-x² + 8x 15 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the vertex of the parabola. Graph the equation y -
Answers
The graph of the function y = -x² + 8x + 15 is added as an attachment
The vertex and the roots are labelled
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = -x² + 8x + 15
The above function is a quadratic function that has been transformed as follows
Shifted up by 15 unitsa = -1, b = 8 and c = 15Next, we plot the graph using a graphing tool by taking note of the above transformations rules
The graph of the function is added as an attachment
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Related Questions
A 16-ounce bottle of Spring Water is $2.08. A 20-ounce
bottle of Fresh Water is $2.40. Which statement about
the unit prices is true?
Answers
Step-by-step explanation:
spring water is 2.08/16= 13 cents per ounce
fresh water is 2.40/20= 12.5 cents per ounce
fresh water is .5 cents per ounce less expensive
a map has a scale of 1/2 inches:12 miles if the actual distance between the cities is 480 miles how far apart are they on the map
Answers
Answer:
20 inches
Step-by-step explanation:
Since there are 480 miles in total, we have to divide it by 12 so we can see how many half inches that would be.
480÷12 = 40
That would mean you can fit forty 12's in 480. Since 12 miles equals 1/2, you would multiply it by 40.
1/2 × 40 =20
This means that the distance between the cities on the map would be 20 inches.
For every 6 boys in the school, there are 7 girls. If there are 35 girls on any given day, how many boys would there be?
Answers
Answer:
30
Step-by-step explanation:
6/7=x/35
35/7=5
6x5=30
x=30
Three trains are made of identical train cars, so each car has the same number of seats. The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats. How many cars are in each train if no train has more than 25 seats
Answers
If no train has more than 25 seats. Then the number of cars in the first, second, and third train will be 17, 18, and 20 respectively.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Three trains are made of identical train cars, so each car has the same number of seats.
The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats.
If no train has more than 25 seats.
Then the number of the cars on each train will be
Let x, y, and z be the number of the cars in the first, second, and third train.
Then we have
x = 418 / 25
x = 16.75
x ≅ 17
y = 456 / 25
y = 18.24
y ≅ 18
z = 294 / 25
z = 19.76
z ≅ 20
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Answer:
11 cars in the 1st train, 12 cars in the 2nd train and 13 cars in the 3rd train
Step-by-step explanation:
There is a difference of 38 between the numbers 418, 456 and 494.
\(418/38=11\\456/38=12\\494/38=13\)
Trust me, this is 100% the correct answer!
hope this helps!
myopenmath.comSuppose that 14% of people own dogs. If you pick two people at random, what is the probability thatthey both own a dog?Give your answer as a decimal rounded to 4 places.CalculatorScratchwork Area
Answers
Answer:
\(0.0196\)Explanation:
The statement "Suppose that 14% of people own dogs," implies that the probability of owning a dog is given as;
\(Pr(Dog\text{ Owner) =}\frac{14}{100}\)Therefore, if two people are selected randomly for owning dogs, they would have the same probability attached to them.
We can then combine both probabilities by using the "and" symbol. which implies "multiplication."
Workings
\(\begin{gathered} pr(2\text{ dog owners) =}\frac{14}{100}\times\frac{14}{100} \\ =\frac{196}{10000} \\ =0.0196 \end{gathered}\)
50 points pls help!!!!!!
Make sure you are right I will have to retake this if you are wrong
if the terminal point of Ø is (0,1), what is tan Ø?
undefined
1
1/2
0
Answers
Answer:
undefined
Step-by-step explanation:
Since, the terminal point of is (x,y), thus
\(tan\) Ø \(\frac{y}{x}\)
x-coordinate is 1 and the y-coordinate is 0. Using \(tan0=\frac{y}{x}\) we get:
\(tan\) ∅ \(=\frac{1}{0}\)
\(tan\) ∅ \(=0\)
Therefore, tan Ø is undefined.
Or we can just do 1/0 which is undefined
~Lenvy~
A sample of 1000 observations taken from the first population gave x1 = 290. Another sample of 1200 observations taken from the second population gave x2 = 396.a. Find the point estimate of p1 − p2.b. Make a 98% confidence interval for p1 − p2.c. Show the rejection and nonrejection regions on the sampling distribution of pˆ1 − pˆ2 for H0: p1 = p2 versus H1: p1 < p2. Use a significance level of 1%.d. Find the value of the test statistic z for the test of part c. e. Will you reject the null hypothesis mentioned in part c at a significance level of 1%?
