Answer:
112560
Step-by-step explanation:
The total profit is the sale price of the helmet is $ 60 is:
$ 27,600
Step-by-step explanation:p denote the total profit and s denote the sale price.
The total profit in terms of the sale price is given by the function :
[tex]p(s)=-24s^2+2200s-18000[/tex]
Now we are asked to find the value of p when the s=60
when s=60 we have:
[tex]p(60)=-24\times (60)^2+2200\times 60-18000\\\\\\p(60)=-24\times 3600+132000-18000\\\\\\p(60)=-86400+132000-18000\\\\\\p(60)=27600[/tex]
Hence, the total profit when sale price is $ 60 is:
$ 27,600
Find the value of x.
Answer:
[tex]\large\boxed{2\sqrt7}[/tex]
Step-by-step explanation:
Look at the picture.
ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{AD}=\dfrac{AB}{AC}[/tex]
We have
[tex]AC=x,\ AD=2,\ AB=2+12=14[/tex]
Substitute:
[tex]\dfrac{x}{2}=\dfrac{14}{x}[/tex] cross multiply
[tex]x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7[/tex]
PLEASE HELP Do NOT GET HOW TO DO THIS
Answer:
they both have the equilateral lines on each side
Step-by-step explanation:
Jack estimates that the cost per mile, in dollars, for operating a certain truck is between 15% and 21% of the number of miles driven. This is shown by the system of inequalities below, where x represents the number of miles driven and y represents the cost of operating the truck.
y ≥ 0.15x
y ≤ 0.21x
Based on this information, which statement is true?
A) If Jack drives over 15 miles, it will cost 15 · 0.15 to operate the truck.
B) If Jack drives less than 21 miles, it will cost 21 · 0.21 to operate the truck.
C) If Jack drives the truck 100 miles, it will cost either $15 or $21.
D) If Jack drives 200 miles, it will cost anywhere between $30 and $42.
Answer:
D) If Jack drives 200 miles, it will cost anywhere between $30 and $42
Step-by-step explanation:
The cost is said to be a range of possibilities. The first three answer choices seem to assume the cost is at one extreme or the other. They incorrectly interpret the statement of cost.
Write all possible digits to make the number 132* multiple of 2 and 3 but not 5.
Answer:
6
Step-by-step explanation:
In order for 132* to be a multiple of 2, the digit * must be even.
In order for 132* to be a multiple of 3, the sum of all digits must be a multiple of 3. That is (1 +3 +2 + *) = 6+* is a multiple of 3. Since 6 is already a multiple of 3, then * must be a multiple of 3.
Single-digit values of * that are both even and a multiple of 3 are 0 and 6. We know that any number ending in 0 will be a multiple of 5, so we cannot use that digit.
The only possible digit that makes 132* a multiple of 2 and 3, but not 5, is 6.
The stock market lost 777.68 points in one day. It ended at 10,364.45 points on the same day. How many points did the stock market start with on that day
Answer:
jnd8663393765422345678
Step-by-step explanation:
nhbkjnm.l,n aels ewdlasmjDQLKd
A beach ball rolls off a cliff and onto the beach. The height, in feet, of the beach ball can be modeled by the function h(t)=64–16t^2, where t represents time, in seconds.
What is the average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air?
You are given h(t) = 64–16t^2.
You need to find h(1.25).
Set up:
h(1.25) = 64 - 16(1.25)^2
Take it from here.
Answer:
Step-by-step explanation:
Given the height of a beach ball rolling off a cliff as a function of time
h = 64 — 16t²
We want to find the average change in height when t = 1.25s
The rate of change of height is the differentiation of the height I.e
∆h/∆t → dh/dt
Therefore
h = 64 — 16t².
Therefore
Differential of a constant is zero
dh/dt = —32t
At t = 1.25s
dh/dt = —32(1.25)
dh/dt = —40 ft/s
So, the height is reducing at a rate of 40ft in every seconds.
The cost of 3 slices of pizza is $4.89. What is the cost of each slice of pizza? $1.63 $1.89 $2.45 $2.88
1.63
4.89 divided by 3 = 1.63
1.63 just divided the total by 3
Fayyaz bought a mobile phone for ?180 he sold it at a profit of 22% how much money did fayyaz sell the mobile phone for?
Answer:
$219.6
Step-by-step explanation:
we know that
The sell price is equal to the cost price plus the profit
Let
C ----> the cost price
S----> the sell price
P ----> the profit
so
S=C+P
we have
C=$180
Find the profit
22%=22/100=0.22
P=0.22*(180)=$39.6
Find the sell price
S=$180+$39.6=$219.6
Kim and Casey want to compare the prices of their favorite snack nexus determine which is less expensive the table below shows the price of each box of snack mix and the number of ounces in each box.One box cost $3.84 for 24 ounces and the other box is $4.48 for 32 ounces which is the cheapest
Answer:
The box of 32oz is cheaper by 2 cents per ounce.
Step-by-step explanation:
1. 3.84/24 ($0.16/oz)
2. 4.48/32 ($0.14/oz)
___
Hope this helps you! :)
Brian and Christina started keeping track of their workouts. Brian did 85 sit-ups the first week and 90 sit-ups each week after that. Christina did 65 sit-ups the first week and 90 sit-ups each week after that. How many sit-ups will each person have done after 5 weeks?
After 5 weeks, Brian will have completed 445 sit-ups, and Christina will have completed 425 sit-ups.
To calculate the total number of sit-ups Brian and Christina will have done after 5 weeks, we can use arithmetic progressions since the number of sit-ups increases by the same amount each week after the first.
For Brian:
Week 1: 85 sit-upsWeeks 2 to 5: 4 weeks x 90 sit-ups each week = 360 sit-upsTotal after 5 weeks: 85 + 360 = 445 sit-upsFor Christina:
Week 1: 65 sit-upsWeeks 2 to 5: 4 weeks x 90 sit-ups each week = 360 sit-upsTotal after 5 weeks: 65 + 360 = 425 sit-upsTherefore, after 5 weeks, Brian will have done 445 sit-ups and Christina will have done 425 sit-ups.
PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
B
Step-by-step explanation:
2 || 1 - 4 6 - 4
2 -4 4
==================
1 -2 2
x^2 - 2x + 2 with no remainder.
Looks like the answer is B
Note: Note that the two in x - 2 changes sign. That always happens when using synthetic division as long the number in front of the x is positive.
A model rocket is fired from the ground at time t=0, and it’s height is given in cm by the formula h=-490t^2 +1470t where t is measured in seconds.
Write an equation to find when the height of the rocket is 980 cm.
Solve the equation by factoring.
Explain why there are two solutions to this problem.
Step-by-step explanation:
h = -490t² + 1470t
When h = 980:
980 = -490t² + 1470t
Simplifying:
0 = -490t² + 1470t - 980
0 = t² - 3t + 2
Factoring:
0 = (t - 1) (t - 2)
t = 1, 2
There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.
The rocket reaches a height of 980 cm at 1 second and 2 seconds. The equation is factored to find these solutions, symbolizing the ascent and descent of the rocket.
To find when the height of the rocket is 980 cm, we set the height formula equal to 980 cm:
h = -490t² + 1470t = 980.
We then solve the equation by factoring:
-490t² + 1470t - 980 = 0
Divide by -10:
t²- 3t + 2 = 0
Factor:
(t - 1)(t - 2) = 0
Setting each factor to zero gives us the solutions:
t = 1 second
t = 2 seconds
There are two solutions because the rocket reaches 980 cm twice: once on its way up and once on its way down. This is demonstrated by the positive and negative components of the parabolic trajectory represented by the quadratic equation.
PLEASE HELP WILL GIVE 98 POINTS!!
The number of cases of a new disease can be modeled by the quadratic regression equation y= -2x^2+40x+8, where x represents the year.
Which is the best prediction for the number of new cases in year 15?
