The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?


A. The skaters’ paths intersect once, but that point is outside the rink.

B. The skaters’ paths intersect once, and that point is inside the rink.

C. The skaters’ paths intersect twice, but only one of those points is inside the rink.

D. The skaters’ paths intersect twice, and both points are inside the rink.

Answers

Answer 1

Answer:

Option C:The skaters path intersect twice, but only one of those points is inside the rink.

Step-by-step explanation:

Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m

We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²

Thus, the total area on which the skaters are skating will be given by the equation;

x² + y² = 35²

Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5

While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)

From equation of a parabola, the path along which like is skating can be modeled by;

(x - 8)² = 4a(y + 9)

To find a, we will substitute the coordinate started at to get;

(10 - 8)² = 4a(-21 + 9)

4 = 4a × -12

Divide both sides by 4 to get;

a = -1/12

Thus;

(x - 8)² = 4(-1/12)(y + 9)

(x - 8)² = (-1/3)(y + 9)

This gives: 3(x - 8)² = -(y + 9)

I've drawn the graph on demos and attached it.

From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.

Thus, correct answer is Option C.

The Center Of An Ice Rink Is Located At (0, 0) On A Coordinate System Measured In Meters. Susan Is Skating
Answer 2

Answer:

C

Step-by-step explanation:

just took the quiz


Related Questions

On the beach boardwalk there are 20 different places to get food 20% of them are ice cream shops how many ice cream Shoppe’s are in the park

Answers

4 ice cream shops
hope this helps!

Answer:

( 4 )

Step-by-step explanation:

Hope this helps

also go to g-mail to check out my

Type in Brandon Acevedo

okay

Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. What is Herman’s final position, relative to ground level?

Answers

Answer:

Are there answers

Step-by-step explanation:

Answer:

answer

Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. ...

A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?

Answers

Answer:

B

Step-by-step explanation:

To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.

The solution is:

a) V (max) = 36.6 in³

b) x = 1.3 in

The volume of a cube is:

V(c) = w×L×h  ( in³)

In this case, cutting the length  "x" from each side, means:

wide of the box    ( w - 2×x )   equal to  ( 7 - 2×x )

Length of the box ( L - 2×x )   equal to  ( 9 - 2×x )

The height  is  x

Then the volume of the box,  as a function of x is:

V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x

V(x) = ( 63 - 14×x - 18×x + 4×x²)×x

V(x) = 4×x³ - 32×x² + 63×x

Tacking derivatives,  on both sides of the equation

V´(x) = 12×x² - 64 ×x + 63

If   V´(x) = 0      then      12×x² - 64 ×x + 63 = 0

This expression is a second-degree equation, solving for x

x₁,₂ = [ 64 ± √ (64)² - 4×12*63

x₁ =  ( 64 + 32.74 )/ 24

x₁ = 4.03     this value  will bring us an unfeasible solution,  since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)

x₂ = ( 64 - 32.74)/24

x₂ = 1.30 in

The  maximum volume of the box is:

V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3

V(max) = 4.4 × 6.4 × 1.3

V(max) = 36.60 in³

To chek for maximum value of V when x = 1.3

we find the second derivative of V  V´´,  and substitute the value of x = 1.3,    if the relation is smaller than 0,  we have a maximum value of V

V´´(x) = 24×x - 64 for x = 1.3

V´´(x) = 24× 1.3 - 64            ⇒   V´´(x) < 0

Then the value  x = 1.3 will bring maximum value for V

Related Link: https://brainly.com/question/13581879

Daniel has 15 yards of fabric to make baby blankets. It takes 1 and 1/2 yards of fabric to make each blanket, and the expression that models the situation is 15 minus three-halves y. Which of the following are possible numbers of blankets that Daniel could make? Select all that apply.

Answers

Answer:

any number between 0 and 10

Step-by-step explanation:

15 - 3/2y

how many times can 3/2 go into 15?

10 times. The most blankets he can make is 10, so any number less than 10 and greater than zero would be a correct solution

can i get brainliest please?

Answer:

9 and 10

Step-by-step explanation:

Complete the point-slope equation of the line through (2,3)(7,4)
y-4=

Answers

y-4=1/5(x-7) is the answer

What is the rate of return when 10 shares of Stock
A, purchased for 20 $/share, are sold for $310? The
commission on the sale is $6.
rate of return = [?] %
Give your answer as a percent rounded to the
nearest tenth.

