Mathematics High School

The center of a circle is at (-5, 7) and its radius is 6 units. Which of the following is the equation for this circle?

A) (x - 5)2 + (y + 7)2 = 36
B) (x + 5)2 + (y - 7)2 = 36
C) (x - 5)2 + (y + 7)2 = 12
D) (x + 5)2 + (y - 7)2 = 12

Answers

Answer 1

Answer:
Option B, (x + 5)² + (y - 7)² = 36

Explanation:

The equation for a circle is (x - h)² + (y - k)² = r² where r represents the radius of the circle and the center is ordered pair (h, k).

We can then plug the given information into the formula and simplify where possible.

Center at (-5, 7), radius = 6:
[x - (-5)]² + (y - 7)² = (6)²

(x + 5) + (y - 7)² = 36, which matches option B.

Related Questions

|-x-2y| for x =-3 and y=3

Answers

[tex]|-x-2y|\ for\ x=-3\ and\ y=3.\\\\substitute:\\\\|-(-3)-2\cdot3|=|3-6|=|-3|=3[/tex]

Which additional information is needed to solve this problem?



John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?


A.
total amount John can save in 1 week

B.
the cost of the game

C.
amount John earns per hour babysitting

Answers

Hi there!

The answer is B.
the cost of the game.

We need to know the cost of the game in order to find out how many weeks John has to save money. If we don't know this price, we'll never know whether John has saved enough money.

We can find out the total amount of money John can save in 1 week (so A. is not the answer). The amount of money John earns per hour doesn't matter to answer the question (so C. is wrong).

~ Hope this helps you!
the answer is B he won't know how much to save if he does not know the cost of the game

what is the value of the expression?

Answers

To solve this we are going to use the unitary circle and the fact that [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex]

From our circle we can infer that [tex]sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2} [/tex] and [tex]cos\frac{5 \pi }{3}= \frac{1}{2} [/tex].

Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]

We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].

Use addition to solve the linear system of equations. Include all of your work in your final answer.

x - y = 4
x+ 2y = 4

Answers

we have that
x - y = 4-------> multiply by -1-----> -x+y=-4-----> equation 1
x+ 2y = 4------> equation 2

add equation 1 and equation 2
-x+y=-4
x+2y=4
-----------------
0+3y=0-----> y=0
x+2y=4------> x+0=4------>x=4

the solution is the point (4,0)

What is the slip of the line given by the equation y=-1/3 x

Answers

the slip?  I don't think it has any slip, but as far as the slope goes, well, the equation is in slope-intercept form, thus

[tex]\bf y=\stackrel{slope}{-\cfrac{1}{3}}x~~\stackrel{y-intercept}{+0}[/tex]

Tina can paint a room 1.5 times faster than Joey can. If they work together, they can paint a room in 6 hours. How long would it take the slower person working alone to paint the room?

Answers

So, the rate is 1 job / hours, so:
1/n + 1/1.5n = 1/6
We'll make the denominator 3n:
3/3n + 2/3n = 1/6
5/3n = 1/6
Cross multiply:
3n = 30
n = 10
It will take the slower person 10 hours to complete the room.

PLS HELP! Tanisha is planning a party. She will serve hamburgers, potato salad, strawberry shortcake, and lemonade. Including Tanisha, 28 people will be at the party. Tanisha expects that each person will drink two 8−ounce glasses of lemonade at the party, and makes 448 ounces of lemonade. Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 ounces of lemonade. Does Tanisha need more lemons?

Answers

Shee needs 448 ounces of lemonade.

448 ÷ 80 =5.8
⇒ There are 5.6 80-ounce of lemonade.

80 ounces of lemonade needed 8 lemons.
448 ounces of lemonade needed 8 x 5.6 = 44.8 lemons.

Tanisha has 38 lemons. 
She does not have enough lemons.
She needs 44.8 - 38 = 7 more lemons.

Answer: Tanisha needs more lemons. She needs 7 more.

Answer: 7 more lemons

Step-by-step explanation:

Since she needs 448 ounces of lemonade you have to divide which is 5.6 . As a result there are 5.6 80 ounces of lemonade. 80 ounces needs 8 lemons.  448 ounces of lemonade are needed 8 x 5.6 = 44.8 lemons.  Tanisha only has 38 lemons, which isn't enough. 44.8 - 38 =  is about 7 more lemons.

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. tables Which of the following correctly represents the given data in the problem?

Answers

We have that 48 students are in the band and that 24 out of them also play sport. Hence, in total 24 students are in the band but dont play sports. We have that there are 4 categories and we know the other 2 categories (do both, do none). There is a 4th category, only sports. We know that the sum of all those categories is 80 (since a student either does or does not a combination of those). Hence, 80=24+24+22+x. We have that x=10, hence 10 students play sports but are not in the band.

D) a = 24, c = 48, e = 22, i = 80


someone please help asap! Which statement is most likely true for this distribution?

Answers

Answer:

C) The mean is greater than the median.

Step-by-step explanation:

This distribution is right skewed; that means it has a longer tail to the right and the data is "bunched up" at the left.

In a right skewed distribution, the majority of data points are at the smaller end; for this reason, the median will be towards the left side of the graph.

The higher numbers in the "tail" will bring the mean up, making it larger than the median.

The correct statement for the distribution is the mean is greater than the median.

What is mean and median?

The mean is the average of a data set. The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle term of a distribution.

It measure determines the middle value of a dataset listed in ascending order.

Therefore, from the distribution the data are rightly skewed. The higher numbers in the "tail" will bring the mean up, thereby making it larger than the median.

learn more on mean and median here: https://brainly.com/question/14299269

#SPJ2

The perimeter of the base of a pentagonal prism is 25 inches and one of its lateral edges is 4 inches. The lateral area of the prism is ________ square inches.

Answers

Answer:

Lateral area=100 square inches

Step-by-step explanation:

It is given that the perimeter of the base of a pentagonal prism is 25 inches, therefore each sides of the pentagon will be of 5 inches.

Also, one of its lateral edge is 4 inches, therefore each lateral face has area which will be equal to=[tex]5{\times}4[/tex]=[tex]20[/tex]square inches.

Since, there are 5 lateral faces of the pentagonal prism, therefore the lateral area of the prism will be: [tex]5{\times}20[/tex]

                                       = [tex]100[/tex]square inches.

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town

Answers

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

HELP!!!!!!What is the equation of the graph below?

Answers

The answer to your question is y = sin(x + 90) as we have a sine graph phase shifted 90 units left

Which expression is equivalent to 4 sqrt 16x^11y^8/81x^7y^6

Answers

Final answer:

The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.

Explanation:

The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.

We start by simplifying the square root of each component:

Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.

Now, divide and simplify:

(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)

Therefore, we get:

(4/9) * x^2 * y

This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.

Answers

Your choice is correct. The slope of the function on the interval is negative. The slope of the inverse function is the reciprocal of that, still negative.

It is NOT true that [tex]\dfrac{d}{dx} \left( f^{-1}(x) \right) \ge 0[/tex]

The unt informs club has 16 members. they need to elect a president, a vice president, a secretary and a treasurer. how many different ways can this group of 4 officers be formed? (order is important)

Answers

If they needed to elect just the president there could be 16 possible combination. If they needed to elect the president and the vice there could be 16×15 possible combination, because each president could have 15 possible vice. So the possible combination are 16×15×14×13=43 680.

Hope this helped!

Vanessa is opening a clothing store. She plans to start by selling gym shorts. If it costs her $4 for each pair of shorts, $3 for the ink per pair of shorts, and $0.20 a bag, what is her unit cost per pair of shorts?

Answers

Unit cost=(total cost)/(number of units)
cost of shorts=$4
Number of pairs=1
thus
unit cost=4/1=4 dollars per pair

Answer: 4 dollars per pair

Answer:

its $7.20 on APEX

Step-by-step explanation:

QS is the perpendicular bisector of PR solve for x

Answers

2x-20=70-x
3x=90
so the answer is x=30

2x - 20 = 70 - x


3x - 20 = 70


3x = 90


x = 30

simplify radical (1-cos0)(1+cos0)/ cos^2 0

HELP ME PLS!! ASAP

Answers

that would be tan

(1-cos)(1+cos)=1-cos² which equals to sin²

√sin²/cos²= sin/cos which equals to tan

trignometry help what's the answer?

Answers

You have the 175 on the wrong line, the problem says 175 feet from the base, this is the bottom of the tree.

 See attached picture for solution:

The line plot represents the heights of students in a second-grade classroom. Which statement is true?

A. The median is less than the mode.


B. The median height is 42 inches, and the mode height is 36 inches.


C. Most of the students in the class are shorter in height.


D. The mode is less than the median.

Answers

The correct answer is A

Answer:

B. The median is less than the mode

Step-by-step explanation:

HEEEELLLPP!!!!!!!!!!!!!!!WILL GIVE THE BRAIN!!!!!POINTS!!!!!!!
plz

Answers

If you observe the graph, it has a minimum point at x = -2

It is the local minimum as it is the minimum point in the neighboring. The term local is used, as it is the lowest point within a short interval and not for the entire function. 

The interval which correctly shows the local minimum is [-3, -1]

So, the correct answer is option Third

Calculate the total cost of the order: Veggiburger with cola and soup, sales tax 4%, tip 15.

Veggiburger: $3.25
Cola: $1.50
Soup: $2.25

A $8.33
B $7.28
C $7.00
D $5.50

Answers

Add the prices of the food together to get $7. Then you calculate the sales tax, which is 1.04 * $7 = $7.28. The tip is 15% I am assuming, and not 15, so it would be $7 * 0.15 = $1.05. Add $1.05 with $7.28 to get $8.33, so the answer is A.
Final answer:

The cost of the order, including the sales tax of 4%, comes out to be $7.28. However, the tip is unclear in the question. If it's 15%, the cost rises to $8.37, but none of the provided options match this result.

Explanation:

The first step is to calculate the total cost of the Veggiburger, cola, and soup by adding them together. So, $3.25 (Veggiburger) + $1.50 (cola) + $2.25 (soup) = $7.00. Next, apply the 4% sales tax on this amount which is $7.00 * 4/100 = $0.28. So the subtotal now is $7.28 ($7.00 + $0.28). Finally, the tip mentioned in the problem is not clear whether it is a percentage or a fixed amount. If it is a 15% tip, then calculate 15% of the subtotal, i.e $7.28 * 15/100 = $1.09 (Approx). Adding this to the subtotal we get $8.37 which is not an option in the given answers. If $15 is a fixed tip amount, the total cost would be substantially larger. Please ensure the tip amount is correct.

Learn more about Sales Tax and Tip Calculation here:

https://brainly.com/question/9622811

#SPJ2

a triangle with a base of 6cm and a height of 8cm is similar to a triangle with base 21cm. What is the height of the second triangle

Answers

Make a proportion.

Do base over height; [tex] \frac{base}{height}[/tex].

[tex] \frac{6}{8} = \frac{21}{h} [/tex]
h is the height of the second triangle. Solve for h.

Cross multiply.
[tex] \frac{6}{8} = \frac{21}{h} [/tex] 
6h = 168
h = 28

The height of the second triangle is 28 cm.

Cans of juice cost 25p each to produce
There are 6 cans in a pack.
12 packs are sold at £3.60 each.
What is the profit?

Answers

 the profit is 1.60 beacuse at 25  cents times 6 is two dollars and since it is 3.60 the profit is 1.60 and 1.60 times twelve is 19.20 so the answer is 19 dollars  and twenty cents

Henry has a defined benefit plan that promises a 2.5% annual retirement benefit based on the average of his last five years of salary. At retirement Henry has 21 years of service and an average salary over the last five years of $95,000. What will his annual benefit be?

Answers

Henry's annual retirement benefit will be $2,375.

We have,

To calculate Henry's annual retirement benefit, we need to find 2.5% of his average salary over the last five years.

First, let's calculate 2.5% of $95,000:

2.5% = 2.5/100 = 0.025

Annual benefit = 0.025 * $95,000

Annual benefit = $2,375

Therefore,

Henry's annual retirement benefit will be $2,375.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

During a family vacation, Ms. Walker drove 918 miles on 3 tanks of gasoline. Her daughter, Amani, wants to create an equation in the form em equals square tee, to represent the total number of miles, m, her mom can drive on t tanks of gasoline. What number should Amani put in the square to complete her equation?

Answers

To complete the equation Amani needs the rate of the miles driven per tank, this will be given by:
Rate=(miles)/(number of tanks)
thus the rate will be:
miles=918 mile
tanks=3 tanks
thus
rate=918/3=306 miles/tank

Compute the stock turnover in dollars for a product that has sales of $6,000 and an average value of inventory investment of $1,500.

Answers

Question: It should be inventory turnover.

Solution:
Inventory turnover = Cost of goods sold/Average inventory

Substituting the values given for cost of goods and average inventory;
 Inventory turnover = 6,000/1,500 = 4

Answer: 4

Step-by-step explanation:

Given: Cost of product sold = $6,000

Average value of inventory= $1,500

We know that the inventory turnover formula is given by :-

[tex]\text{Inventory turnover}=\frac{\text{ Cost of product sold}}{\text{Average value of inventory}}[/tex]

[tex]\\\Rightarrow\ \text{Inventory turnover}=\frac{\$6,000 }{\$1500}\\\\\Rightarrow\ \text{Inventory turnover}=4[/tex]

Therefore, the stock turnover for a product that has sales of $6,000 and an average value of inventory investment of $1,500 = 4

what is the sum of the geometric series E (-2)(-3)^n-1

Answers

Sum of the geometric series: S=?
S=(-2)(-3)^(1-1)+(-2)(-3)^(2-1)+(-2)(-3)^(3-1)+(-2)(-3)^(4-1)
S=(-2)[(-3)^0+(-3)^1+(-3)^2+(-3)^3]
S=(-2)[1+(-3)+9+(-27)]
S=(-2)(1-3+9-27)
S=(-2)(-20)
S=40

Answer: Third option 40

Answer:

The sum is 40.