A. 276
B. 394
C. 72
D. 158
Answer:
D. 158
Step-by-step explanation:
Fill in the x's with a 15:
[tex]y=-2(15)^2+40(15)+8[/tex]
so y = 158
The best prediction for the number of new cases in year 15 is 158.
What is Quadratic Equation?Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation.
Here, Given quadratic equation
y = -2x² + 40x + 8
at put the value of x = 15, we get
y(15) = -2 X (15)² + 40 X 15 + 8
y(15) = -2 X 225 + 600 + 8
y(15) = -450 + 600 + 8
y(15) = 150 + 8
y(15) = 158
Thus, the best prediction for the number of new cases in year 15 is 158.
Learn more about Quadratic Equation from:
https://brainly.com/question/17177510
#SPJ2
Male and female students were surveyed about dancing and playing sports. They had the following preferences: Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 0.25 0.27 0.52 Female students 0.17 0.31 0.48 Column totals 0.42 0.58 1 Which of the following is a two-way conditional frequency table for gender? (2 points) Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 0.48 0.52 1 Female students 0.35 0.65 1 Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 25% 27% 52% Female students 17% 31% 48% Column totals 42% 58% 100% Do you prefer dancing or playing sports? Playing sports Dancing Male students 0.60 0.47 Female students 0.40 0.53 Column totals 1 1 Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 50 54 104 Female students 34 62 96 Column totals 84 116 200
The option that shows a two-way conditional frequency table is option B as shown in the image attached.
What is a two-way conditional frequency table?A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:
Gender.Preferred activity.Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.
Which option is correct?The correct option is option B because it meets the following requirements:
It displays the two variables: gender and preferred activities.It uses frequency values such as 0.48 rather than percentages or the number of people, which would be incorrect.The row totals are displayed in a third column than in a new row.Learn more about variables in: https://brainly.com/question/787279
Answer:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.48 0.52 1
Female students 0.35 0.65 1
Step-by-step explanation:
This is the answer
The athlete’s salary, in thousands, for the first two years is $400 and $400(1.05). The approximate salary, in thousands, earned each year for the first five years is $400, $420, $441, $463, and $486. Explain how you can evaluate the fifth partial sum. What does the fifth partial sum represent?
Answer:
Add the five terms.
Use the formula for the fifth partial sum.
The fifth partial sum represents the total amount of money the athlete earns over the first five years.
Step-by-step explanation:
Add the five terms.
Use the formula for the fifth partial sum.
The fifth partial sum represents the total amount of money the athlete earns over the first five years.
Answer: The fifth partial sum = 2210
The fifth partial sum represent the sum of the first 5 terms in the sequence.
Step-by-step explanation:
We know that he partial sum of a sequence gives the sum of the first n terms in the sequence.
Thus, the fifth partial sum represent the sum of the first 5 terms in the sequence.
The given geometric sequence : $400, $420, $441, $463, and $486.
Now, the fifth partial sum of the above sequence will be :
[tex]S_5=\$400+ \$420+ \$441+ \$463+\$486=\$2210[/tex]
Any number that can be written as a ratio of two integers
Final answer:
A number that can be expressed as a ratio of two integers is called a fraction. Ratios compare quantities and can be written in various forms, like fractions or with a colon. Proportions represent the equivalence of two ratios and are widely used in both mathematics and science.
Explanation:
Any number that can be written as a ratio of two integers is known as a fraction. A fraction is a type of ratio where one integer, the numerator, is divided by another integer, the denominator. For instance, 5/8 is a fraction because it represents 5 parts out of a total of 8.
A ratio can compare any two quantities, not just parts of a whole. These can be written as fractions, with a colon, or with the word 'to'. Examples include 2/3, 2:3, . Ratios are often used to compare dimensions, such as on a map where a unit scale is provided. For example, a map might state that 1 inch represents 100 feet, which is a ratio written as 1 inch/100 ft. Ratios are also essential in the health sciences, for instance, when describing solutions with a certain proportion like 1:1000.