Answers

Answer:

Rate of return = 52%

Step-by-step explanation:

Cost of Investment = 10 shares × $20 = $200

Gain on Investment = amount sold - commission on the sale

Gain on Investment = $310 - $6 = $304

Using the formula:

ROR = (Gain on investment - cost of Investment)/cost of Investment × 100

Plug in the values into the formula:

[tex] ROR = \frac{304 - 200}{200} * 100 [/tex]

[tex] = \frac{104}{200} * 100 [/tex]

[tex] = \frac{104*100}{200} [/tex]

[tex] = \frac{104}{2} = 52 [/tex]

Rate of return = 52%

How do you do this question?

Answers

Answer:

Diverges

Step-by-step explanation:

an = 7 / n^(1 + 1/n)

As n approaches infinity, an approaches 7 / n.

bn = 7 / n

Apply Limit Comparison Test.

lim(n→∞) an / bn

= lim(n→∞) [7 / n^(1 + 1/n)] / (7 / n)

= lim(n→∞) n / n^(1 + 1/n)

= lim(n→∞) 1 / n^(1/n)

= lim(n→∞) 1 / n⁰

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1 52 probability.

Required:
a. List the sample points in the event a jack is selected.
b. List the sample points in the event a club is selected.
c. List the sample points in the event a face card ( jack, queen, or king) is selected.
d. Find the probabilities associated with each of the events in parts (a), (b), and (c).

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

A deck of card:

Number of hearts = 13

Diamond = 13

Spade = 13

Club = 13

Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)

Hence, a club, diamond, spade and heart has one of each of the above numbers.

a. List the sample points in the event a jack is selected.

Jack : ( heart, club, diamond, spade)

B.) club is selected :

Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)

C)

Jack : ( heart, club, diamond, spade)

Queen : (heart, club, diamond, spade)

King : (heart, club, diamond, spade)

D) probability = required outcome / Total possible outcomes

P(jack selected) = 4 /52 = 1/13

P(club selected). = 13/52 = 1/4

P(face card selected) = 12 / 52 = 3/13

Turn 2 1/8 into an improper fraction. Explain your steps

Answers

Answer:

17/8

Step-by-step explanation:

2 1/8    multiply 2 times 8 and 1 which equals to 17/8. The whole number times the denominator plus the numerator basically.

Answer:

17/8

Step-by-step explanation:

8 x 2 = 16

16 + 1 = 17

solve the following equation for a: -g + 3/4a = y

Answers

9514 1404 393

Answer:

  a = (4/3)(y+g)

Step-by-step explanation:

Isolate 'a' term, then multiply by the reciprocal of its coefficient.

  [tex]-g+\dfrac{3}{4}a=y\qquad\text{given}\\\\\dfrac{3}{4}a=y+g\qquad\text{add $g$}\\\\\boxed{a=\dfrac{4(y+g)}{3}}\qquad\text{multiply by $4/3$}[/tex]

which number is the same as 0.000 000 1: 10^7 or 10^-7​

Answers

Answer:

= 1 × 10^-7

(scientific notation)

= 1e-7

(scientific e notation)

= 100 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.0000001

(real number)

Step-by-step explanation:

10^7 = 10000000

Six and forty-two ten-thousandths as a decimal

Answers

6.0042 is the answer
6.042 is the answer hope u get this

Please Help! :(
Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. Now there are 78 players on the field. Write and solve an algebraic equation whose solution is the number of players, p, on each team.

Write the Equation and the answer please

Answers

Answer: there is 90 players in total

Step-by-step explanation:

6x 2= 12

78 + 12 = 90

Answer:

x=15

Step-by-step explanation:

6(x−2)=78 (or 6x−12=78), x=15

PLEASE ANSWER I WILL GIVE YOU BRAINLIEST!
Name the points which satisfy the conditions. In the second quadrant

Answers

9514 1404 393

Answer:

  C, M

Step-by-step explanation:

The second quadrant is the upper left quadrant. There, x-values will be negative and y-values will be positive.

__

Point G is on the boundary with the 3rd quadrant, so is probably not considered to be in either of those quadrants.

Answer: C M

Step-by-step explanation:

I toss a coin 60 times. It lands on tails 24 times. What percent of the time does it land on tails?

Answers

40% is my answer, hope it helps

Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions.
Let n = a number. Choose the inequality that represents the given relationship.

Answers

The inequality I believe is 3(n-2) >5n

P.S Make sure to put a line under the inequality sign to represent greater than or equal to ;)

Answer:

D on edge

3(n – 2) ≥ 5n

Step-by-step explanation:

the next question's answer is  B

Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.

Answers

Answer:

11x-6+(19x+6)=180°

11x+19x-6+6=180°

30x=180

x=180/30

x=6

it means that

19x+6=19*6+6=114+6=120°

What is the measure of angle F?
E. 20
D. 90
F.?

