The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
Answers
The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
How to determine the legs of the triangle?The complete question is in the attached image
The given parameters are:
Area = 24
Legs = x and x + 2
The area of the triangle is calculated as:
Area = 0.5 * Base * Height
This gives
0.5 * x * (x + 2) = 24
So, we have:
0.5(x)(x + 2) = 24
Divide through by 0.5
(x)(x + 2) = 48
Expand
x^2 + 2x = 48
Subtract 48 from both side
x^2 + 2x - 48 = 0
Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
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Related Questions
Kitty has invested £5500 for 3 years in a savings account. She is paid 6% per annum compound interest. How much did she have in her savings account at the end of the 3 years?
Answers
The value of her investment at the end of 3 years is £10955.08
How to determine the value?The given parameters are
Principal, P = £5000Rate, r = 6%Time, t = 3 yearsThe value is then calculated as:
Value = P * P(1 + r)^t
So, we have:
Value = 5000 + 5000 * (1 + 6%)^3
Evaluate the expression
Value = 10955.08
Hence, the value of her investment at the end of 3 years is £10955.08
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What steps should be taken to complete the conversion?
Answers
To complete the conversion, the following will be gotten:
12880 m
How to convert distance?Using conversion technique,
8 mi / 1 × 1.61 k / 1 mi × 1000m / 1k
we have to cancel out similar units in the numerator and denominator.
Therefore,
8 mi / 1 × 1.61 k / 1 mi × 1000m / 1k
8 / 1 × 1.61 / 1 × 1000m / 1 = 12.88 / 1 × 1000m
Hence,
12.88 / 1 × 1000m = 12880 m
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1. Write a linear equation with the given information
Through (4,-5), parallel to y = -x + 1(4 Points)
2. Write a linear equation with the given information
Through (2,-1), perpendicular to y = -2/3x + 5(4 Points)
(please step by step thank you)
Answers
1. The equation of the parallel line is y = -x - 1.
2. The equation of the perpendicular line is y = 3/2x - 4.
What are the Equations of Parallel and Perpendicular Lines?Lines that are parallel have the same slope while slope values for perpendicular lines are negative reciprocals.
1. The slope (m) of y = -x + 1 is -1. Substitute m = -1 and (x, y) = (4, -5) into y = mx + b:
-5 = -1(4) + b
-5 = -4 + b
-5 + 4 = b
b = -1
Substitute b = -1 and m = -1 into y = mx + b
y = -x - 1
2. The slope (m) of y = -2/3x + 5 is -2/3.
Negative reciprocal of -2/3 is 3/2.
Substitute m = 3/2 and (x, y) = (2, -1) into y = mx + b:
-1 = 3/2(2) + b
-1 = 3 + b
-1 - 3 = b
b = -4
Substitute b = -4 and m = 3/2 into y = mx + b
y = 3/2x - 4
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Solve the following system of equations by graphing. 9x-2y= -8
Answers
The solution of the equation are
(0, 4)(1, 8.5)(-0.66, 1)(-0.44, 2)What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given:
9x -2 y =-8
By graph we can see that the solution for the graph is
(0, 4)
(1, 8.5)
(-0.66, 1)
(-0.44, 2)
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You need 450 mL of a 65% alcohol solution. On hand, you have a 10% alcohol mixture. How much of the 10% alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need_____ mL of the 10% solution and___ mL of pure alcohol.
Answers
You will need 292.5 mL of the 10% solution and 2925 mL of pure alcohol.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
You require 450 mL of a 65% alcohol solution.
On hand, you have a 10% alcohol mixture.
Then the amount of the 10% alcohol mixture and pure alcohol that you need to obtain the desired solution will be
Let x be the amount of the 10% of alcohol is needed.
Then the equation will be
⇒ 450 · 0.65
⇒ 292.5 mL pure alcohol
Then the alcohol mixture will be
0.1x = 292.5
x = 2925 mL of alcohol mixture
You will need 292.5 mL of the 10% solution and 2925 mL of pure alcohol.
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I think I made a small mistake and I need help to spot my mistake and the correct steps to solve my question, I hope someone can help me asap. I will be very much appreciated!!