Step-by-step explanation:

Given,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}[/tex]

We know that,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1}[/tex]

[tex]=(-2)(-3)^{0}+(-2)(-3)^1+(-2)(-3)^2+(-2)(-3)^3[/tex]

[tex]=-2\times 1 - 2\times - 3 - 2\times 9-2\times -27[/tex]

[tex]=-2+6-18+54[/tex]

[tex]=40[/tex]

Hence,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=40[/tex]

match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
A.

B.

C.

D.

Answers

The correct linear system for the student's question is D. x + 3y \<= 38, x + y \<= 12, which matches the conditions of Lewis's situation for acquiring baseball cards.

The student is looking to match a situation with a linear system. The situation is that Lewis wants at most 12 packages of baseball cards, some containing 4 rookie cards and others 3 rookie cards, with a total of 38 rookie cards at most.

To match the situation with the correct linear system, we must set up two inequalities: one for the number of packages and another for the number of rookie cards.

Let x represent the number of packages with 4 rookie cards and y represent the number of packages with 3 rookie cards.

The first condition is that Lewis can have at most 12 packages, which gives us the inequality x + y \<= 12. The second condition is that the total number of rookie cards is at most 38, which gives us the inequality 4x + 3y \<= 38.

Considering these conditions, the correct answer is: D. x + 3y \<= 38,  x + y \<= 12.

Tom has been given 35 chores to complete today this morning he finished seven of them how many chores does he now have left to do

Answers

Simple equation: 35-7=28 chores left to do
He should only have 28 left to do.
Other Questions
Studies suggest that the amount of caffeine in as many as ________ of coffee per day yields little health risk. 2,2-dimethyl-4-propyloctane has how many secondary carbons? view available hint(s) 2,2-dimethyl-4-propyloctane has how many secondary carbons? five nine six seven In the equation x + 2y = -3, the x-intercept is -3 and the y-intercept is -1.5. please show with a graph In the stage of intercultural communication awareness known as conscious competence: Which of the following is the best example of a domestic policy? A resolution to join an international trade organization A decision to limit immigration to the United States A decision to send financial aid to another country after a natural disaster A resolution declaring war on another country __________ is the breeding of fish in freshwater ponds, lakes, and canals or in fenced-off coastal bays and estuaries or enclosures. Shavon is going to wrap a box that is shaped like a rectangular prism. The box is 12 inches long, 8 inches wide, and 3 inches high. What is the least amount of wrapping paper that Shavon will need to completely cover the Box? Translate into an algebraic expression. Use x and y for any variables.The sum of four times a number plus four times another number. Please please help. I have a bunch of these and I dont understand it at all What is the name for the protein that forms the basic fibers of body tissue? The Roman Empire began in 27 B.C. and ended in 476 A.D. The Persian Empire lasted approximately 5/11 as long as the Roman Empire. Based on this approximation, if the Persian Empire began in 550 BC, in what year did it end?Round all years to the nearest whole number. Bill is the biological son of ed and marilyn, who divorced when bill was three years old. for two years, bill and marilyn lived alone. then, when bill was five, bill and marilyn moved in to jeff's home with jeff and his three children when jeff and marilyn got married. in order, bill's family type changed from The ______ resolution was passed by the u.s. congress in 1964 and allowed the president to expand american involvement in vietnam.eastersaigon On the first day of the year you have $700 in your bank account you spend $35 per week your friend starts the year with 450 in his bank account he said to $15 per week solve the equation 700-35W equals 450+15 W to find out how many weeks W it will take for you and your friend to have the same amount of money in your bank account What is one reason that white mobs attacked blacks in northern cities in the 1800s? Cans of juice cost 25p each to produceThere are 6 cans in a pack.12 packs are sold at 3.60 each.What is the profit? A solution with a volume of 1.00 l is 0.450 m in ch 3 cooh(aq) and 0.550 m in ch 3 coona(aq). what will the ph be after 0.0800 mol of hcl is added to the solution? What is the advantage of the gram stain over the simple stain? How many social security numbers are available if the only restriction is that the number 000-00-0000 cannot be assigned? If you were trying to build a sound proof room, which of the following materials would you choose in order to absorb the most sound, based on the coefficient of absorption for each material