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
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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!
Which of the following is a key property of the linear parent function? It is in quadrats | and |||.
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Answer:
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Step-by-step explanation:
i will solve if u give me brainliest.
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Answer:
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Step-by-step explanation:
Answer:
huh?
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.
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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
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
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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.
pleas help ill give extra points and brainlyest
Answers
Answer:
its B
Step-by-step explanation:
B. $27,500
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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
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Step 4: Divide both sides by -3.
−3x
−3
<
−9
−3
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Answer:
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Step-by-step explanation:
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.
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Answers
Answer:
34 - 25 = 9
Step-by-step explanation:
guys they meant 2/5 and 3/4...
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。 • ﾟ 。
. . . 。 。 .
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
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The line passes through (8, - 1) with y- coordinate - 1, thus
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--------------------------------------------------------------------
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x = c
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Answers
Answer:
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Step-by-step explanation:
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
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с
The temperature in the classroom is uncomfortable if the temperature is lower than or equal to
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D
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Answers
Answer:
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Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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△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.
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Answers
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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 :))
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Answers
Answer:
Step-by-step explanation:
7- is (0,1)(1,3)
8- is(-3,0)(-3,0)
xx f(x)f(x)f, left parenthesis, x, right parenthesis
-5−5minus, 5 -2−2minus, 2
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555 444
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Give an exact number.
Answers
Answer:
4
Step-by-step explanation:
khan
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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 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:
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
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:
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.
calculate doudle of 15.5
show the workout
Answers
Or 15.5+15.5 = 31 It’s double the same number...
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
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
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: