Use the parabola tool to graph the quadratic function f(x)=−12x2+7. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
The vertex of parabola is [tex]( \frac{-b}{2a},f( \frac{-b}{2a})) [/tex]
Here,
b = coefficient of x term
a = coefficient of x² term
For given parabola, b = 0 , a = -12
So,
[tex] \frac{-b}{2a}= \frac{0}{-24} =0 [/tex]
And,
[tex]f( \frac{-b}{2a} )=f(0) = -12(0)+7=7[/tex]
Thus the vertex of parabola is (0, 7)
To find another point on parabola, substitute x by 1.
[tex]f(1)=-12( 1^{2}) +7=-12+7=-5[/tex]
So the second point on parabola is (1,-5)
The plot of parabola is shown in image below:
Here are a bunch of CORRECT answers, your answer is somewhere in there. For the first CORRECT answer the second point is -5,-9. Don't make the same mistake I did on question 3, but it still shows the correct answer. I love to help.
Related Questions
PLEASE HELP MATH MADD POINTS
The rates of change of two data sets can be compared by finding:
A-the initial values.
B-the slope of each trend line.
C-how close the points are to the line.
D-the y-intercepts.
Answers
The rate of change is the same as the slope.
Ana walked 13/3 miles write 13/3 as a mixed numder
Answers
If there is a remainder, keep that as fraction.
.
4 1/3
12/3=4
4= whole number
13-12=1
1/3
4 + 1/3 = 4 1/3
Your answer is 4 1/3
In a distribution, a score of X=60 has a z-score of -3.0.. A score of X=85 has a z-score of 2.0. What are the mean and standard deviation for this population?
Answers
[tex]z=\frac{X- \mu}{\sigma}[/tex]
We don't have μ, the mean, or σ, the standard deviation. We can, however, set up a system of two equations with the information we do have. We know:
[tex]-3=\frac{60- \mu}{\sigma} \text{ and } 2=\frac{85- \mu}{\sigma}[/tex]
We can make this look more like a "typical" system of equations by cancelling the fractional part of each equation. We do this by multiplying the bottom of each equation by σ:
[tex]-3*\sigma=\frac{60- \mu}{\sigma}*\sigma \text{ and } 2*\sigma=\frac{85- \mu}{\sigma}*\sigma \\ \\-3\sigma=60- \mu \text{ and } 2\sigma=85- \mu[/tex]
Now we'll get the variables on the same side of the equation. We'll do this by adding μ to both sides:
[tex]-3\sigma + \mu=60- \mu + \mu \text{ and } 2\sigma+ \mu =85- \mu + \mu \\ \\-3\sigma+\mu=60 \text{ and } 2\sigma+\mu=85[/tex]
Now we'll write this vertically:
[tex] \left \{ {{-3\sigma+\mu=60} \atop {2\sigma+\mu=85}} \right. [/tex]
We will "eliminate" μ by subtracting the bottom equation:
[tex] \left \{ {{-3\sigma+\mu=60} \atop {-(2\sigma+\mu=85)}} \right. \\ \\-5\sigma=-25[/tex]
Divide both sides by -5:
[tex]\frac{-5\sigma}{-5}=\frac{-25}{-5} \\ \\\sigma=5[/tex]
Our standard deviation is 5. Substituting this into our top equation we have:
-3(5)+μ=60
-15+μ=60
Cancel the -15 by adding it to both sides:
-15+μ+15=60+15
μ=75
Our mean is 75.
Final answer:
By using the z-score formula and solving a system of linear equations, we find that the mean (μ) of the population is 75, and the standard deviation (σ) is 5.
Explanation:
To find the mean (μ) and standard deviation (σ) of the distribution based on the given z-scores, we can use the z-score formula:
z = (X - μ) / σ. Rearranging this formula, we can express X as X = zσ + μ.
For the two provided z-scores and X values:
For X = 60 and z = -3.0: 60 = (-3)σ + μ
For X = 85 and z = 2.0: 85 = (2)σ + μ
We now have a system of linear equations that can be solved to find μ and σ:
-3σ + μ = 60
2σ + μ = 85
Solving for σ and μ:
Multiplying the first equation by 2, and the second equation by 3 and adding them gives us:
(-3)(2)σ + 2μ = 120
(2)(3)σ + 3μ = 255
Adding these together yields 5μ = 375, so μ = 75.
