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:
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.
Answer:
C
Step-by-step explanation:
just took the quiz
Related Questions
PLEASE Use rigid motion to prove that figure ABC is congruent to figure EFG
Answers
Answer:
a) Translate ABC using directed line segment AE. Rotate A'B'C' using E as the center until C' coincides with G.
Step-by-step explanation:
If we consider ABC figure as a rigid body, then we can translate it to any point in space, keeping the lengths and directions of its elements same. So, to prove congruency of two figures we will try to make them coincident on each other. So, first we translate the figure ABC, along a straight line projected from A to E, such that point A meets Point E. We call this repositioned figure A'B'C' Now, another property of rigid body is that it can rotate as a whole body about any of its internal points.
Since, A' and E are coincident now so, we rotate figure A'B'C', with A' as the center of rotation. This rotation is anti-clockwise and we rotate it until C' coincides with G. Now, both figures are coincident. Hence, their congruency is proven.
Therefore, the correct answer is:
a) Translate ABC using directed line segment AE. Rotate A'B'C' using E as the center until C' coincides with G.
In this exercise, we have to use the knowledge of solid rotation to identify the alternative that best represents what happened in the image, so we have that the best alternative is:
Letter A.
If we consider ABC figure as a rigid body, then we can translate it to any point in space, keeping the lengths and directions of its elements same. So, to prove congruency of two figures, we will try to make them coincident on each other.
First we translate the figure ABC, along a straight line projected from A to E, such that point A meets Point E. Now, another property of a rigid body is that it can rotate as a whole body about any of its internal points.Second we rotate figure A'B'C', with A' as the center of rotation. This rotation is anti-clockwise, and we rotate it until C' coincides with G.Now, both figures are coincident. Hence, their congruency is proven. Therefore, the correct answer is:
The letter A, which means that translate ABC using directed line segment AE. Rotate A'B'C' using E as the center until C' coincides with G.
See more about rotation at brainly.com/question/1571997
When multiplying the factors 2/3 and 4/7 what is the product of the denominators
Answers
Answer:
21
Step-by-step explanation:
When multipling fractions you go straight across so, all you have to do in the furture is multiply the demonators, anyways all i had to was 3x7 which is 21. Hope this helps and have a wonderful day!
Answer:
21
Step-by-step explanation:
2/3+4/7= 8/21
the top number is the numerator and the bottom number is the denominator.
There are 800 rooms on the Voyager cruise ship, and 60% of them have a balcony. How many of the rooms have a balcony?
Answers
Answer:
480
Step-by-step explanation:
does anyone know how to do this ??
Answers
Answer:
I may be wrong but I believe it is 106°
Step-by-step explanation:
please help me lol aaaaa
Answers
Answer:
−0.125 or - 1/8
Step-by-step explanation:
Sally buys a shirt of 5.00. New York's sales tax is 8.200. What is the final price?
Show your work and explain or I report and delete answer.
Answers
Answer: $5.40
Sales tax is a price you add to every 100 cents purchased.
Sally purchased a shirt of 5.00, and New York's sales tax is 8.200.
So, we multiply 8 by 5. We get the number 40, right?
You now add 0.40 to 5.00.
The answer totals at 5.40 because 5.00 + 0.40 = 5.40.
Hope this helps you out!
pleas help ill give extra points and brainlyest
Answers
Answer:
its B
Step-by-step explanation:
B. $27,500
Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far are the divers from each other?
Answers
Answer:
66.25 ft
Step-by-step explanation:
25.5 + 40.75
66.25
They are 66.25 feet away from each other.
Please let me know if I'm wrong!
How do you describe a quadratic equation?
Answers
Answer:
an equation of the second degree, meaning it contains at least one term that is squared.
Step-by-step explanation:
A quadratic equation contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.
What is the climate like in summer of the Middle Atlantic states?
cool
temperate
hot
cold
Answers
Answer:
The passage says "Summers are hot and winters are cold in the Middle Atlantic states." so the answer is hot
Keiko is going for a walk.she takes 3 hours to walk 7.5 miles.what is her speed
Answers
Answer:
2.5 mph
Step-by-step explanation:
Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
How much longer did Sarah practice than Eloise?
Answers
Answer:
34 - 25 = 9
Step-by-step explanation:
guys they meant 2/5 and 3/4...
Which only lists multiples of 18? O 1,2,3, 4, 6, 9, 18 O1,2,3, 6, 9, 18 O 18, 27, 36, 45 18, 36, 54,72
。 • ﾟ 。
. . . 。 。 .
. 。 ඞ 。 . •
• Red_kid was not the Impostor. 。 .
Answers
Answer: 18,36,54,32
Step-by-step explanation:
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:
Please help! Number 7 and 8 don't forget to put the graph points thank you!
Answers
Answer:
Step-by-step explanation:
7- is (0,1)(1,3)
8- is(-3,0)(-3,0)
5(3 - x) < -2x + 6 please solve for me <3
Answers
Answer:
>3
Step-by-step explanation:
−5x+15<−2x+6
Step 2: Add 2x to both sides.
−5x+15+2x<−2x+6+2x
−3x+15<6
Step 3: Subtract 15 from both sides.
−3x+15−15<6−15
−3x<−9
Step 4: Divide both sides by -3.
−3x
−3
<
−9
−3
i need help with this please
Answers
Answer:
y = - 1 and x = 8
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the lune passes through.
