The solution set to the given system of inequalities is represented by the shaded region under the curve of f(x) = x^2 – 3 (including the points on the curve) and above the curve of g(x) = –x^2 + 2 (excluding the points on the curve). The overlapping region between these shaded areas represents the solution set to the system.
To graph the solution set to the system of inequalities y ≤ x^2 – 3 and y > –x^2 + 2, we can modify the graphs of f(x) = x^2 – 3 and g(x) = –x^2 + 2 accordingly. Here's how:
For the inequality y ≤ x^2 – 3:
The original graph of f(x) = x^2 – 3 is an upward-opening parabola with a vertex at (0, -3).
To graph y ≤ x^2 – 3, we need to shade the region below or on the parabola. This includes all points on the parabola itself.
Therefore, we shade the area under the curve of the original graph of f(x) and include the points on the curve.
For the inequality y > –x^2 + 2:
The original graph of g(x) = –x^2 + 2 is a downward-opening parabola with a vertex at (0, 2).
To graph y > –x^2 + 2, we need to shade the region above the parabola. This excludes all points on the parabola itself.
Therefore, we shade the area above the curve of the original graph of g(x) but exclude the points on the curve.
By modifying the graphs of f(x) and g(x) according to these shading instructions, we can graphically represent the solution set to the system of inequalities.
The solution set can be identified by observing the overlapping region or the intersection between the shaded area under the curve of f(x) and the shaded area above the curve of g(x). The points within this overlapping region satisfy both inequalities simultaneously.
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The circular fountain in front of the park has
a diameter of 14 feet. What is the
circumference of the fountain?
A.
43.98 ft
B.
87.96 ft
C-21.99 ft
D-153.94 ft
15 it was rigth in khan academy if u got the letter one its A
The circumference of the fountain will be 43.98 square feet. Thus, the correct option is A.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let d be the diameter of the circle. The circumference of the circle will be given as,
C = πd units
The diameter of the circular fountain is 14 feet. Then the circumference is calculated as,
C = π x 14
C = 43.98 square feet
Thus, the correct option is A.
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Brainliest for correct answer
Answer:
1/2
Step-by-step explanation:
Scale factor = (new figure measurement)/(original figure measurement)
Find IP using pythagorus
IP²=(y[tex]_{I}[/tex]-y[tex]_{P}[/tex])²+(x[tex]_{I}[/tex]-x[tex]_{P}[/tex])²
IP²=(4-(-4))²+(4-2)²
IP²=8²+2²
IP²=68
IP=[tex]\sqrt{68}[/tex]
Find I'P' using pythagorus
I'P'²=(y[tex]_{I'}[/tex]-y[tex]_{P'}[/tex])²+(x[tex]_{I'}[/tex]-x[tex]_{P'}[/tex])²
I'P'²=(2-(-2))²+(2-1)²
I'P'²=4²+1²
I'P'²=17
I'P'=[tex]\sqrt{17}[/tex]
Scale factor = (new figure measurement)/(original figure measurement)
=[tex]\sqrt{17}[/tex]/[tex]\sqrt{68}[/tex]
=1/2
What is the answer to this problem?
Answer:32?
Step-by-step explanation:
The ratio of red cars to blue cars in a parking lot was 5 : 3. If there were 40 red cars, how many blue cars were there?
Answer:
24 blue cars
Step-by-step explanation:
In this problem, one is given the ratio of red to blue cars in the parking lot. One is given the actual number of red cars, and one is asked to find the number of blue cars. One can set up a proportion; ratio to actual, then solve to find the number of actual blue cars using the method of cross-products. One can set up the proportion using the ratios, but it is easier to express the proportion as the equality of two fractions. Thus, the following equation can be formed, let the parameter (x) represent the actual amount of blue cars;
[tex]\frac{red}{blue}= \frac{5}{3} = \frac{40}{x}[/tex]
Cross products,
[tex]5x = 120[/tex]
Inverse operations,
[tex]x = 24[/tex]
PLS HELP IVE BEEN ASKING FOR 3 1/2 DAYS IM ABOUT TO FAIL 7th GRADE ITS OVERDUE WILL GIVE BRAINLIEST IF YOU ANSWER THIS TYSM
Answer:18 days
Step-by-step explanation:
Answer:
18 days to consume the apple
Step-by-step explanation: 18 because it takes 3 days for a half so six days equals 1 whole apple multiply that by 3 an you'll get 18
To find the area of a trapezoid, use the expression ½h(b¹ + b²), where h represents the height, b, represents the length of the top base, and by represents the length of the bottom base. What is the area of the trapezoidal table?
is there supposed to be an image?? (comments, ill give answer if not, im
just confused)
Hey! I am stuck on this question anyone mind helping me? and tysm for the people who helped me! <3 have a nice day!