Answers
a. The point estimate of p1 - p2 is (290/1000) - (396/1200) = 0.29 - 0.33 = -0.04.
b. To make a 98% confidence interval for p1 - p2, we first need to calculate the standard error.
SE = sqrt(p1_hat*(1-p1_hat)/n1 + p2_hat*(1-p2_hat)/n2)
where p1_hat = x1/n1 and p2_hat = x2/n2.
Substituting the given values, we get
SE = sqrt((290/1000)*(1-290/1000)/1000 + (396/1200)*(1-396/1200)/1200) = 0.0231
The 98% confidence interval for p1 - p2 is (-0.04 ± 2.33(0.0231)) = (-0.092, 0.012).
c. To show the rejection and nonrejection regions on the sampling distribution of pˆ1 - pˆ2, we need to first calculate the standard error of pˆ1 - pˆ2.
SE(pˆ1 - pˆ2) = sqrt(p_hat*(1-p_hat)*(1/n1 + 1/n2))
where p_hat = (x1 + x2)/(n1 + n2).
Substituting the given values, we get
SE(pˆ1 - pˆ2) = sqrt((290+396)/(1000+1200)*(1-(290+396)/(1000+1200))*(1/1000 + 1/1200)) = 0.0243
Using a significance level of 1%, the rejection region is pˆ1 - pˆ2 < -2.33(0.0243) = -0.0564. The nonrejection region is pˆ1 - pˆ2 ≥ -0.0564.
d. The value of the test statistic z for the test of part c is (pˆ1 - pˆ2 - 0) / SE(pˆ1 - pˆ2) = (-0.04 - 0) / 0.0243 = -1.646.
e. At a significance level of 1%, the critical value for a one-tailed test is -2.33. Since the calculated test statistic (-1.646) does not fall in the rejection region (less than -0.0564), we fail to reject the null hypothesis. Therefore, we cannot conclude that p1 is less than p2 at a significance level of 1%.
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Find the qigenvalues and eigenvectors for A=[13 20]
[-4 -3]
the eigenvalue a + bi = __ has an eigenvector
[___]
[___]
the eigenvalue a-bi = __ has an eigenvector
[___]
[___]
Answers
The eigenvalues and eigenvectors of the matrix A = [[13, 20], [-4, -3]] can be found using the eigenvalue equation.
The eigenvalues are a + bi and a - bi, where a and b are real numbers. The eigenvectors corresponding to these eigenvalues can be determined by solving the system of equations (A - λI)v = 0, where λ is the eigenvalue and v is the eigenvector. For A, the eigenvalues are 5 + 4i and 5 - 4i, and the corresponding eigenvectors are [4i, 1] and [-4i, 1], respectively.
To find the eigenvalues and eigenvectors, we start by solving the eigenvalue equation (A - λI)v = 0, where A is the given matrix, λ represents the eigenvalue, I is the identity matrix, and v is the eigenvector. In our case, A = [[13, 20], [-4, -3]].
First, we subtract λI from A:
A - λI = [[13 - λ, 20], [-4, -3 - λ]]
Next, we set the determinant of (A - λI) equal to zero and solve for λ to find the eigenvalues. The determinant equation is:
det(A - λI) = (13 - λ)(-3 - λ) - (20)(-4) = λ^2 - 10λ + 43 = 0
Solving the quadratic equation, we find the eigenvalues:
λ = (10 ± √(-36)) / 2 = 5 ± 4i
So, the eigenvalues are 5 + 4i and 5 - 4i.
To find the eigenvectors corresponding to each eigenvalue, we substitute the eigenvalues into the equation (A - λI)v = 0 and solve for v.
For λ = 5 + 4i:
(13 - (5 + 4i))v1 + 20v2 = 0 => 8 - 4i)v1 + 20v2 = 0
-4v1 + (-3 - (5 + 4i))v2 = 0 => -4v1 - 8 - 4i)v2 = 0
Simplifying the equations, we get:
(8 - 4i)v1 + 20v2 = 0
-4v1 - 8 - 4i)v2 = 0
Dividing the second equation by -4, we get:
v1 + 2 + i)v2 = 0
We can choose a value for v2 to find v1. Let's choose v2 = 1, then v1 = (-2 - i).
Therefore, the eigenvector corresponding to the eigenvalue 5 + 4i is [(-2 - i), 1].
Similarly, for λ = 5 - 4i, we can find the eigenvector:
(8 + 4i)v1 + 20v2 = 0
-4v1 - 8 + 4i)v2 = 0
Dividing the second equation by -4, we get:
v1 + 2 - i)v2 = 0
Choosing v2 = 1, we find v1 = (-2 + i).
Thus, the eigenvector corresponding to the eigenvalue 5 - 4i is [(-2 + i), 1].
The eigenvalues of the matrix A = [[13, 20], [-4, -3]]
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What is the value for y
When x=20
Y=-2x+8
Answers
Answer:
y = -32
Step-by-step explanation:
Y=-2x+8
Let x= 20
y = -2 * 20 +8
y = -40+8
= -32
In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?
m∠X + m∠Z 90°
∠X and∠Y are complementary
m∠X + m∠Y < 90°
Answers
Answer:
m < X + m < Y < 90
Step-by-step explanation:
For the triangle XYZ, m∠Z > m∠X + m∠Y we see that because the total internal angles of a triangle is 180,m∠X + m∠Y < 90° is a true assertion
Option C is correct
What must be true about triangle XYZ?Generally, A triangle's major feature is its total internal angles as 180
Therefore
if m∠Z > m∠X + m∠Y this means that m<z must be greater than 90 degrees
This goes to show us that
m<X + m<Y < 90 because as we earlier mentioned the total internal angles of a triangle is 180 .
In conclusion, For the triangle XYZ
m∠X + m∠Y < 90° is a true assertion
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Please help!! Did I do the right thing? If not, please write how to do it
Answers
Answer:
The answer is 1/3
you were close
Step-by-step explanation:
Frank+pedro+Tanisha=1
14/24+1/12+x=1
7/12+1/12+x=1
8/12+x=1
x=1-8/12
x=1-2/3
x=1/3
The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 $600
3 $720
6 $840
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 7 days? (2 points)
Answers
To find the slope of the function g(x), we can use the formula:
slope = (change in y) / (change in x)
Using the values given in the table, we can calculate:
slope = (g(3) - g(0)) / (3 - 0) = (720 - 600) / 3 = 40
The slope of the function g(x) is 40. This means that for each day that passes, the balance in the bank account increases by $40.
Part B:
To write the equation of the line in point-slope form, we can use the point-slope formula:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Using the point (0, 600), we can write:
g(x) - 600 = 40(x - 0)
Simplifying, we get:
g(x) = 40x + 600
This is the equation of the line in point-slope form.
To write the equation of the line in slope-intercept form, we can rearrange the equation as:
g(x) = 40x + 600 = 40(x) + b
where b is the y-intercept. From the equation, we can see that b = 600. Therefore, the equation of the line in slope-intercept form is:
g(x) = 40x + 600
To write the equation of the line in standard form, we can rearrange the equation in slope-intercept form as:
-40x + g(x) = 600
This is the equation of the line in standard form.
Part C:
To write the equation of the line using function notation, we can use the slope-intercept form:
g(x) = 40x + 600
This is the equation of the line in function notation.
Part D:
To find the balance in the bank account after 7 days, we can use the equation of the line:
g(x) = 40x + 600
Substituting x = 7, we get:
g(7) = 40(7) + 600 = 880
Therefore, the balance in the bank account after 7 days is $880.
Nelson LLC, has earnings before interest and taxes of €10,350 and net income of €2,528.50. The tax rate is 25%. What is the interest coverage ratio (times interest earned)?
A) 0.62
B) 0.96
C) 1.04
D) 1.48
Answers
The interest coverage ratio (times interest earned) for Nelson LLC is approximately 1.04, option C.
The interest coverage ratio is calculated by dividing earnings before interest and taxes (EBIT) by the interest expense. EBIT represents the operating income of the company before deducting interest and taxes.
Given the values:
EBIT = €10,350
Net Income = €2,528.50
Tax Rate = 25%
To calculate the interest expense, we subtract the net income from the EBIT and multiply it by (1 - tax rate):
Interest Expense = (EBIT - Net Income) × (1 - Tax Rate)
= (€10,350 - €2,528.50) × (1 - 0.25)
= €7,821.50 × 0.75
= €5,866.12
Now, we can calculate the interest coverage ratio by dividing EBIT by the interest expense:
Interest Coverage Ratio = EBIT / Interest Expense
= €10,350 / €5,866.12
≈ 1.04
Therefore, the interest coverage ratio for Nelson LLC is approximately 1.04, indicating that the company's earnings before interest and taxes are 1.04 times greater than its interest expense.
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Below is the graph of y=bx. Find b. On a coordinate plane, an exponential function approaches the x-axis in quadrant 1 and increases exponentially in quadrant 2. b =
Answers
Answer:
b=0.5
and the other part is:
B.) The graph shows exponential decay
D.) The graph shows y=2^x reflected over the y-axis
Step-by-step explanation:
i just did this problem on edge 2020
Answer: 0.5, B&D
Step-by-step explanation:
Can you please help
#6 GRADE
Answers
Answer:
the interger would be 15 because you earn 15 so therfore it would be 15.
Step-by-step explanation:
John weighed 156 pounds give or take 8 pounds, ten years ago.
Write the absolute value inequality representing the range of John's weight.
Answers
The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.
What is absolute value of inequality?An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.
What is absolute value expression?An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.
As per the given question,
If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.
To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:
| x - 156 | ≤ 8
This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.
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Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 9 6 5 20 Female 18 20 10 48 Total 27 26 15 68 If one student is chosen at random, Find the probability that the student was NOT a male that got a "B"
Answers
The probability that the student was NOT a male that got a "B" is 62/68, which can be simplified to 31/34. To find the probability that the student was NOT a male that got a "B," we need to first calculate the total number of students that fit this criteria.
From the table, we know that there were a total of 26 students who did not receive a "B" (15 females and 11 males). Out of those 26 students, there were 11 males who did not receive a "B".
Therefore, the probability of choosing a student who was NOT a male that got a "B" is:
(15 + 11) / 68 = 26 / 68 = 0.382 or approximately 38.2%
So the probability that the student chosen at random was NOT a male that got a "B" is 0.382 or 38.2%.
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What is the equation of the line that passes through the point (-5,-3)and has a slope of -3/5 ?
Answers
Answer: y = -3/5x - 6
Step-by-step explanation:
There are a few equations that can be used for this, but the simplest one would be y = mx + b
We are given:
y = -3
m = -3/5 (slope)
x = -5
b = ?
Our equation is this, we are solving for b
==> -3 = -3/5 ( -5) + b
==> -3 = -3/5 ( -5) + b ( multiply the brackets)
==> -3 = 3 + b ( subtract 3 to both sides)
==> -6 = b
Now we can make the desired equation in slope intercept form;
y = -3/5x - 6
Hope this helped! Have a great day :D
Find the equation of the line passing through the points (-3,3) and (2,-32). Write your answer in the form Y=mx+b
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
point 01 (-3, 3)
point 02 (2 , -32)
Step 02:
equation of the line (y = mx + b)
slope = m
\(m=\frac{y2-y1}{x2-x1}=\frac{-32-3}{2-(-3)}=\frac{-35}{2+3}=\frac{-35}{5}=-7\)(y - y1) = m (x - x1)
(y - 3) = -7 (x - (-3))
y - 3 = -7 (x + 3)
y = -7x - 21 + 3
y = -7x - 18
The answer is:
y = -7x - 18
This is my question, if you can solve this in under 2 minutes you are skilled!
Answers
Answer:
they both ate the same amount
Step-by-step explanation:
tito
1/4+3/8+1/2= 1 1/8
luis
5/8 + 1/2= 1 1/8
Help, please
A: 2
B: -2
C: 1/2
D:-1/2
Answers
Answer:
\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \sqrt{x} \left \{ {{y=2} \atop {x=2}} \right. \frac{x}{y} \alpha \alpha \alpha =\beta\)
Step-by-step explanation:
Convert 1000000 seconds to hrs, min and seconds
Answers
The value of the conversion is;
16, 666. 67 minutes
277.78 hours
What is conversion of units?Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.
