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.
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
Compare: -7 -4
PLEASE HELP ME!
I will mark who ever right brainliest
Answer: answer is 155
Step-by-step explanation:
Find the Slope And Y- Intercept .
Answer:
slope= 3/4
y intercept= 1/2
Step-by-step explanation:
First find the slope using the formula y2-y1/x2-x1.
the points given: (-6,-4) and (2,2)
so plug in the points into the formula and you'll have:
2-(-4)/2-(-6)=
2+4/2+6=
6/8=
3/4
to find the y intercept, use the formula y-y1=m(x-x1)
y+4=3/4(x+6)
y+4=3/4x+9/2
y=3/4x+1/2
Each of the four shapes represents a positive whole number. The sum of the shapes in each row and column is displayed at the end of each row and column. Using this information, determine the numerical value of each shape.
Answer:
C₁ C₂ C₃ C₄ T
R₁ 4 3 3 1 11
R₂ 1 2 1 2 6
R₃ 2 3 4 2 11
R₄ 1 1 3 1 6
T 8 9 11 6
Step-by-step explanation:
1.-For inspection column 4 (C₄) is equal to row 2 ( R₂ ), and column 3 (C₃) is equal to row 1 (R₁)
2.- Let´s assume spiral is equal to 1 and the zebra rectangle is equal to 2
star 3 and pentagon 4
C₁ C₂ C₃ C₄ T
R₁ 4 3 3 1 11
R₂ 1 2 1 2 6
R₃ 2 3 4 2 11
R₄ 1 1 3 1 6
T 8 9 11 6
Express the number 7,980 in scientific notation.
Answer:
7.98x10^3
Step-by-step explanation:
10^3=1000
Answer:7.980 × 10^3
Step-by-step explanation:
What is the determinant of A=
3
1
11
-1
-14 is the Determinant of given matrices A.
What is the determinant?A scalar value connected to the square matrix is known as the determinant. If X is a matrix, then |X| or Det is used to indicate the matrix's determinant (X).
Given a Mtrix A:
3 1
11 -1
The formula for the determinant of a matrix:
The determinant of a 2x2 matrix A = [ a b c d ] is |A| = ad - bc. It is simply obtained by cross-multiplying the elements starting from the top left and then subtracting the products.
In our case,
Determinants of A = (3 * -1 ) - (1 * 11)
Determinants of A = -3 -11
Determinants of A = -14
Therefore, the Determinant of given matrices A is -14.
Learn more about determinants here:
https://brainly.com/question/13369636
#SPJ1
Complete question:
What is the determinant of
A= 3 1
11 -1
Greta writes a fraction that is greater than 1 and less than 2. Jullo writes a fraction that is greater than 3 and less than 4. Greta and Julio
find the product of the fractions they write, which statement about the value of the product must be true?
The product is greater than 1 and less than 2.
The product is greater than 3 and less than 4.
The product is greater than Julio's fraction
The product is less than Greta's fraction,
Please help me with all the answers please say like 1: the answer 2: the answer like that thank you so much
Can someone help and explain? 4 + 5x - 1
Answer:
5x+3
Step-by-step explanation:
1. Subtract 1 from 4
4+5x-1
2. Solution
5x+3
Ryan, a baker, measured the weights of cakes baked in each batch at his bakery and found that the mean weight of each cake is 500 grams. He performed a hypothesis test to find the mean weight of each cake by setting H subscript 0 equals 500 and H subscript a less than 500. Select the statement that indicates a Type I error.
a) Rejecting the mean weight of each cake as 500 grams when H subscript 0 equals 500.
b) Rejecting the mean weight of each cake as 500 grams when H subscript 0 less than 500.
c) Failing to reject the mean weight of each cake as 500 grams when H subscript 0 equals 500.
d) Failing to reject the mean weight of each cake as 500 grams when H subscript 0 less than 500.
Answer: Rejecting the mean weight of each cake as 500 gram when H subscript 0 equals 500
Step-by-step explanation:
Given that :
Null hypothesis : H0 =500
Alternative hypothesis : Ha < 500
Type 1 Error: Type 1 error simply occurs when we reject the Null hypothesis when the Null is true. Alternatively, type 11 error occurs when we fail to reject a false null hypothesis.
Hence, in the scenario above, a type 1 error will occur when we reject the mean weight as 500 even though the Null hypothesis is True.
Answer: A) Rejecting the mean weight of each cake as 500 grams when H₀ = 500.
Step-by-step explanation:
Type I error is when we incorrectly reject a true null hypothesis
If angle 1= 36 degrees and angle 4= 115 degrees what is the measurement of angle 2 ?
A light bulb consumes 3450 watt-hours-in 5 days and 18 hours. How many watt-hours does it consume per day
Answer:
5 days = 5 * 24 = 120 hours
120 + 18 = 138hours
3450/138 * 24 = 600 watt hours
600watt hours
I need help ASAP
what is the principal if the interest earned is $22 the simple annual interest rate is 2% and the time is one year
Answer:
1,100
Step-by-step explanation:Well first find the principal first Multiply the rate 0.02 by the time 1 year this gives us 0.02 then divide the interest ($22) by 0.02 then you get $1,100
Answer:
not 1,100 its 1100
Step-by-step explanation:
Jana and Jenn are training to run a race. Jana runs 3 miles in 1/3 hour. Jenn runs 5 miles in 3/4 hour. Who runs faster, and what is the unit rate of her speed in minutes per mile?
