Final answer:
The standard form equation of a circle centered at the origin and passing through (-1,3) is x² + y² = 10, where √10 is the radius of the circle calculated using the distance formula.
Explanation:
To write the equation of a circle in standard form that is centered at the origin and passes through the point (-1,3), you first need to calculate the radius using the distance formula. The distance formula is √((x2-x1)² + (y2-y1)²), where (x1, y1) is a point on the circle and (x2, y2) is the center of the circle. Since the circle is centered at the origin, (0,0), we can compute the radius as follows:
Radius = √((-1 - 0)² + (3 - 0)²) = √(1 + 9) = √10
The standard form of the equation for a circle centered at (h, k) with a radius r is:
(x - h)² + (y - k)² = r²
Since our circle is centered at the origin, h = 0 and k = 0, and the radius r = √10, the equation becomes:
x² + y² = 10
hat is the solution to the compound inequality 5x + 7 > −8 and 3x + 7 ≤ 19?
your elapsed time is 9 and 3/4 and you finishrd at 6:00 pm. what ime did you start?
sin(a)+sin(b)=sqrt(5/3) and cos(a)+cos(b)=1. Compute cos(a-b).
I drew out triangles and modeled the sines and cosines of a and b, but that doesnt help me find cos(a-b). What do I do?
Solve for x. 3.3x = 29.04 A) 8.0 B) 8.2 C) 8.6 D) 8.8
Felicia paid $2,879 for a new wall oven with her credit card. Felicia’s credit card has an APR of 13.89%, compounded monthly. It took Felicia seven years of identical monthly payments to pay for her oven, and she made no other purchases with her card until it was paid off. Over the ten years that she kept the oven, it used an average of $2.97 per week in electricity. Between the electricity and the interest, which component of the lifetime cost of the oven was greater, and how much greater was it? (Round all dollar values to the nearest cent.) a. The interest cost $94.12 more than the electricity. b. The interest cost $1,638.52 more than the electricity. c. The electricity cost $1,334.60 more than the interest. d. The electricity cost $463.32 more than the interest.
The lifetime cost of the oven shows that A. The interest cost $94.12 more than the electricity.
How to calculate the cost?From the given information, over ten years that she kept the oven, it used an average of $2.97 per week in electricity. This will be calculated as:
= 2.97 × (10 × 52)
= 2.97 × 520
= $1544.30
Then, using the interest, the computed value will be:
= [(53.78 × (12 × 7)] - 2879
= (53.78 × 84) - 2879
= 1638.52 - 1544.40
= $94.12
Therefore, the interest cost $94.12 more than the electricity.
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Where a linear equation crosses the y-axis, that point is called the A) x-intercept. B) y-intercept. C) point of termination. D) point of translation.
Answer:
B) Y- Intercept
Step-by-step explanation:
I Took The USATP Quiz ^_^
1 tin of 500ml blue paint costs $11.50. to finish a bedroom i need 4litre of blue paint. how much wi this cost me.
Anita sees in her nutrition book that a 7.5-ounce cake has 900 calories how many calories will she save if only takes 2.5-ounce piece help please
(4u)(5v^2)-2u+uv^2-4uv^2
Ms. O bought 2 1/2 pounds of blueberries on Monday. She Gavs 1/4 of the blueberries to her students before school ended A. How many pounds of blueberries did she give to students on monday B.How many blueberroes were left? C. On Tuesday she ate 1/3 of the remaining blueberries. How many did she eat on Tuesday? D. Did Ms.O eat more blueberries on Monday or on Tuesday? Explain your reasoning
A point undergoes two transformations. The x-coordinate's sign changes and the y-coordinate increases. What were the transformations?
Answer: The correct option is
(C) The point was reflected over the y-axis and translated up.
Step-by-step explanation: Given that a point undergoes two transformations as follows :
"The x-coordinate's sign changes and the y-coordinate increases."
We are to select the correct transformations.
We know that
when x co-ordinate's sign changes, the point (x, y) becomes (-x, y). This is reflection across y-axis.
And, if y co-ordinate increases by k units, then (x, y) becomes (x, y+k). That is, the point (x, y) is translated k units upwards.
Thus, the required transformations are
The point was reflected over the y-axis and translated up.
Option (C) is CORRECT.
