How would you find the quadratic that goes through the point (4,0), the axis of symmetry is x=7, and it also goes through the point (1,5)?
Answers
9514 1404 393
Answer:
y = (5/27)(x -7)^2 -5/3
Step-by-step explanation:
Use the given points to find the unknowns in the equation.
If the axis of symmetry is x=7, then the equation can be written in the form ...
y = a(x -7)^2 +b
Filling in the two point values, we have two equations:
0 = a(4 -7)^2 +b ⇒ 9a +b = 0
5 = a(1 -7)^2 +b ⇒ 36a +b = 5
__
Subtracting the first equation from the second, we have ...
(36a +b) -(9a +b) = (5) -(0)
27a = 5
a = 5/27
Substituting that value into the first equation gives ...
9(5/27) +b = 0
5/3 +b = 0
b = -5/3
So, the quadratic can be written in vertex form as ...
y = (5/27)(x -7)^2 -5/3
Related Questions
Which of the following have
a value equal to [-12]?
![Which of the following havea value equal to [-12]?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Nt8aYKvxfjThcdy36tWLZIXRIwKzaYlO.png)
Answers
Answer:
option 3) ii, iv, v
Step-by-step explanation:
|-12| means write the absolute value, which means just the number without the sign.
Therefore |-12| = 12
So, ii. 12
iv. |12| is also = 12
v. -( -12) is also = 12
Answer:
12.00000000000000000
The time required find an entry in a list is uniformly distributed from 0 to 60 minutes. What is the probability that I will find the entry I am searching for in between 30 and 32 minutes
Answers
Answer:
The probability of finding the entry in the period between 30 and 32 minutes is 5%.
Step-by-step explanation:
Given that the time required to find an entry is uniformly distributed between 0 and 60 minutes, it implies that 100% of the chances are in that period of time distributed equally. Therefore, since 100/60 is equal to 1.66, each minute has a 1.66% chance that the entry will be there.
Thus, since between minutes 30 and 32 there are 3 minutes in total (30, 31 and 32), to determine the probabilities of finding the entry in that period it is necessary to perform the following calculation:
1.66 x 3 = X
5 = X
Therefore, the probability of finding the entry in the period between 30 and 32 minutes is 5%.
whats 2+7 because i really need help
Answers
Answer:
9 LOL-
Step-by-step explanation:
Exercise 1: ABC is a triangle such that AB=5cm. A=50°and AC=5cm 1) Construct the triangle ABC. 2) What is the nature of the triangle ABC? Justity. 3) Calculate ABC and ACB. 4) Draw the height [AH) issued from A to [BC]. 5) a. Calculate BAH and CAH. b. What does [AH] represents for BAC? Justify.
Answers
Answer:
2) Acute triangle, isosceles
3) Both are 65 degrees
4) (diagram)
5) a) both 25 degrees
b) midpoint
Step-by-step explanation:
2) If you're struggling search up "draw a triangle" and you'll find a website that will draw it for you. It will help you get an idea of it looks like and its nature.
3) We know that sides AB and AC are 5cm. So this triangle is an isosceles which makes the 2 remaining angles equal (if you draw a diagram it will be clear)
So:
180-50/2 = 65
ABC and ACB = 65 degrees each
4) Construct the line AH down the middle like in the diagram I drew.
5) a) Since AH is a straight line, we know that the angle AHB will be 90 degrees. After question 3 we also know that angle ABH is 65 degrees.
BAH = 180-90-65
BAH = 25 degrees
CAH = 50 - 25
CAH = 25 degrees
b) AH is the midpoint for BAC because the 2 segments formed are both 25 degrees.
Yomaro is buying soil for his garden. He needs to fill one pot with 12 cups of soil and another pot with 2 gallons of soil.
If the price of soil is $1.50 per quart, how much will he pay in all?
Answers
Answer the answer to your question is $7.50
Convert the rectangular coordinates to polar coordinates
(1, -9)
Answers
The polar coordinates of (1, -9) are (9.06, -1.47 radians).
To convert from rectangular coordinates to polar coordinates, we can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:
r = √(1² + (-9)²) = √82 ≈ 9.06
θ = tan⁻¹((-9)/1) ≈ -1.47 radians
Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).
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One jar of spaghetti sauce is made with 1/4 of a cup of tomatoes. How many full jars of spaghetti sauce can be made with 3 cups of tomatoes?
Answers
Answer:
you can make 12 cans of them
Henri necesita empacar en la menor cantidad de de cajas, cinta de color rojo y cinta de color verde si hay 120 metros de cinta de color rojo y 160 metros de cinta de color verde ¿que cantidad de cinta roja y verde deberá empacar Henri en cada caja?