In more complex applications, proportions are used to express equivalences between two ratios. For example, 1/2 is equivalent to 3/6, and this relationship forms a proportion. Proportions are useful in various fields, for setting up equivalencies and solving for unknown quantities.
Identify the equation of the circle X that passes through (−3,−5) and has center (4,−7). HELP ASAP!!
Answer:
(x - 4)² + (y + 7)² = 53
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (4, - 7), so
(x - 4)² + (y + 7)² = r²
The radius is the distance from the centre to a point on the circle.
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)
r = [tex]\sqrt{(-3-4)^2+(-5+7)^2}[/tex]
= [tex]\sqrt{(-7)^2+2^2}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]
Hence r² = ([tex]\sqrt{53}[/tex] )² = 53
(x - 4)² + (y + 7)² = 53 ← equation of circle
If [tex]z=-1-\sqrt{3}i[/tex] and [tex]z^{6}=a+bi[/tex], then [tex]a[/tex] = _ and [tex]b[/tex] = _
Rewriting [tex]z[/tex] in polar form makes this trivial.
[tex]z=|z|e^{i\mathrm{arg}(z)}[/tex]
We have
[tex]|z|=\sqrt{(-1)^2+(-\sqrt3)^2}=2[/tex]
[tex]\mathrm{arg}(z)=\tan^{-1}(-1,-\sqrt3)=-\dfrac{2\pi}3[/tex]
(not to be confused with the standard inverse tangent function [tex]\tan^{-1}x[/tex]. Here [tex]\tan^{-1}(x,y)[/tex] is the inverse tangent function that takes into account position in the coordinate plane; look up "atan2" for more information)
So we have
[tex]z=-1-\sqrt3\,i=2e^{-2\pi/3\,i}[/tex]
Then
[tex]z^6=2^6\left(e^{-2\pi/3\,i}\right)^6=64e^{-4\pi\,i}=64[/tex]
so that [tex]a=64[/tex] and [tex]b=0[/tex].
PLEASE HELP THIS IS THE LAST DAY I CAN TURN THIS IN!!! 75 points!!
PLEASE EXPLAIN YOUR WORK ALSO!
Cameron relies on his customers to tell their friends about his business. His business grows as each customer continues to tell others about his or her experience and they in turn tell others as well.
The table shows the number of people who have recommended Cameron’s business for different days after it first opens.
Time (days), x 3 4 7 10 12 13 17 18 21 27 30
Number of personal recommendations, y 12 14 18 23 28 31 46 50 67 118 157
(a) Write the exponential regression equation that models the data.
(b) Use the equation to estimate the number of personal recommendations 60 days after Cameron opens his business. Show your work.
Using technology, the regression equation is
y=9.08292(1.09965)ˣ.
The number of recommendations after 60 days is 2113.277 ≈ 2113.
Explanation
I used Desmos to graph the points, then entered the expression y₁~a*bˣ to calculate the regression.
I then substituted 60 in for x in the regression equation to get the answer of 2113.
In the figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠3=130°.
What is m∠6?
Answer:
The measure of angle 6 is m∠6=50°
Step-by-step explanation:
we know that
m∠3+m∠6=180° ----> supplementary angles (interior consecutive angles)
so
we have
m∠3=130°
substitute
130°+m∠6=180°
m∠6=180°-130°=50°
Write the english phrase as an algebraic expression. then simplify the expression. let x represent the number. the difference between five times a number and one more than three times the number.
Answer:
5x-(3x+1) or 2x-1
Step-by-step explanation:
The difference (subtraction) between five times x (5x) and one more (+1) than three times x (3x.) 5x-(3x+1)
Simplified, 5x-3x-1=2x-1.
URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the circumference of the circle? Use 22/7 for pi
44 cm
55 cm
100 cm
110 cm
circumference of the circle is d=35/2cm
For this case we have that by definition, the circumference of a circle is given by:
[tex]C = \pi * d[/tex]
Where:
d: It is the diameter of the circle
They tell us that:
[tex]d = \frac {35} {2}\\\pi = \frac {22} {7}[/tex]
Substituting:
[tex]C = \frac {22} {7} * \frac {35} {2}\\C = \frac {770} {14}\\C = 55 \ cm[/tex]
Thus, the circumference of the circle is 55 centimeters.