Clara's savings account has an APR of 10.95% calculates interest daily and pays interest at the end of the month if during the month of september her balance was $700 for the first 10 days of the month, $1900 for the next 10 days of the month, and $1400 for the last 10 days of the month, how much total interest did clara earn in september
A. $12.78
B. $11.20
C. $12.00
D. $11.30
Answer:
The correct option is C. $12.00
Step-by-step explanation:
Annual Principal Rate = 10.95%
= 0.1095
Time duration = 10 days
[tex]\text{Time duration in years =}\frac{10}{365}=0.027\:\:years[/tex]
First finding interest rate for $700
Interest = 700 × 0.1095 × 0.027
= $2.10
Now finding interest rate for $1900
Interest = 1900 × 0.1095 × 0.027
= $5.70
Then finding interest rate for $1400
Interest = 1400 × 0.1095 × 0.027
= $4.20
Total Interest paid = 2.10 + 5.70 + 4.20
= $12.00
Hence, The correct option is C. $12.00
John bought 12 books 2/3 of the books are science fiction how many of the books are science fiction
Carter is playing a video game he needs to score more than a hundred points to move on to the next level write an inequality to show how many points Carter needs to earn
mr. Dell taught the six members of the chess club to play chess. each member taught three classmates. each classmate taught two more friends. how many people were taught to play chess?
Mr. Dell taught six members of the chess club who then taught 18 classmates, and those classmates taught 36 friends, resulting in 60 people being taught how to play chess in total.
To find the total number of people taught, we compute as follows:
First level (by Mr. Dell): 6 members
Second level (6 members x 3 classmates each): 18 classmates
Third level (18 classmates x 2 friends each): 36 friend
To determine the total number of people taught to play chess, we sum the three levels: 6 members + 18 classmates + 36 friends = 60 people. Therefore, a total of 60 people were taught to play chess
Brian spent 60% of a weeks time working on drawings for a new apartment building. If Brian spent 18 hours working on projects other than the apartment building, compute the total hours worked
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression.
Answer:
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.
Step-by-step explanation:
The total points scored in the game as a variable expression is 2c + c + 3.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
It is given that Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended:
Let consider Central High School score be c
We knowt that the variable, c, represents Central's score before the three-pointer.
So, when Eastern doubled the score of Central, it is 2c
A Central scored a three-pointer as the game ended, it is + 3
To get the total points scored in the game, add all the actual variables
= (Eastern double points + Central single point + Central three-pointer)
= 2c + c + 3
So, the total points scored in the game as a variable expression is 2c + c + 3.
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Brian is playing a video game. He earns the same number of points for each star he picks up. He earned 2,400 points for 6 stars, 4,000 points for 10 stars, and 5,200 points for 13 stars. Which is the independent variable in the situation?
The solution is, the independent variable is number of stars, in the situation.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
from the given information, we get,
Points are a function of stars, so stars is the independent variable.
The variable that depends on that, the dependent variable, is points.
now, we have,
2400/6= 400
4000/10= 400
5200/13= 400
we get,
y=400x
Every star is 400 points and the independent variable is number of stars Brian picks up because the amount of points he gets is dependent on the number of stars he has.
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Yesenia took three tests in her accounting class. She scored 91 points on her first test and 73 points on her second test. If her average for the three tests is 79, what score did she get on her third test?
Let Yesenia's score in the third test be represented by the letter "x".
Now, we know that, by definition, the average in our case is the ratio of the sum of the points scored in the tests to the total number of tests taken.
We know that Yesenia scored 91 points on her first test and 73 points on her second test.We also know that Yesenia's average is 79. We have already assumed that she scored "x" in the third test. Thus, by definition of average, we get the following equation as:
[tex] 79=\frac{91+73+x}{3} [/tex]
Cross multiplication gives us:
[tex] 79\time 3=164+x [/tex]
Thus, [tex] x=237-164=73 [/tex]
Thus, Yesenia got a score of 73 in her third test.
plz put graph form
1) 2x - y = -13
y = x + 9
2)3x + 2y = 10
6x - y = 10
3)4x - 3y = 5
3x + 2y = -9
4)x + y = 7
x - y = -1
Which is greater 770 meters or 7 kilometers
Find the function y1 of t which is the solution of 16y′′−81y=0 with initial conditions y1(0)=1,y′1(0)=0.
can someone help me please
The first step to solve this problem is to compute first for the area of the bigger rectangle:
A = LW
A = 12m (10m)
A = 120 m^2
Next step is to find the area of the smaller rectangle:
A = LW
A = 7m (2m)
A = 14 m^2
The last step is to deduct the area of the smaller rectangle to the area of the larger rectangle:
Area of larger rectangle – Area of the smaller rectangle = Area of the shaded region
120 m^2 – 14 m^2 = 106 m^2
Therefore, the area of the shaded region is 106 square meters.
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For what value of x:
is the square of the binomial x+1 twenty greater than the square of the binomial x–3?