Answer:
Jenn runs faster at 9 minutes/mile.
Step-by-step explanation:
Jana runs 3 miles in 1/3 hour.
1/3 hour is equivalent to 1/3*60 = 20 minutes
The ratio time/distance is the reciprocal of the speed and is greater as the speed is lower and vice-versa.
This ratio for Jana is 20/3=16.7 minutes/mile
As for Jenn, she runs 5 miles in 3/4 hour.
3/4 hour is equivalent to 3/4*60=45 minutes
The ratio time/distance is 45/5=9 minutes/mile
Since Jenn has a lower ration, her speed is greater than Jana's, thus Jenn runs faster.
Use the figure to decide the type of angle pair that describes 4 and 5
Answer:
Alternate interior angles
Step-by-step explanation:
Angles 4 and 5 are alternate interior angles
What’s the height of the building if it 77% of 596
José correctly answered 80% of the
questions on a language arts quiz. If he
answered 16 questions correctly, how ma
questions were on the language arts quiz
Answer:
20
Step-by-step explanation:
80% needs 20% more to be 100% so we devide 16 by 4 to get the awnser for 20% witch is 4 so 16+4 is equal to 80% + 20% so 20
Answer:
20
Step-by-step explanation: 16 you need to 2 more question to get 100 so if you use your brain and imagine doing a test and you get an 80 percent and answered 16 correct go back to the test to see what you have
What is the unit rate for meters per second if a car travels 414 meters in 23 seconds?
Answer:
18 meters per second
Step-by-step explanation:
414/23=18
Not trying to be rude but you should know how to do this with or without a calculator
What is 1.6 + 4x > 14.
Answer:
Simplifying
1.6 + 4x = 14
Solving
1.6 + 4x = 14
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1.6' to each side of the equation.
1.6 + -1.6 + 4x = 14 + -1.6
Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 4x = 14 + -1.6
4x = 14 + -1.6
Combine like terms: 14 + -1.6 = 12.4
4x = 12.4
Divide each side by '4'.
x = 3.1
Simplifying
x = 3.1
Step-by-step explanation:
12-14 plzzz if u see the picture
Answer:
I can't see it very well sorry
9. Show that the polygons
are congruent by using
rigid motions and by
identifying all the
congruent corresponding
parts. Then write a
congruence statement.
Rigid motions are, exclusively, rotations, reflections, and translations. If you can move one polygon onto the other by using only those motions, they are congruent. One pentagon can, for example, be translated onto another pentagon, making them congruent. If, after being translated, point A is on point F and B on G and C on H and D on I and E on J, the congruence statement is: [tex] ABCDE\cong FGHIJ.[/tex]
To show that the triangles are congruent, triangle ABC could be transformed by which movement(s) to fit exactly on triangle XYZY
a rotation of 180° clockwise about the origin followed by a dilation of 1.2 with the center of dilation at the origin
a rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units
a rotation of 270° clockwise about the origin followed by translations left 1 unit and up 10 units
a reflection over the x-axis followed by a reflection over the y-axis
Answer:
a rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units
Step-by-step explanation:
Rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units is the required transformation.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
We have to show that triangle ABC could be transformed by which movement(s) to fit exactly on triangle XYZ.
Rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
So if triangle ABC is rotated about 90 degrees clockwise about the origin followed by translated down 1 unit and left 10 units we get XYZ.
Hence, rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units is the required transformation.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ2
What is 471,284 rounded to the nearest
thousands
Answer:
471,000
Step-by-step explanation:
Rahul deposited Rs. 12,000 in a bank for 2 years. If it is compoundedannuallyat 9% p.a., what amount will he receive on maturity? (at the end of two years).
Answer:
Rs 14257.2
Step-by-step explanation:
From the formula;
A= P(1 + i)^n
A= amount
P= principal
i= rate
n= time
A= 12000(1 + 0.09)^2
A=12000(1.09)^2
A=Rs 14257.2
The correct Standard Form of the equation y=−2/7x−11/7
Answer:
y=-(2)/(7)x-5
Step-by-step explanation:
what divide by -1/2 equals -7/3
Andrew drew a square with each side measuring 3 inches. Lindsay drew a triangle with each side measuring 4 inches. Which shape has a greater perimeter? Write an equation to help explain your answer.
Answer:
they have the same perimeter.
Step-by-step explanation:
3in × 4 = 12in
4 in × 3 = 12in
The expression (Ux²+x-T) (2x-1) can be written in the form (2x-1)²(x+S) where U, T and S are constant. Find the values of U, T and S....... Please help me solve this polynomial
Answer:
U=2, S=1, T=1
Step-by-step explanation:
(Ux²+x-T) (2x-1)=(2x-1)²(x+S)
(Ux²+x-T)=(2x-1)(x+S)=2x²+(2S-1)x-S
U=2
2S-1=1 --> S=1
T=S=1
Find three consecutive even integers whose sum is -42
Answer:
Three consecutive even integers are x, x+2, x+4.
Step-by-step explanation:
Their sum is x+x+2+x+4 = 3x+6.
Hope this helped! <3