Now, substitute the μ value into either equation to find σ:
-3σ + 75 = 60
σ = (75 - 60) / 3
σ = 5
Therefore, the mean (μ) of the population is 75 and the standard deviation (σ) is 5.
solve by substitution
2y+x=-15
5x=3y
Answers
2y + 3/5y = -15
2 3/5y = -15
y = -5.77
x = -3.46
Dianne spends 40% of her net income on rent and 15% of her net income on food. If she spends a total of $1375 per month on rent and food, what is her net monthly income?
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The nth even number is 2n, the next even number after 2n is 2n+2, explain why.
Answers
For example:
2n=2
2n+2=4
4 is the next even number after 2
Managers at a company rate employee's on performance and attitude and find that an employee's attitude depends on their performance. They find a linear relationship and the line of best fit is y = 11.7 + 1.02x. What does 1.02 mean in the context of the problem?
A)That if their attitude rating was 0 the performance rating would be 1.02.
B)That if the performance rating was 0, their attitude rating would be 1.02.
C)That for every point their performance rating goes up their attitude rating improves by 1.02 points.
D)That for every point their attitude rating goes up their performance rating improves by 1.02 points.
Answers
A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election. Which statement describes a method that will help him accurately estimate this percentage?
A.) He could contact every resident in the town, ask whether the resident will vote for the particular candidate, and then calculate the percentage of residents who say they will vote for the particular candidate.
B.)He could ask employees at the newspaper which candidate each will vote for, and then calculate the percentage who will vote for the particular candidate.
C.)He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.
D.)He could ask his readers to respond to a survey that asks which candidate the reader will vote for and then calculate the percentage of people who say that they will vote for the particular candidate.
Answers
A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election. Which statement describes a method that will help him accurately estimate this percentage?
Answer: In order to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election, a news reporter can randomly take a sample from the registered list of voters and based on their opinion a reporter can accurately estimate percentage of registered voters who will vote for a particular candidate in an upcoming election. Therefore, the option C will be correct.
Therefore the correct method is C) He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.
The other options to gather the opinion about the percentage of the sample who will vote for the particular candidate are non probabilistic and there is every possibility of introduction of bias in the estimate. The only option which is probabilistic is option c because it involves random selection of respondents. Therefore the appropriate option is c.
X is less than or equal to -8 graphed on a number line
Answers
x <= - 8
Notice that the inequality solution is
(-inf, -8]
In the graph the parenthesis implies that the value of minus infinity is not included. The bracket implies that the value x = -8 is included in the solution of the inequality.
See attached graph.
Graphing x \<= -8 involves placing a solid circle at -8 on a number line and shading everything to the left to represent all numbers less than or equal to -8.
To graph x \<= -8 on a number line, you need to include every number that is less than or equal to -8. Start with a number line and locate the point -8 on it. Then, draw a solid circle at -8 to indicate that -8 is included in the solution (because of the '<=' symbol). Next, shade or draw a thick line to the left of -8, going towards the negative direction, to cover all numbers that are less than -8. This shaded area represents all the possible values for x that satisfy the inequality x \<= -8.
Visual Representation on Number Line
A visual representation helps to understand the solutions to the inequality. When graphing, remember that the area to the left of the chosen point on a number line includes all numbers less than the indicated value, and if the circle is solid, that point is also part of the solution set.
The process described here provides a straightforward approach to graphing linear inequalities on a number line, which is a fundamental concept in algebra.
There are 20 trees in a yard that each produced 1 gallon of syrup. If the syrup needs to be put into 3 gallon containers, how many containers are necessary to hold all of the syrup?
Answers
For this case we have that if 20 trees produce 1 gallon of syrup each, then we have 20 gallons of syrup.
We must find the number of containers for the 20 gallons, knowing that each container has a capacity of 3 gallons.
[tex]\frac {20} {3} = 6.67[/tex]
So, we need 7 containers.
Answer:
7 containers
PLEASE NEED HELP
Azul performed an experiment to determine which crank powered radio works best. He cranked 15 randomly selected radios of each brand 30 times at the same speed and measured how long the radios played in minutes before running out of power. The result of the experiment is displayed in the box plot below.
Secure hike emergency radio 4.0
21,22,24,25,25,25,25,26,27,29,30,30,30,30,33
Streamline radio
25,25,27,28,29,30,30,30,34,36,36,38,39,42
A. 50% of streamline crank radios are likely to play 30 minutes or longer after 30 cranks, while only 25% of secure hike emergency radios ARE LIKELY to play 30 minutes or longer after 30 cranks.
B. 75% of secure hike emergency radios ARE LIKELY to play 30 minutes or longer after 30 cranks, while only 50% of streamline crank radios ARE LIKELY to play 30 minutes or longer after 30 cranks.
C. 100%of x- streamline crank radios ARE LIKELY to play 30 minutes or longer afte
Answers
A wall is 4 m by 3 m. Which is the correct unit of measurement to use when figuring out how much paint to buy to cover the wall? A. m B. m3 C. m2
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melanie's food bill at a restaurant is $28.45, the sales tax rate was 6%. if she added 20$ of the amount before tax as a tip, what was the total cost of the meal
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Find these measures for the number of days in the months of a leap year
Answers
All the others have 31
Except February which hath 28 and
29 on a year that leaps.
How can the Associative Property be used to mentally find 48 +82? i know the answer is 130. don’t answer the expression plz.❗️❗️❗️
Answers
48 and 2, split 82 in 80 and 2 and then associate the numbers conveniently
48+ (2+80)=
(48+2)+80=
50+80 which you can do it and is 130 or
50+80=
50+50+30=
100+30 which is 130
A retail store marks up its OTC (over-the-counter) merchandise 50% based on acquisition cost. What's the retail price of an item that costs $2?
Answers
A community center has an l shaped swimming pool that is 10 feet deep. What is the volume of the pool?
A. 640 cubic feet
B. 880 cubic feet
C. 1200 cubic feet
D. 1040 cubic feet
Answers
Answer:
1,040 cubic feet
Step-by-step explanation:
volume = width * length * height
In order to find this split the pool into two separate rectangular prisms.
The first one's measurements are 4ftx16ftx10ft
4*16*10 = 640
the next prism is 4ftx10ftx10ft
4*10*10 = 400
640+400= 1040 cubic feet
how can you add a figure to a composite figure without increasing its perimeter? Draw a diagram to support your answer
Answers
Anyone please help me please solving these maths problems not sure.Thanks.
Answers
If 2 more violinists join the orchestra and 1/2 the orchestra are violinists already what fraction of all musicians would play a stringed instrument
Answers
If two more violinists join the orchestra, there would be 102 players and 52 violinists.
52/102 is the fraction you are looking for. Simplified it would be 26/51.
Hope this helps!
26/51. Hope it helps! :)
Which statement or statements are TRUE?
I. The data distribution is skewed
II. The interquartile range is 6
III. The median is 10
A) I only
B) II only
C) I and II only
D) II and III only
Answers
Answer: A. I only
Step-by-step explanation:
Most of the observations are on the lower end, so the distribution is skewed right. The interquartile range is indicated by the length of the box, about 14. The median is indicated by the vertical line running through the box, about 13
Describe two ways to express the edge length of a cube with a volume of 64
Answers
They both mean the exact same thing.
Hope this helps!
The edge length of a cube with a volume of 64 cubic units can be expressed as 4 units, which is the cube root of 64, or algebraically as V⅛ or 64⅛.
Explanation:To express the edge length of a cube with a volume of 64 cubic units, we can use the formula for the volume of a cube, which is V = L³, where V is volume and L is the length of an edge. Since we have the volume (V), we can solve for L (the edge length) by taking the cube root of the volume. Consequently, the cube root of 64 is 4, so one way to express the edge length is simply as 4 units.
Alternatively, we can express the edge length in terms of the formula for volume. If the volume V is a constant 64 cubic units, the edge length can be represented as V⅛, or 64⅛ in this specific case. This second expression emphasizes the relationship between volume and edge length in a cube and is particularly useful in algebraic and geometric applications.