From the information given, we have;
10⁶ seconds
But, we have to take note of;
60 seconds = 1 min
Then 10⁶ seconds = x min
cross multiply
x = 16, 666. 67 minutes
Also,
60 minutes = 1 hour
Then 16, 666. 67 minutes = x
cross multiply
x = 277.78 hours
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please hurry not much more time answer even if its too late somebody else can use the answer.
6. Middle school class representatives conducted a poll during lunch to see which activity students wanted for their year-end party. The results are shown in this relative frequency table below:
a) For the entire school, which was more popular, water slides or roller skating? (1 point)
THE ANSWER FOR A IS: ROLLER SKATING
b) 34% of the 6th graders and 50% of the 7th graders want to go to the water slides. What percentage of the 8th graders want to go to the water slides? (1 point)
c) Does there seem to an association between grade level and field trip choice? (2 points)
d) If this trend continued, would you expect 9th graders to prefer the water slides or roller skating? Explain your answer. (2 points)
Answers
The table of the relative frequencies show that 70% of 8th graders want the water slides.
There is an association between grade level and field trip choice with the higher grades preferring Water slides more than roller skating.
9th graders would prefer waterslides if the trend continues.
What does the frequency table show?The percentage of 8th graders who want to go to water slides is:
= 0.14 / 0.20 x 100%
= 70%
As the grades increase, less people want to go roller skating which means that should this trend continue, 9th graders would prefer water slides.
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Answer:
See below
Step-by-step explanation:
From the table:
a) roller skating is 54 percent.....slides is only 46 percent
b) 8 th graders who want water slide = .14 / ( .14 + .06) = 70 percent
c) yes higher grade, higher want water slide
d) water slides ( see answer c )
What is the slope of the line through (−1,−7) and (3,9)?
Answers
Answer:
The slope is 4.
Step-by-step explanation:
Point slope form is y-y1 over x-x1. I put the coordinates in like this.
9-(-7) over 3-(-1) so thats 9+7 over 3+1. 16 over 4 is 4.
Answer:
The answer is 2
Step-by-step explanation:
Combine like terms to simplify the expression:
Answers
Answer:
\(\frac{5k -6}{10}\)
Answer:
1/5k + 3/5
Step-by-step explanation:
2/5 * 2/2 = 4/10
4/10k + 1/10k = 5/10k = 1/2k
1/2k + 3/5
What is 90.125 written in expanded form?
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
A map scale is give as 1:10000
What is the real distance between two points 20cm apart on the map?
Give your answer in kilometres.
Answers
Answer:
2km
Step-by-step explanation:
Simplify the expression
a. x^2
b. x^3
c. x^1/3
d. x^1/2
Answers
Answer:
d
Step-by-step explanation:
When you exponent an exponent with another exponent, you multiply them together
\(Answer:\ x^\frac{1}{2}\)
Step-by-step explanation:
\((x^\frac{1}{6})^3=\\\\ x^\frac{1*3}{6}=\\\\ x^\frac{3}{2*3} =\\\\x^\frac{1}{2}\)
Imhotep the architect wants to paint the great pyramid.He wants one red side , one blue side , one green side and one yellow side .
How many different ways can he paint it?
Answers
Answer:
24
Step-by-step explanation:
If Imhotep wants to paint each side of the pyramid a different color, then he has 4 sides to paint with 4 different colors (red, blue, green, and yellow). The number of different ways he can paint the pyramid can be calculated using the permutation formula, which is:
nPr = n! / (n - r)!
where n is the total number of items (in this case, 4 colors) and r is the number of items selected (in this case, 4 sides of the pyramid).
So, the number of different ways Imhotep can paint the pyramid is:
4P4 = 4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, there are 24 different ways that Imhotep can paint the pyramid if he wants to paint each side a different color.
Factor the expression into an equivalent form.
Answers
Answer: the answer is C.
Step-by-step explanation: factor out 3 from the expression (4y2 -25)
using a2 -b2=(a-b)(a+b), factor the expression. Then your answer is 3(2y-5)(2y+5)