(Question b)
Answers
The values of x in 2cos(2x) = 11cos(x) + 1 are x = 1.82 and x = 4.46
How to solve for x?The equation is given as:
2cos(2x) = 11cos(x) + 1
Expand cos(2x)
2(cos²(x) - sin²(x)) = 11cos(x) + 1
sin²(x) = 1 - cos²(x)
So, we have:
2(cos²(x) - 1 + cos²(x)) = 11cos(x) + 1
Evaluate the like terms
2(2cos²(x) - 1) = 11cos(x) + 1
Expand
4cos²(x) - 2 = 11cos(x) + 1
Rewrite as:
4cos²(x) - 11cos(x) - 2 - 1 = 0
4cos²(x) - 11cos(x) - 3 = 0
Let cos(x) = y.
So, we have
4y² - 11y - 3 = 0
Expand
4y² + y - 12y - 3 = 0
Factorize
y(4y + 1) - 3(4y + 1) = 0
Factor out 4y + 1
(y - 3)(4y + 1) = 0
Solve for y
y = 3 or 4y = -1
This gives
y = 3 or y = -1/4
Recall that y = cos(x)
So, we have:
cos(x) = 3 or cos(x) = -1/4
The cosine of x is always between -1 and 1 (inclusive).
So, we have:
cos(x) = -1/4
Take the arc cos
[tex]x =\cos^{-1}(-1/4)[/tex]
Evaluate the arccos (in radians)
x = 1.82 and x = 4.46
Hence, the values of x in 2cos(2x) = 11cos(x) + 1 are x = 1.82 and x = 4.46
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Dana's phone has zero battery. After charging her phone for 1 minute, it has
2% battery. After 2 minutes, her phone has 6% battery. Based on this, predict
the number of minutes it will take for Dana to charge her phone's battery so
that it has 50% power and 90% power.
Answers
From the first two inference, it takes her phone 1 minute to charge 2% i.e 1 minute of charge = 2% of battery.
Therefore; charging from scratch,
1 min = 2%
x mins = 50%.
using cross multiplication,
x mins = (50% × 1 min) ÷ 2%.
x = 25 mins.
For 90%, applying the same formula,
y min = (90% × 1 min) ÷ 2%
y = 45 mins.
So from zero percent, it will take Dana's phone 25 minutes to charge to 50% and 45 minutes to charge to 90%.
Question 9 of 10
Which of the following lists of ordered pairs is a function?
OA. (2, 5), (3, 6), (6,9)
OB. (2, 5), (3, 6), (2, 1)
C. (-1, 2), (2, 3), (3, 1), (2, 5)
O D. (1, 2), (4, 0), (3, 5), (4,3)
Answers
Answer: A. (2, 5), (3, 6), (6,9)
Step-by-step explanation:
Each value of x maps onto only one value of y.
Please Help I’m confused give clear answers thank you
Answers
Answer:
1: [tex]y=-1x-3[/tex]
2: [tex]y=0.8x+4.2[/tex]
3: [tex]y=2x-3[/tex]
Step-by-step explanation:
Question 1: When lines are parallel, that means they're slope is the same and there y-intercept is different. So the first step is to calculate the slope of BC. If you look at BC you'll notice it goes down by 2 and goes forward by 2 so the slope is -2/2 or -1. This completes one part of the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept. The y-intercept will be calculated using the point A. since the equation passes through point A
-1 = (-2)(-1) + b
-1 = 2 + b
-3 = b
y=-1x-3
Question 2: Same concept here, if you look at AC, you'll see it "rises" by 4 and "runs" by 5, thus the slope is 4/5. Since it passes through B we'll use that to find the y-intercept
5 = (4/5)(1) + b
5 = 4/5 + b
b = 4.2
Question 3: It "rises" by 6 and "runs" by 3, thus the slope is 6/3 which is 2.
Plug in known values
3=(3)(2) + b
3 = 6 + b
-3 = b
Which statements are true of the given function?
Check all that apply.