Can someone help me find the value of q? Thanks!
Answers
Please help ASAP ! I need it buy 11:30 thanks !
Answers
Yellow 55%
Blue ?
55+25=80
100-80=20
Blue 20%
Now we r going to do
20/100=?/150
And now cross multiply and let’s change ? to x
100x=3000
And now divide both sides by 100 to get x
x=30
The spinner would land on blue about 30 times which in the 150 spins
In a video game, Val scored 30\%30%30, percent fewer points than Peeta. Peeta scored 1060 points.
How many points did Val score?
Answers
1060-318=742
Val scored 742 points
Answer:
3533.33333333
Step-by-step explanation:
A prism with a volume of 270 m³ is dilated by a factor of 3. What is the volume of the dilated prism? Enter your answer in the box.
Answers
A prism with a volume of 270 m³ is dilated by a factor of 3. What is the volume of the dilated prism? Enter your answer in the box.
If we dilate each dimension by 3, then the volume of the figure will be dilated by [tex] 3^{3} [/tex] .
[tex] 3^{3} [/tex] =3*3*3 =27
So, the volume of the dilated prism is [tex] 3^{3} [/tex] *volume of original prism
Volume of dilated prism=27*270[tex] m^{3} [/tex]
Volume of dilated prism=7290[tex] m^{3} [/tex]
The volume of a prism when dilated by a factor of 3 increases to 7290 m³,
A prism with a volume of 270 m³ that is dilated by a factor of 3 will have its new volume calculated by cubing the scale factor and multiplying it by the original volume.
Original Volume (V1) = 270 m³
Scale Factor (k) = 3
Dilated Volume (V2) = V1 × k³
So, V2 = 270 m³ × 3³
V2 = 270 m³ × 27
V2 = 7290 m³
Hence, the volume of the dilated prism is 7290 m³.
what is the quotient of 4 2/3 divided by 4 1/5 :fraction
Answers
4 2/3 is 14/3
4 1/5 is 21/5
rewrite
14/3 ÷ 21/5
since it is pretty complicated to divide two fractions,
you change it to multiplication
keep the first fraction, change the division sign to multiplication, then flip the second fraction
(you can remember KEEP, CHANGE, FLIP whenever dealing with division of fractions :) )
14/3 * 5/21
multiply across
(14 * 5) / ( 3 * 21)
70/ 63
simplify to 10/9
this can be written as 1 1/9
Hope this helps
Answer:
1 1/9
Step-by-step explanation:
The following six students – Andy, Betty, Chris, Frank, Mark and Mary are standing in line outside of a classroom: Chris, the last one in line, is right behind Andy; Mark is between Mary and Betty; Frank, who is one ahead of Betty, is the first one in line. Where is Mary in the line?
Answers
Mary is fourth in line.
A bee with velocity vector
r'(t)
starts out at
(5, −5, −3)
at
t = 0
and flies around for 5 seconds. Where is the bee located at time
t = 5
if
5
0
r'(u)du = 0?
Answers
Final answer:
The bee returns to the starting point at (5, -5, -3) after 5 seconds since the integral of its velocity over that period is zero, indicating no net change in position.
Explanation:
To find where the bee is located at time t = 5, we start by looking at the given velocity vector r'(t). Since ∫05r'(u)du = 0, this implies that the integral of the velocity function over the interval from 0 to 5 seconds results in zero net displacement. Thus, the total change in position of the bee over these 5 seconds is zero.
Since the bee starts at the position (5, −5, −3) at t = 0, and there is no net change in position over 5 seconds, the bee must return to the starting point at t = 5. Therefore, the bee is located at (5, −5, −3) at time t = 5 seconds.
what is the area of the trapezoid?
Answers
[tex] A = \dfrac{(B + b)h}{2} [/tex]
where B = larger base, b = smaller base, and h = height.
For this trapezoid, you have
B = 10 + 7 + 7 = 24
b = 10
h = 9
[tex] A = \dfrac{(24 + 10) \times 9}{2} [/tex]
[tex] A = 153 [/tex]