula! :
π · d = circumference
(3.142) · (1.8)
3.142 · 1.8 = 5.6556
let's round our answer to 1 decimal place,
remember, if the next digit is ≥5 we round up; < 5 we keep the same
so, our answer is 5.7 cm
hope this helps!! have a lovely day :)
Which of the following functions best describes this graph?
Answers
Answer:
Option D
Step-by-step explanation:
Looking at the graph each jump is 2 units on the x-axis and y-axis :
We are looking for a quadratic with x values of 3 and 6 when y=0
Solving the last quadratic gives us :
(x-3)(x-6)=0
x = 3 , x = 6
Our answer will be Option D
Hope this helped and have a good day
Answer:
D: [tex]y=x^{2} -9x+18\\[/tex]
Step-by-step explanation:
x intercept of the curve is 3 and 6
meaning that when y=0, x is either 3 or 6
mathematically stated:
0 = (x - 3) (x - 6)
0=x(x-6)-3(x-6)
[tex]0=x^{2} -6x-3x+18\\therefore \ y=x^{2} -9x+18\\[/tex]
A=42°, b=10, c=12. What is the length of a to the nearest tentH
Answers
The length of a in the triangle to the nearest tenth is 8.1 units.
How to find side of a triangle?The side a of the triangle can be found using cosine formula.
Therefore,
a²= b² + c² - 2bc cos A
a² = 10² + 12² - 2 × 10 × 12 cos 42°
a² = 100 + 144 - 240cos 42
a² = 244 - 178.354758115
a = √65.6453
a = 8.10217871933
a = 8.1
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In the graph locate the point (3,0) and draw a line parrallel to Y-axis passing through (3,0). Then your line will cut the graph of f (x) at some point, that point's y-coordinate will be your value of f (3)
Answers
The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The graph passes through the point (3, 0) and parallel to the y axis, the equation of this line is x = 3.
The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.
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4. In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Answers
A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways
How to determine the number of ways?The selections are given as:
3 boys from 5 boys
3 girls from 4 girls
Each selection is calculated using:
[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]
So, we have:
[tex]Ways = ^5C_3 * ^4C_3[/tex]
Apply the combination formula
[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]
Expand
[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]
Simplify
Ways = 5 * 2 * 4
Evaluate
Ways =40
Hence, the number of ways is 40
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Just an easy question for 100 points! :)
Answers
If the function is translated 4 units down, the resulting function will be
y = x - 4 while the vertical stretch by 3units will be y = 3(x-4)
Transformation of functionsTransformation of function is a way of changing the position of a line or curve on an xy place.
Given the equation of a line as shown;
y = x (This will serve as the parent function)
If the function is translated 4 units down, the resulting function will be
y = x - 4. If the resulting function is stretched by a factor of 3, the final function will be y = 3(x - 4)
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Select the correct answer from each drop-down menu.
A toy chest is shown.
TUFFETY
Which shapes best model the parts of the toy chest?
The bottom part of the chest is best modeled by
The top part of the chest is best modeled by
because each face is a
because some faces are
Answers
Answer: What you picked
Step-by-step explanation:
I can't see the dropdown menus, but those answers make sense.
Answer:
The bottom part of the chest is best modeled by rectangular prism because each face is a rectangle The top part of the chest is best modeled by part of a cylinder because some faces are curved
Need help with this question
Answers
Now, ORQ is a straight angle and RS its bisector.
It means:
ORS = QRS = 180°/2 = 90°So, ∠ORS and ∠QRS are supplementary.
We also have ray RP, that divides the angles ORQ and QRS.
It gives us one more pair of supplementary angles:
∠ORP and ∠QRP.Since ∠QRS is right angle, its parts are forming a pair of complementary angles:
∠SRP and ∠QRP are complementaryUrgent help please help me!
Answers
Answer:
(x + 4)(x - 2) = x · x
(option L)
Step-by-step explanation:
we know that area = length × width
So, can write out the lengths and widths that we know:
(note: I will use the square as the reference point, because we can simply say "x" for both of its side lengths--you'll see why this is easier later)
Rug A:
length = x
width = x
Rug B:
length: x + 4
(4 feet greater than rug A length)
width: x - 2
(2 feet less than rug A width)
we can now set these areas to be equal to each other:
(rug A) = (rug B)
(length · width of A) = (length · width of B)
(x · x) = [ (x + 4)(x - 2) ]
So, the equation:
(x + 4)(x - 2) = x · x
can be used to find x (the length in feet) of rug A
hope this helps!! have a lovely day :)