01²2=2²
Of(0) = 2/1/20
O f(1) = -1
Of(2)=1
□f(4)=1/12/2
Answers
Step-by-step explanation:
23 by 13 is the answer cause 23 i s23
The statements that are true of the given function f(x) = 1/2x + 3/2 are:
f(0) = 3/2
f(2) = 7/2
f(4) = 7/2
We have,
Let's evaluate the given function f(x) = 1/2x + 3/2 for the given values of x and check which statements are true:
f(-1/2) = 1/2 * (-1/2) + 3/2 = -1/4 + 3/2 = (6 - 1)/4 = 5/4 = 1.25
Statement: f(-1/2) ≠ 2 (False)
f(0) = 1/2 * 0 + 3/2 = 0 + 3/2 = 3/2
Statement: f(0) = 3/2 (True)
f(1) = 1/2 * 1 + 3/2 = 1/2 + 3/2 = 4/2 = 2
Statement: f(1) ≠ -1 (False)
f(2) = 1/2 * 2 + 3/2 = 1 + 3/2 = 2 + 3/2 = 4/2 + 3/2 = 7/2
Statement: f(2) = 7/2 (True)
f(4) = 1/2 * 4 + 3/2 = 2 + 3/2 = 4/2 + 3/2 = 7/2
Statement: f(4) = 7/2 (True)
Therefore,
The statements that are true of the given function f(x) = 1/2x + 3/2 are:
f(0) = 3/2
f(2) = 7/2
f(4) = 7/2
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Kim's car gas tank holds 2 gallons of gas and gets M miles per gallon and she drove D miles. lf gas cost $1.25 per gallon how many gallons had to be replaced?
Answers
Answer:
see below
Step-by-step explanation:
D miles / M miles per gallon = gallons used
Will give brainliest!
2. The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady
Answers
The expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662
The expected population in 2025The expected population of each country is calculated as:
P(n) = a *(1 + r)^n
Where:
a represents the initial populationr represents the growth raten represents the number of years since 20002025 is 25 years since 2000.
This means that:
n = 25
So, we have:
Australia
P(25)= 19169000 * (1 + 0.6%)^25
P(25)= 22261221
China
P(25)= 1261832000* (1 + 0.6%)^25
P(25)= 1465382683
Mexico
P(25)= 100350000 * (1 + 0.6%)^25
P(25)= 116537821
Zaire
P(25)= 51965000* (1 + 0.6%)^25
P(25)= 60347662
Hence, the expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662
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Use the Histogram below to answer. Please help
Answers
The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:
The middle 68% of a normal distribution would be within 1 standard deviation of its mean.The middle 95% of a normal distribution would be within 2 standard deviations of its mean.The middle 99.7% of a normal distribution would be within three standard deviations of its mean.By applying the empirical rule to the data contained in the histogram, we can logically deduce the following points:
There is approximately 95% of the data between -2 and 102.There is approximately 68% of the data between 1 standard deviation of its mean.Read more on Empirical Rule here: https://brainly.com/question/10093236
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Solve for x using
cross multiplication.
2x=4 =
2x – 4
3
x + 1
2
x = [?]
Enter
Answers
Hello,
look at the picture
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x2 = 17
A. 3 ,–3
B. 4.12, –4.12
C. 0.73, –0.73
D. 1.37, –1.37
Answers
Answer:
D. 1.37, -1.37
Step-by-step explanation:
9x² = 17
x² = (17 / 9)
x = ± √(17 / 9)
x = ± (√17) / 3
x = 1.37, - 1.37
Chang caught a 3- pound fish. How much did it weigh in ounces? 4 Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
Answer:
Step-by-step explanation:
pounds to ounces: 16 ounces in a pound a trick to know is if you look at the pound symbol lb it looks like 16 in a way so 16*3= 48 48 is your answer
i need help with this only answer
Answers
Answer:
27.03 or 27 3/100
Step-by-step explanation:
Plug in numbers
The solution to the fraction expression at x = 1¹/₁₀ is: 10.97
How to solve Fraction Problems?The fraction expression is given as:
3(5 - ¹/₆x) + ¹/₈(32 + 6x) + 7.3x - 5 * 0.05x
Breaking this down gives us:
15 - ¹/₂x + 4 + ³/₄x + 7.3x - 0.25x
= 19 - 7.3x
Now, we want to plug in 1¹/₁₀ for x.
1¹/₁₀ can be expressed as ¹¹/₁₀ and as such:
19 - 7.3(¹¹/₁₀) = 10.97
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Sam ran 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday. How many total miles did Sam run?
Answers
Sam run for total 6.08 miles.
Sam run 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday.
What is fraction?Fraction is ratio of integers. example- 7/8.
Sam run [tex]3\frac{1}{4}[/tex] miles on Tuesday.
on [tex]2\frac{5}{6}[/tex] on Wednesday
Total run =Run on tuesday + Run on wednesday
Total run = [tex](3\frac{1}{4} )+(2\frac{5}{6} )[/tex]
= 13/4 + 17/6
Total run = 6.08
Thus Sam run for total 6.08 miles
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A train goes from springfield, MA, to boston at 40 mph. On the way back, it returns with a speed 80 mph. If it takes an hour less time to return, what is it's average speed?