Answer: 166 2/3m
Step-by-step explanation:
Area of a rectangle = length times width
Length: 16 2/3
To find the width, multiply it by 3/5.
w = 16 2/3 · 3/5
w = 10
Then, multiply the length by the width.
a = l · w
a = 16 2/3 · 10
a = 166 2/3m
Jillian picked coins from her piggy bank and recorded the number of coins in the table below.
Based on the results shown in the table, what is the probability that the coin Jillian picks will be a quarter
Answer:
1/8
Step-by-step explanation:
There are 24 coins total. 3 of them are quarters. So Jillian has a 3 in 24 chance of picking up a quarter. Simplifying 3/24 we get 1/8
The probability of randomly picking a quarter is P = 0.125
How to get the probability?
If we assume that all the coins have the same probability of being randomly picked, the probability of picking a particular type of coin is equal to the quotient between the number of coins of that type that we have, and the total number of coins.
In this case, we have 3 quarters, and a total of:
T = (6 + 7 + 8 + 3) = 24
Then the probability of randomly picking a quarter is:
P = 3/24 = 0.125
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15 FT
-
12 FT
16 FT
9 FT
What is the Volume:
What is the Total Surface Area:
Answer:
28 ft
Step-by-step explanation:
i used my fingers
Find the point of intersection between the ray y = -5/12x when x < 0, and the unit circle.
Need answer asap, brainliest for correct answer
Answer:
last one
Step-by-step explanation:
what is the x value such that y =15 -3x and y = 0?
Answer:
Step-by-step explanation:
. -6x - 2(0) = - 18. -6x = -18. x = 3 Tht
Answer:
x=5
Step-by-step explanation:
0=15-3x, then -15=-3x, divide the -15 by-3 and the answer is x=5
Mimi is tacking 6 posters on her wall. Every poster needs a tack in each corner. What is THE LEAST number of tacks Mimi needs to hang the posters so that each can be seen completely?
Answer:
36 if the posters have 3 corners
Step-by-step explanation:
you would just multiply the corners by 6
which expression is equivalent to ×7*×8?
Answer: If you mean 7 times 8 that is 56
Other expressions that are equal
- 56 times 1
- 1 times 56
- 2 times 28
- 4 times 14
Select all the expressions that contain the coefficient 3.
Answer:
b/c
Step-by-step explanation:
In the figure below if M(ABD) 45 M(ABC)=100then find A,M(<ACD) B,M(<BAC) C,M(<BPC)
Answer:
Step-by-step explanation:
Multiply −12y(9y − 7).
How many cubes with side lengths of 1/4 cm does it take to fill the prism?
Answer:2 14
Step-by-step explanation:
9514 1404 393
Answer:
135
Step-by-step explanation:
The prism is 9/4 cm = 9×(1/4 cm) = 9 cubes wide.
The prism is 3/4 cm = 3×(1/4 cm) = 3 cubes deep.
The prism is 5/4 cm = 5×(1/4 cm) = 5 cubes high.
The number of cubes that will fill the prism is ...
9 × 3 × 5 = 135 . . . cubes to fill the prism
find the total service area of this cone. leave your answer in terms of pi.
r=10in h=24in
Answer:
36pie inch²
Step-by-step explanation:
Answer attached
Hope it helps :)
If the matrix of coefficients of a homogeneous system of n linear equations in n unknowns does not have an inverse, then the system has infinitely many solutions. (a) Always true (b) Sometimes true (c) Never true, i.e., false (d) None of the above
Answer:
(a) Always true
Step-by-step explanation:
In the case when there is a matrix of coefficient for a homogeneous system for n linear equations so it does not have an opposite and then the system would be have the infinite various solutions
So this is always true as in this it can be unique test or infinite.
So according to the given situation, the option a is correct
BRAINLIEST FOR CORRECT ANSWER, IM FAILING SCHOOL AND NEED HELP ASAP. EVEN OFFICIAL HELP COUNTS
Answer:
1. Supplementary angles
2. alternate exterior
3. verticle angles
4. alternate interior
The box matches the numbers. 1 is the answer in the first box, and so on.
Let me know if you have any questions
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find the
time that the rocket will hit the ground, to the nearest 100th of second.
y= -16x2 + 1812 + 59
Answer:
The rocket will hit the ground after 113.28 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
The height of a rocket, after t seconds, is given by:
[tex]h(x) = -16x^2 + 1812x + 59[/tex]
Using this equation, find the time that the rocket will hit the ground.