Answer:
Option B
Answer:
55 im not sure
Step-by-step explanation:
please help! tysm i really appreciate it!
Answer:
Correct: A, D, F
Step-by-step explanation:
Consider right triangle EFG.
By the definition of the cosine function,
[tex]\cos \angle E=\dfrac{EG}{EF}\\ \\\cos 30^{\circ}=\dfrac{EG}{EF}\\ \\\dfrac{\sqrt{3}}{2}=\dfrac{EG}{EF}\\ \\EG=\dfrac{\sqrt{3}}{2}EF[/tex]
Option F is correct.
By the definition of the sine function,
[tex]\sin \angle E=\dfrac{FG}{EF}\\ \\\sin 30^{\circ}=\dfrac{GF}{EF}\\ \\\dfrac{1}{2}=\dfrac{GF}{EF}\\ \\GF=\dfrac{1}{2}EF\\ \\EF=2FG[/tex]
Option D is correct.
By the definition of tangence,
[tex]\tan \angle E=\dfrac{FG}{EG}\\ \\\tan 30^{\circ}=\dfrac{GF}{EGF}\\ \\\dfrac{1}{\sqrt{3}}=\dfrac{GF}{EG}\\ \\GF=\dfrac{1}{\sqrt{3}}EGF\\ \\EG=\sqrt{3}FG[/tex]
Option A is correct
Yoshi is making blueberry muffins. he needs 1 1/4 cups of blueberries to make 1 batch muffins. How many cup of blueberries does Yoshi need to make 2 1/2 batches?
Answer:
3 3/4
Step-by-step explanation:
I've no idea if this is right, but this is how I'd do it:
For 2 batches you need 2 1/2 cups of blueberry
So, half of that is 1 and 1/4
So the total is 3 3/4
Answer:
The answer is 3 3/4
Step-by-step explanation:
I got it right on my test.
WILL GIVE BRAINLIEST AND 25 POINTS HURRY (has to be correct tho !)
Answer:
i am assuming 2 and 5 because they are the only ones that are not like the others
Step-by-step explanation:
Answer:
Angles 2 and 5
Step-by-step explanation:
Supplement angles are the angles which up to 180 degrees.
And all the angles shown are Vertically opposite angles and these angles are always the same.
Vertically opposite angles:
Angles 2 and 5
Angles 1 and 3
Angles 6 and 4
As shown in the picture, Angle 2 is 90 degrees and angle 5 being a vertically opposite angle, angle 5 is 90 degrees too.
90 + 90 = 180 degrees.
The tallest living man at one time had a height of 265 cm. The shortest living man at that time had a height of 109.1 cm. Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm. Which of these two men had the height that was more extreme?
Answer:
tallest man height is more extreme.
Step-by-step explanation:
Given:
Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.
Concept used:
Convert height into z scores for comparison of deviation from the mean.
Solution:
Tallest man height = 265 cm
[tex]Z_{tall} =\frac{265-173.73}{8.65} \\=10.55[/tex]
Shortest man height = 109.1 cm
[tex]Z_{short} =\frac{109.1-173.73}{8.65} \\=-7.47[/tex]
Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.
Hence tallest man height is more extreme.
The tallest living man at one time had a more extreme height compared to the shortest living man at that time.
Explanation:In this question, we are given the heights of the tallest and shortest living men at a specific time, as well as the mean and standard deviation of heights at that time. To determine which man had a more extreme height, we need to compare their heights to the mean and see how many standard deviations away they are.
The tallest man had a height of 265 cm, which is 265 - 173.73 = 91.27 cm above the mean.
The shortest man had a height of 109.1 cm, which is 173.73 - 109.1 = 64.63 cm below the mean.
Since the tallest man's height is significantly farther away from the mean compared to the shortest man's height, we can conclude that the tallest man had a more extreme height.