Answers
The average speed for the entire journey will be 53.333 miles per hour.
What is the average speed?The average speed is the ratio of the total distance traveled to the total time taken by the body. Its unit is m/sec.
The distance from the Springfield, MA, to Boston is, L
v₁ is the velocity during traveling from Boston to Springfield, MA
v₂ is the velocity during traveling from Springfield, MA to Boston
t₁ is the time needed to travel from Boston to Springfield, MA
t₂ is the time needed to travel from Springfield, MA to Boston
t is the total time period of the journey
v is the average speed
From the formula of distance;
Distance = speed × time
The speed of train for the going from Springfield, MA, to Boston is 40 mph. The time period is calculated as;
L = v₁ × t₁
t₁ = L/v₁
t₁ = L/40
The speed of train for the going from Boston to Springfield, MA, is 80 mph. The time period is calculated as;
L = v₂ × t₂
t₂ = L/v₂
t₂ = L/80
The total time is taken;
t = t₁ + t₂
t = (L/40)+( L/80)
t=3L/80
The ratio of total distance traveled to the total time spent by the body is known as average speed, calculated as;
Average speed = Total distance / Total time
v = 2L / (3L/80)
v= (2L × 80)/3L
v = 160 / 3
v = 53.333 miles per hour.
Hence the average speed for the entire journey will be 53.333 miles per hour.
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Simplify by using radical. Rationalize denominators. 2a^-1/2
Answers
Answer:
[tex] \dfrac{2\sqrt{a}}{a} [/tex]
Step-by-step explanation:
[tex] 2a^{-\frac{1}{2}} = [/tex]
[tex]= 2 \times \dfrac{1}{\sqrt{a}}[/tex]
[tex]= 2 \times \dfrac{1}{\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}[/tex]
[tex] = \dfrac{2\sqrt{a}}{a} [/tex]
Select the correct answer. A system of linear equations is given by the graph. A diagonal curve declines from (negative 6, 4) through (negative 5, negative 3 point 2). A diagonal curve rises from (negative 7, negative 3) through (7, 0 point 2). Both curves intersect at (3 point 5, 2 point 2). What is the system shown? A. B. C. D.
Answers
The system of equations shown in this graph of a system of linear equations are:
y = -2/3xy = 3/4x - 5.How to determine the system of equations?In order to determine the required system of equations from this graph of a system of linear equations, we would find the slope of each line as follows:
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
For line 1, we have:
Points (x, y) = (0, 0) and (3, -2)
Slope = (-2 - 0)/(3 - 0)
Slope = -2/3.
Therefore, y = mx + c ⇒ y = -2/3x + 0.
For line 2, we have:
Points (x, y) = (0, -5) and (4, -2)
Slope = (-2 - (-5))/(4 - 0)
Slope = (-2 + 5)/(4 - 0)
Slope = 3/4.
Therefore, y = mx + c ⇒ y = 3/4x - 5.
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Answer:
O.B y = − 2/3x
y = 3/4x − 5
Step-by-step explanation:
Pierre Hugo is handling the estate of a prominent businesswoman. The will states that the surviving spouse is to receive 1/3 of the estate and the remaining 2/3 of the estate will be divided equally among 3 surviving children. What fraction of the estate does each child receive?
Answers
Each child will receive 0.125 (or 12.5%) of the estate.
If the surviving spouse gets one half of the estate, the other half has to be divided among the four surviving children.
What is the fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
So it's 0,5 divided among the 4 surviving children.
That is 0.125 or 12.5% of the estate.
Each child will receive 0.125 of the estate. a
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Mr. Robert charges $50 per hour for math tutoring and charges $40 per hour for language arts tutoring. How many hours of math tutoring must be mixed with 5 hours of ELA Tutoring to make $45 per hour?
Answers
5 hours of math tutoring must be mixed with 5 hours of arts tutoring to make $45 per hour.
Mr. Robert charges $50 per hour for math tutoring and charges $40 per hour for language arts tutoring.
Let, he mixed x hours of math tutoring to 5 hours of arts tutoring.
Then, Income from x hours of math tutoring = $50x
Income from 5 hours of arts tutoring = 5×$40 = $200
Total mixed income in (x+5) hours = $(50x+200)
According to the question, in mixed process he make $45 per hour. So, for (x+5)hours he earns $(x+5)45
So, The equation becomes,
50x+200 = (x+5)45
⇒ 50x+200 = 45x+225
⇒ 50x-45x = 225-200
⇒ 5x = 25
⇒ x = 25/5
⇒ x = 5
So, 5 hours of math tutoring must be mixed.