This is x for which [tex]h(x) = 0[/tex]. So
[tex]-16x^2 + 1812x + 59 = 0[/tex]
Then [tex]a = -16, b = 1812, c = 59[/tex]
[tex]\Delta = (1812)^2 - 4(-16)(59) = 3287120[/tex]
[tex]x_{1} = \frac{-1812 + \sqrt{3287120}}{2*(-16)} = -0.03[/tex]
[tex]x_{2} = \frac{-1812 - \sqrt{3287120}}{2*(-16)} = 113.28[/tex]
The rocket will hit the ground after 113.28 seconds.
Find the slope and y - i intercept of the line y = 4/3 * x - 3 .
Answer:
(2,-4)
hope this helps
Step-by-step explanation:
Answer:
slope: 4/3
y-intercept: -3
Step-by-step explanation:
the number before x is the slope.
the number at the end of the equation is the y-intercept.
Will give brainliest
Find the area of this triangle.
Round to the nearest tenth.
8 m
62°
12 m
[?] m2
Answer:
A, 1/2*b*h*sin
A, 1/2*12*8*sin 62
=43.3
Also use symbolab for this kid equations
Step-by-step explanation:
what is a grid with 4 quadrants and 2 axes?
Answer: The point at which the two axes intersect is called the origin. ... The intersecting x- and y-axes divide the coordinate plane into four sections. These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.
Step-by-step explanation:
A grid with 4 quadrants and 2 axes is called as cartesian plane.
What is a cartesian plane?The cartesian plane is defined as a two-dimensional coordinate plane, which is formed by the intersection of the x-axis and y-axis.
What is a grid?A grid is a framework of spaced bars that are parallel to or cross each other.
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You just completed your math course and you want to calculate your overall grade. You know that tests are weighted 15%, quizzes 10%. projects 35%, participation 35%, and the final exam 5%. What is your overall grade if you scored the following in each category?
Your overall grade, rounded to the nearest hundredth, is approximately 86.35%.
To calculate your overall grade, we need to assign weights to each category and then calculate the weighted average based on your scores.
Let's assume your scores in each category are as follows:
Tests: 85%
Quizzes: 90%
Projects: 92%
Participation: 80%
Final Exam: 88%
Now, let's calculate the weighted average:
Tests: 15% weight × 85% score = 12.75
Quizzes: 10% weight × 90% score = 9.00
Projects: 35% weight × 92% score = 32.20
Participation: 35% weight × 80% score = 28.00
Final Exam: 5% weight × 88% score = 4.40
Overall Grade = Sum of weighted scores / Total weight
Overall Grade = (12.75 + 9.00 + 32.20 + 28.00 + 4.40) / 100
Overall Grade ≈ 86.35%
Therefore, your overall grade, rounded to the nearest hundredth, is approximately 86.35%.
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Which statement about the figure below is true?
A cruise ship travels at a constant speed. In 3 hours, the ship travels 72 nautical miles. If the ship continues to travel at the same rate, how far would it travel in 11 hours. (No links) (if it’s wrong I will report and delete) (explain)
Answer:
264
Step-by-step explanation:
72 divided by 3= 24
24x11=264
Peggy constructed the 95 percent confidence interval (4.8,5.2) to estimate the slope of a regression model for a set of bivariate data with 24 data values. Peggy claims that the width of the confidence interval will increase if a sample size of 30 is used, all other things remaining the same. Quincy claims that the width of the confidence interval will decrease if a sample size of 30 is used. Which statement is true about the claims made by Peggy and Quincy?
Answer:
Quincy's claim is correct.
Step-by-step explanation:
Margin of error of a confidence interval:
The margin of error of a confidence interval decreases is the sample size increases, that is, if the sample size increases, the width of the interval decreases.
In this question:
Sample size of increases to 30 from 24, which means that the width of the interval will decrease.
Quincy's claim is correct.
A group of neighbors is holding an end of summer block party. They buy p packs of hot dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party. Write an equation to describe this situation. How many packs of hot dogs did the neighbors buy?
Answer:
8 * X = 56
Step-by-step explanation:
8 * X = 56
Now assume a 95% confidence level. Without performing any calculations, complete the sentence below. The margin of error for a 95% confidence level will be
Answer: greater than 0.3
Step-by-step explanation:
On edge
The margin of error for a 95% confidence level will be greater than 0.3.
What is a confidence interval?A random population parameter is likely to be included in a confidence interval, which is a range of values that is limited by the statistic's mean. The confidence level is the percentage of probability, or certainty, that, after repeated random sample draws, the confidence interval would include the true population parameter.
Given:
A confidence level is 95%.
The formula to calculate the margin of error:
The margin of error = Z x S/√n.
Where S is the standard deviation and n is the sample size.
The corresponding z-score of the confidence level is 95%.
So, the margin of error will be always greater than 0.3.
Therefore, the margin of error will be always greater than 0.3.
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