The sum of 5 consecutive even numbers is 310. What are the numbers?
These 5 numbers can be written as [tex]x,x+2,x+4,x+6,x+8[/tex], so their sum is
[tex]x+(x+2)+(x+4)+(x+6)+(x+8)=5x+20=310[/tex]
[tex]\implies5x=290[/tex]
[tex]\implies x=58[/tex]
Then the numbers are 58, 60, 62, 64, and 66.
Please help. what is the quotient of 4m^12/x-1÷x^2/8m^3 assume x ≠ 0 and m≠0
Answer:
[tex]\frac{32m^{15}}{x^3-x^2}[/tex]
Step-by-step explanation:
The given expression is: [tex]\frac{4m^{12}}{x-1}\div \frac{x^2}{8m^3}[/tex]
We multiply by the reciprocal of the second fraction:
[tex]\frac{4m^{12}}{x-1}\times \frac{8m^3}{x^2}[/tex]
We cancel out the common factors to get;
[tex]\frac{32m^{12+3}}{x^2(x-1)}[/tex], where [tex]x\ne0[/tex] and [tex]m\ne0[/tex]
We simplify to get:
[tex]\frac{32m^{15}}{x^3-x^2}[/tex]
Answer:
To simplify all that its D
Step-by-step explanation:
A homeowner has 5 cherry tomato plants in her garden. Over the course of the season the yields (in pints of tomatoes per plant) are: Plant 1 2 3 4 5 Yield 4 3.5 4.5 4.2 3.8 What is the average yield per plant, and what is the standard deviation (to two decimal places)? Average:
Answer:
Step-by-step explanation:
5
The average yield per plant is 4.00 pints, and the standard deviation is approximately 0.35 pints.
To calculate the average yield per plant:
1. Add up all the yields: 4 + 3.5 + 4.5 + 4.2 + 3.8 = 19.0 pints.
2. Divide the total yield by the number of plants (5): 19.0 / 5 = 3.8 pints per plant.
To calculate the standard deviation:
1. Find the mean (average) yield per plant, which we already calculated as 3.8 pints.
2. Calculate the squared differences from the mean for each yield:
- Plant 1: [tex](4 - 3.8)^2[/tex] = 0.04
- Plant 2:[tex](3.5 - 3.8)^2[/tex] = 0.09
- Plant 3: [tex](4.5 - 3.8)^2[/tex] = 0.49
- Plant 4:[tex](4.2 - 3.8)^2[/tex] = 0.16
- Plant 5:[tex](3.8 - 3.8)^2[/tex] = 0
3. Calculate the average of these squared differences: (0.04 + 0.09 + 0.49 + 0.16 + 0) / 5 = 0.156.
4. Take the square root of the variance to get the standard deviation: √0.156 ≈ 0.35 pints.
The average yield per plant provides a measure of the central tendency of the data set, indicating the typical yield for one plant.
The standard deviation measures the spread or variability of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates more variability. In this case, the standard deviation of approximately 0.35 pints suggests that the yields are relatively close to the average of 3.8 pints per plant, with minimal variability.
Complete question
A homeowner has 5 cherry tomato plants in her garden. Over the course of the season the yields (in pints of tomatoes per plant) are: Plant 1 2 3 4 5 Yield 4 3.5 4.5 4.2 3.8 What is the average yield per plant, and what is the standard deviation (to two decimal places)?
Please help me please
Answer:
(x + 5)² + (y + 8)² = 49
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 5, - 8), so
(x - (-5))² + (y - (- 8))² = r², that is
(x + 5)² + (y + 8)² = r²
The radius is the distance from the centre to a point on the circle
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, - 8) and (x₂, y₂ ) = (2, - 8)
r = [tex]\sqrt{(2+5)^2+(-8+8)^2}[/tex] = [tex]\sqrt{7^2+0^2}[/tex] = [tex]\sqrt{49}[/tex] = 7
r = 7 ⇒ r² = 7² = 49
Hence
(x +5)² + (y + 8)² = 49 ← equation of circle