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The sum of series of 4+ 15 + 26 + ….. + 213
Answers
Decompose the terms in the sum as
[tex]4 + 15 + 26 + \cdots + 213 = 4 + (4 + 11) + (4 + 2\times11) + \cdots + (4 + 19\times11)[/tex]
so there are 20 terms in the sum. Then our sum simplifies to
[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + (0+1+2+\cdots+19)\times11[/tex]
Now, if
[tex]S = 1 + 2 + 3 + \cdots + 17 + 18 + 19[/tex]
we can reverse the order of terms to get the same sum,
[tex]S = 19 + 18 + 17 + \cdots + 3 + 2 + 1[/tex]
so that doubling up the sum gives
[tex]2S = (1 + 19) + (2 + 18) + \cdots + (18 + 2) + (19 + 1) = 19\times20 \implies S=19\times10=190[/tex]
So, our sum evaluates to
[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + 190\times11 = \boxed{2170}[/tex]
Which of the following graphs is described by the function given below?
y = x²-4x-12
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
Graph B is the graph that describes the function.
What is a quadratic graph?A quadratic graph is a graph of quadratic functions which have the power of the variable as 2. They are usually u-curved or inverted v-curved.
Analysis:
if we solve the quadratic function, y = [tex]x^{2}[/tex] -4x -12
when the curve touches the x-axis y = 0
[tex]x^{2}[/tex] -4x -12 = 0
[tex]x^{2}[/tex] -6x +2x -12 = 0
x(x-6) +2(x-6)
(x+2)(x-6) = 0
x = -2 or 6
From the graph, The second graph(graph B) shows the points on the x-axis x = -2 and x = 6.
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solve for a
-1/4a - 4 = 7/4a -3
Answers
Answer:
21 because -1/4a - 4 is 22
triangle BIG is similar to triangle MOP. Find v
Answers
Answer:
v = 34 in
Step-by-step explanation:
triangle BIG is similar to triangle MOP
This means that the length of their corresponding sides
are proportional.
Then
[tex]\frac{v}{51} =\frac{60}{90}[/tex]
Then
90v = 51 × 60
then
90v = 3060
Then
v = 3060/90
Then
v = 34
Geometry question Help please! Thanks!
Answers
Answer:
[tex]theta=47.33 degrees[/tex]
Step-by-step explanation:
sin theta=opposite/hyp
sin theta=500/680
theta in degrees=47.33
Answer:
The angle is 47.33°
Step-by-step explanation:
We have the hypotenuse as 680 ft and the opposite side as 500 ft, so we can use sin as a way to find the angle:
sin θ = opposite side / hypotenuse
sin θ = 500 ft / 680 ft
sin θ = 0.7353
θ = sin^-1 (0.7353) [this is called inverse of sine]
θ = 47.33°
If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be
found First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is
the distance from the center to endpoint of the diameter. Finally use the center-radius form to find the equation.
Find the center-radius form for the circle having the endpoints
(9,2) and (-7,4) of a dmiameter.
Type an equation.).
Answers
The equation of the circle would be (x - 1)² + (y - 3)² = 65.
What is the equation of a circle?The equation of a circle with center (h,k) and radius, r in center radius form is given;
(x - h)² + (y - k)² = r²
The coordinates of the center of the circle can be calculated by the formula
((x₁ + x₂)/2, (y₁ + y₂)/2).
The point (x₁,y₁) = (9, 2) and (x₂,y₂) = (-7, 4).
So, ((9 -7)/2, (4 + 2)/2) = (1, 3).
Now, r² = (x₂ - x₁)² + (y₂ - y₁)².
Let (x₁, y₁) = (1, 3) and (x₂, y₂) = (-7, 4).
So, r² = (-7 -1)² + (4 - 3)²
= -8² + 1² = 64 + 1 = 65.
With center (h,k) = (1, 3) and r² = 65, we have
Thus, the equation would be (x - 1)² + (y - 3)² = 65.
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find x and y.
please help !
Answers
Using linear pairs,
[tex]115+5x=180\\\\5x=65\\\\x=\boxed{13}[/tex]
By the exterior angle theorem,
[tex]2y=45+5(13)\\\\2y=45+65\\\\2y=110\\\\y=\boxed{55}[/tex]