The line passes through (8, - 1) with y- coordinate - 1, thus
y = - 1 ← equation of horizontal line.
--------------------------------------------------------------------
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (8, - 1) with x- coordinate 8 , thus
x = 8 ← equation of vertical line
Which statement best explains whether △ABC is congruent to △DEF?
△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a reflection across the y-axis followed by a translation 5 units down.
△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a rotation of 90° counterclockwise about the origin followed by a reflection across the y-axis.
△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a translation 5 units down followed by a reflection across the x-axis.
△ABC is not congruent to △DEF because there is no sequence of rigid motions that maps △ABC to △DEF.
Answers
Answer: △ABC is congruent to △DEF because △ABC can be mapped to △DEF by a translation 5 units down followed by a reflection across the x-axis.
Step-by-step explanation: By moving the shape down 5 units, you are met with DEF. You then mirror it (reflect) across the y axis.
HURRY whats the rate of change
Answers
Answer:
G. -9/2 o -4.5
Step-by-step explanation:
Answer:
G. -9/2
Step-by-step explanation:
this is the rate of change
Select three ratios that are equivalent to 11:1.
Choose 3 answers:
1:11
22:2
55:5
9:99
Answers
Answer:
22:2, 55:5, 1:11
Step-by-step explanation:
Answer:
22:2 55:5 and no others
Step-by-step explanation:
What is the sign of the product (3)(−25)(7)(−24)?
A. Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive
B. Positive, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is positive
C. Negative, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is negative
D. Negative, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is negative
Answers
calculate doudle of 15.5
show the workout
Answers
Or 15.5+15.5 = 31 It’s double the same number...
Alan Jeff and Lucy all take their pets to the same vet. The pets are a dog a cat and a rabbit. The names of the pets are Blackie bandit and Moe. Read the clues to determine the kind of pet each owner has and the name of the pet. Mark the correct boxes on the grid to show your answers.
Answers
Answer:
i need at least a pick of the problom
Step-by-step explanation:
Answer:
huh?
Step-by-step explanation:
The money spent, M , purchasing burritos at a particular fast food restaurant varies directly with the number of burritos purchased, B. When 12 burritos are purchased, $45 is spent. How much money is spent if 28 burritos are purchased? S
Answers
Answer:
multiply 3.75 to 28 and it equals 105
Step-by-step explanation:
The amount of money spent to buy 28 burritos will be $105.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the money spent, M, purchasing burritos at a particular fast food restaurant varies directly with the number of burritos purchased, B. When 12 burritos are purchased, $45 is spent.
The money required to purchase 28 burritos will be calculated as:-
12 burritos = $45
1 burrito = 45 / 12
28 burritos = ( 45 / 12 ) x 28
28 burritos = $105
Therefore, the amount of money spent to buy 28 burritos will be $105.
To know more about expression follow
https://brainly.com/question/723406
#SPJ2
Complete the statement. If a transversal intersects two parallel lines, then _____
A) alternate interior angles are always congruent.
B) same-side interior angles are always complementary.
C) same-side exterior angles are always complementary.
D) corresponding angles are always supplementary.
Answers
Answer:
B)
Step-by-step explanation:
They are intersected to make a same side interior angle.
Answer:
A) alternate interior angles are always congruent.
xx f(x)f(x)f, left parenthesis, x, right parenthesis
-5−5minus, 5 -2−2minus, 2
-4−4minus, 4 222
-3−3minus, 3 000
-2−2minus, 2 111
-1−1minus, 1 000
000 333
111 -7−7minus, 7
222 -8−8minus, 8
333 -3−3minus, 3
444 111
555 444
What is the average rate of change of fff over the interval -4\leq x\leq 5−4≤x≤5minus, 4, is less than or equal to, x, is less than or equal to, 5?
Give an exact number.
Answers
Answer:
4
Step-by-step explanation:
khan
solve the linear equation 7x-3=67 for x
Answers
Answer: x=10
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
when we see something like 7x-3=67, we have to get x alone. the first step is to always cancel out the constant (the number that does not have a variable such as x connected to it). so to make -3 equal to 0 we have to add 3. what we do to one side we have to do to the other so after adding 3 on each side we get 7x=70. now here, we still have to get x alone. 7x means 7 times x so to undo this we have to do the opposite and divide each side by 7. 7 divided by 1 (and 1x is 1 times x which is just x so now we have x alone yaay) and 70 divided by 7 is 10. so x = 10.
I hope this helped :))
Solve each of the following equations for the missing variable.
2x – 14 = -9
x = 10
x = 2.5
x = -2.5
x = -10
Answers
Answer: x = 2.5
Step-by-step explanation: Add 14 to both sides. After that take the number left on the right side (5) and divide it by 2. That leaves you with x = 2.5
Which of the following is a key property of the linear parent function? It is in quadrats | and |||.
Answers
Answer:
bro i need a picture
Step-by-step explanation:
i will solve if u give me brainliest.
For each situation, an inequality is written. Which one has an incorrect inequality?
A Three less than a number is greater than negative four and less than negative one; - 4
B The minimum speed on a highway is forty miles per hour and the maximum speed is
seventy-five miles per hour; 40 58 575
с
The temperature in the classroom is uncomfortable if the temperature is lower than or equal to
60 degrees or higher than or equal to 75 degrees; t < 60 or t > 75
D
All real numbers that are greater than or equal to -
-75 or less than or equal to zero; z < 0 or 22 -75
Answers
Answer:
The answer is D