Mailboxes plus sends packages overnight for $5 plus $0.25 per ounce. United packages cost $2 plus $0.35 per ounce. Mr.Molinari noticed that his package would cost the same to maill using either service. How much does his package weigh?
By setting up an equation equating the cost of shipping with both Mailboxes Plus and United Packages, we determine that Mr. Molinari's package weighs 30 ounces.
Mailboxes Plus charges a flat rate of $5 plus $0.25 per ounce, while United Packages charges $2 plus $0.35 per ounce. Since the cost is the same for either service, we can equate the two expressions and solve for the weight of the package in ounces.
Let x represent the weight of the package in ounces. The cost for Mailboxes Plus is then $5 + $0.25x, and for United Packages, it is $2 + $0.35x. Setting these two expressions equal to each other, we get:
$5 + $0.25x = $2 + $0.35x
Now, we will solve for x:
Subtract $2 from both sides: $3 + $0.25x = $0.35xSubtract $0.25x from both sides: $3 = $0.35x - $0.25xCombine like terms: $3 = $0.10xDivide both sides by $0.10: $3 / $0.10 = xSimplify: 30 ounces = xTherefore, Mr. Molinari's package weighs 30 ounces.
The school is having a bake sale and the math club is bringing cupcakes. They have 180 total cupcakes, both chocolate and strawberry. The number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes. Which system of equations can be used to find the number of chocolate cupcakes, c, and the number of strawberry cupcakes, s? A. c + s = 180 s = 2c - 18 B. c + s = 180 c = 2s + 18 C. c - s = 180 s = 2c + 18 D. c = 2s c - 180 = s
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The difference of two numbers is equal to 0.6. Their quotient is also 0.6. What are the numbers? Please answer both questions below.
What are the numbers?
What are the "or" numbers?
The numbers are:
Or numbers are"
change one letter in the word cave to solve it: A curved stick_______
By changing the 'v' in 'cave' to 'n', we solve the clue: A curved stick, given by the word 'cane'. Although a concave mirror was mentioned, it doesn't fit in this context.
Explanation:The question asks you to change one letter in the word 'cave' to solve the clue: A curved stick. If we change the letter 'v' in 'cave' to 'n', we get the word 'cane'. A cane is typically curved at the top, resembling a stick. Although the reference to a concave mirror is interesting, it does not fit in this context as a concave mirror is a spherical mirror with its reflecting surface on the inner side of the sphere, forming a 'cave' shape. A useful tip to remember for distinguishing between concave and convex is: concave means caved in.
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in an election for sheriff 210 people voted if there where 1260 possible voters write a ratio to compare the number of people who voted to the numbernof possible voters
The ratio of the number of people who voted to the number of possible voters in the sheriff election is 1:6 after simplifying the original ratio of 210:1260.
Explanation:In an election for sheriff where there are 1260 possible voters and only 210 people voted, the ratio of the number of people who voted to the number of possible voters can be written as 210:1260. To simplify this ratio, you divide both numbers by the greatest common divisor, which in this case is 210. So, when you divide both 210 and 1260 by 210, the simplified ratio is 1:6. This means that for every one person who voted, there were six possible voters.
The number of people who voted is 210 and the number of possible voters is 1260. So the ratio is 210:1260. Simplifying this ratio by dividing both numbers by their greatest common divisor, which is 30, we get 7:42. Therefore, the ratio to compare the number of people who voted to the number of possible voters is 7:42.
The circumference of a circle is 6.28 meters. What is the circle's radius? C=6.28 m Use 3.14 for pi
The radius of the circle is 1 meter.
We have,
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, r is the radius, and π is a constant equal to approximately 3.14.
We are given the circumference of the circle as 6.28 meters, so we can substitute this value into the formula:
6.28 = 2πr
Dividing both sides by 2π gives:
r = 6.28 / (2π)
r = 6.28 / (2 x 3.14)
r = 1
Therefore,
The radius of the circle is 1 meter.
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Final answer:
To find the circle's radius with a circumference of 6.28 meters using π=3.14, use the formula C=2πr. By rearranging and solving for r, the radius is found to be 1 meter.
Explanation:
The question is about finding the radius of a circle when the circumference is given as 6.28 meters and using 3.14 for π (pi). To find the radius, we use the formula for the circumference of a circle, C = 2πr, where C is the circumference, r is the radius, and π is Pi. Given C=6.28 m and π=3.14, we rearrange the formula to solve for r: r = C / (2π).
Plugging in the given values, r = 6.28 / (2×3.14) = 6.28 / 6.28 = 1. Therefore, the radius of the circle is 1 meter.