Answers

Answer:

the answer would be 70 because you take 90-20 and you get 70. you have a 90 degree angle is what you're working on right now

Step-by-step explanation:

HELPPPPP!! Is the expression 6 + 3 = 9 an equation ? Explain.

Answers

Answer:

No, because an expression is already solved and an equation is where you have to solve it

Step-by-step explanation:

Answer:

No as said you have to solve and equation yet an expression is already solved for your viewing.

Step-by-step explanation:

Two lines in the same plane that do not intersect are.
A.line segment
B.perpendicular
C.parallel
D.midpoint

Answers

The answer is c they’re parallel

What do I use to make a meat loaf?

Answers

Instructions

1. Preheat oven to 350 degrees Fahrenheit.
2. In a large bowl, add the beef, bread crumbs, onion, milk, egg, 2 tablespoons ketchup, worcestershire sauce, parsley, salt, garlic powder, and pepper. Use your hands to mush and mix these ingredients together until well combined.*
3. Add the meat mixture to a loaf pan. Pat the meat down into an even layer.
4. In a small bowl, add 1/4 cup ketchup, the brown sugar, and vinegar. Stir to combine. Pour the sauce on top of the meatloaf and spread it into an even layer.
5. Bake uncovered for 55 minutes.

Use the information to find the minimum sample size required to estimate an unknown population mean µ. Margin of error: $110, confidence level: 95%, σ = $500. Group of answer choices

Answers

Answer:

The minimum sample size required is 79.

Step-by-step explanation:

The following are given in the question:

e = Margin of error = 110

σ = Standard deviation = 500

Confidence level = 95%

n = Minimum sample size = ?

Therefore, we have:

Zσ = 1.96 at 95% confidence level

s.e. = Standard error = σ / [tex]\sqrt{n}[/tex] = 500 /

Alternatively, margin of error can be calculated as follows:

e = s.e. * Zσ = 110 ................... (1)

Substituting the other values into equation (1) and solve for n, we have:

500 / [tex]\sqrt{n}[/tex] * 1.96 = 110

500 / [tex]\sqrt{n}[/tex]  = 110 / 1.96

500 / [tex]\sqrt{n}[/tex]  = 56.1224489795918

500 = 56.1224489795918 *  [tex]\sqrt{n}[/tex]  

[tex]\sqrt{n}[/tex]  = 500 / 56.1224489795918

[tex]\sqrt{n}[/tex]  = 8.90909090909092

[tex]n^{\frac{1}{2}[/tex] = 8.90909090909092

Squaring both sides, we have:

([tex]n^{\frac{1}{2}[/tex])^2 = (8.90909090909092)^2

n = 79.3719008264465

Approximating to a whole number, we have:

n = 79

Therefore, the minimum sample size required is 79.

Find the product of (18k+ 2m)(m + k)

Answers

Answer:

18k^2+2m^2+20km

Step-by-step explanation:

PLEASE HELP IM TIMEZ) What is the value of the arithmetic series below? A. B. C. D.

Answers

Answer:

id say its C but I'm not sure

Find the selling price of each item original plate price of gold fish at $7.65 discount 10%

Answers

Answer:

6.88 is what I think you're looking for

Step-by-step explanation:

Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the question that​ follows, consider a sample of fifteen randomly selected people who recently booked a hotel.

What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their​ hotel? Round to three decimal places.

A.0.028
B.0.025
C.0.323
D.0.978

Answers

Answer:

the answer is d because 0.978 cool number like yaaaa.

Step-by-step explanation:

It’s d)0.978
Hope it helps
Have a good day
Oh and your the best

Which one of these relationships is different than the other three?



Group of answer choices

A

B

C

D


help!!!1

Answers

Where are the questionsssss?

Answer:

B

Step-by-step explanation:

I got this by looking at the graph and the numbers that I got vertically and horizontally I divided them .

x=4/9,y=1/2, and z=3/5 6wy-3z

Answers

Answer: The answer would be - 7/5 or (-0.46)

Plug in the numbers that each letter equals. So you get 6(4/9)(1/2) - 3(3/5). Then you just simplify.

Picture attached below. Please help

Answers

Answer:

饿着嘎嘎嘎嘎嘎嘎嘎嘎嘎嘎嘎;嘎嘎嘎嘎嘎嘎嘎嘎反反复复

From their location in the diagram, what are two possible values for n and m?

Answers

Answer:

n=7/5 m= 5

Step-by-step explanation:

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