Answers
Answer:
Step-by-step explanation:
Admission to a baseball game is $3.00 $ for general admission and $6.50 $ for reserved seats. The receipts were $5038.50 $ 5038.50 for 1256 1256 paid admissions. How many of each ticket were sold?
Answers
The number of admissions and to the numbers of the reversed seats will be 654 and 396.
What is the solutions to the equation?The distributions of weights to the variables involved that established the equilibrium in the calculations is referred to as a result.
Admission to a baseball game is $3.00 for generally admission and $6.50 for reserved seats. the receipts were $4536.00 for 1050 paid admissions.
Let x be the numbers of admissions and y be the number of seats. Then the equation is given as,
x + y = 1050 ...1
3x + 6.5y = 4536 ...2
From equations 1 and 2, then we have
3(1050 - y) + 6.5y = 4536
3150 - 3y + 6.5y = 4536
3.5y = 1386
y = 396
Then the numbers of x will be given as,
x + 396 = 1050
x = 1050 - 396
x = 654
The number of admissions and the numbers of reversed will be 654 and 396.
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HELP! Below is the graph of a polynomial. Which statement about this graph is true?
A. The point (-2,1) is a maximum
B. The point (5,0) is an extreme
C. The point (2,-1.12) is a minimum
D. The point (2,-1.12) is a maximum
Answers
spherical water tank of radius R = 5m is emptied through a small circular hole of radius r = 0.03 m at the bottom. The top of the tank is open to the atmosphere. The instantaneous water level h in the tank (measured from the bottom of the tank, at the drain) can be determined from the solution of the following ODE:
dh /dt =r²(2gh)^0.5/ 2hR-h²
where g = 9.81 m/s². If the initial (t = 0) water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Answers
Answer:
water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Step-by-step explanation:
water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Jenny has saved $600 from her summer job during the school year she withdraws $20 from her account every week for her daily expenses she wants to keep more than $300 in the account for college the number of weeks w that Jenny can withdraw money from her account is represented by the inequality 600 - 20 w >300 how many weeks can Jenny continue to withdraw $20 from her account
Answers
Answer:
Step-by-step explanation:
The inequality that represents Jenny's situation is:
600 - 20w > 300
To solve for w, we can start by subtracting 600 from both sides of the inequality:
-20w > 300 - 600
-20w > -300
Next, we can divide both sides by -20, remembering to reverse the direction of the inequality because we are dividing by a negative number:
w < (-300) / (-20)
w < 15
Therefore, the number of weeks that Jenny can continue to withdraw $20 from her account is less than 15. Since Jenny cannot withdraw a fractional number of weeks, the largest whole number of weeks that satisfies the inequality is 14.
Therefore, Jenny can continue to withdraw $20 from her account for 14 weeks while still keeping more than $300 in her account for college.
Each marble bag sold by Jane's Marble Company contains 4 purple marbles for every 5 red marbles. If a bag has 24 purple
marbles, how many red marbles does it contain?
Answers
There are 4x purple marbles and 5x red marbles, where x is the common factor.
4x = 24
x = 24/4 = 6.
ANSWER. 5*6 = 30 red marbles.
How to calculate the probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.
Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Give an example of a probability?The likelihood or chance of an event happening is known as probability. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.
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Santos Company provided the following information for 2022:
Common Stock Outstanding 100,000 shares
Convertible Preferred, Total Par Value $50,000; Dividend Rate 4%; Convertible into 1,900 Common Shares Dividend Declared & Paid
Stock Options – A Exercise Price $12; Average Market Price $11; 3,000 Options
Stock Options – B Exercise Price $7; Average Market Price $8; 4,000 Options
Convertible Bonds, 5%, Face Value $1,000,000; Convertible into 40,000 Common Shares
Tax Rate 30%
Net Income $120,000
Round to nearest two decimal places.
Part A: Complete all steps to determine EPS to be reported including:
1. Computation of Basic EPS
2. Individual dilution/anti-dilution with decision making
3. Ranking of potential dilutors
4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.
Part B: Partial Financial Statement Presentation of EPS for this company for the current year (2022) with a proper heading. Start your partial statement with Net Income.
Reminder: You must show all supporting computations
Answers
Answer:
Part A:
1. Computation of Basic EPS
Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²
Net Income = $120,000
Preferred Dividends = 4% x $50,000 = $2,000
Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)
Basic EPS = ($120,000 - $2,000) / 100,000
Basic EPS = $1.18
2. Individual dilution/anti-dilution with decision making
We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.
Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.
EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)
EPS after conversion = $1.16
Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.
Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.
Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).
EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)
EPS after exercise = $1.17
Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.
Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.
EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)
EPS after conversion = $1.19
Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.
3. Ranking of potential dilutors
We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.
The most dilutive security is the convertible preferred with an EPS of $1.16.
The second most dilutive security is the stock options - B with an EPS of $1.17.
The least dilutive security is the convertible bonds with an EPS of $1.19.
4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.
We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.
The first security to include is the convertible preferred.
EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)
EPS with convertible preferred = $1.16
The next security to include is the stock options - B.
EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)
EPS with stock options
A man fell asleep studying for his math exam. He woke up at 9:30 p.m. If he slept for 3 hours and 50 minutes, what time did he fall asleep?
A. 6:20 p.m.
B. 6:05 p.m.
C. 5:40 p.m.
D. 5:20 p.m.
Answers
Answer:
C. 5:40 p.m.
Step-by-step explanation:
Emma Jarmel obtained a $6,000 loan at 10% for home improvements. The monthly payment is $276.60 What is the amount of the a) interest for the first payment, b) payment to principal, and c) new principal?
Answers
The simple interest is given by
\(\begin{gathered} \text{Interest}=\text{ Principal}\times\text{ Rate}\times\text{ Time} \\ \text{Interest}=\text{ 6000}\times\text{ 0.1}\times\frac{1}{12} \\ \text{Interest}=\text{ }50 \end{gathered}\)Therefore, the amount of the interest was $50.
Lets find the payment to the principal.
\(\begin{gathered} \text{ Payment to the principal = Monthly Payment - Interest} \\ \text{ Payment to the principal =}276.60-50 \\ \text{ Payment to the principal =}226.60 \end{gathered}\)Then, her paymento to principal was $226.60
Finally, lets find the new principal.
\(\begin{gathered} \text{ New principal = Previous principal - Payment to principal} \\ \text{ New principal = }6000-226.60 \\ \text{ New principal = }5773.40 \end{gathered}\)Then, Emma's new principal was $5773.40.
4
Select the correct answer.
The y-intercept of the parent quartic function, f(x) = x^4
transformation?
Is translated 3 units to the right and 1 unit down. Which equation represents this
OA. g(t) = (1 + 1)4 + 3
OB. g(t) = (1 - 1)4 + 3
Oc g(1) = (1 – 3)4 – 1
OD. g(x) = (x + 3)4 - 1
Answers
The equation which represents the transformation of the y-intercept of the parent quartic function,\(f(x) = x^4\) is given by \(g(x)=(x-3)^4-1\) .
What is transformation ?Transformation is the act or process of changing completely. In this also the graph changes or transform.
We have,
Parent Quadratic equation \(f(x)=x^4\)
And
It translated \(3\) units to the right and \(1\) unit down.
And the parent quadratic function is in the form of \(f(x) = a(x-h)^4 + k.\)
Here,
"h" tells if the vertex of the parabola is going left or right.
"k" determines if the vertex of the parabola is going up or down.
So, According to the question;
We have,
\((a)\) \(3\) units to the right
\((b)\) \(1\) unit down
So,
Equation would be \(g(x)=(x-3)^4-1\) means that you have moved the vertex of the parabola \(3\) units to the right and \(1\) units down.
(Always remember if moving right means \((x-3)\) sign would be minus because in parent quadratic function is in the form of \(f(x) = a(x-h)^4 + k\) we have minus sign.)
Hence, we can say that the equation which represents the transformation of the y-intercept of the parent quartic function,\(f(x) = x^4\) is given by \(g(x)=(x-3)^4-1\) .
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What is the distance, d, between the points (2, 7/2) and (5/3, 1)
Enter your answer in the box. Enter your answer in simplest radical form.
d =
Please help!
Answers
We need to know about distance between points to solve this problem. The distance between the points is \(\sqrt{229}\)/6 units.
The distance between two points can be referred as the length of the line joining these two points. The distance between two points is calculated by drawing a right angled triangle using these two points. Let there be two points (a,b) and (x,y), the length a-x forms the base of the triangle, b-y forms the height and the lime joining the two points is the hypotenuse. We apply Pythagoras' theorem to find the length of the hypotenuse. Thus the formula for finding distance between two points is given by
d=\(\sqrt{(a-x)^{2}+(b-y)^{2} }\)
Here the two points are (2,7/2) and (5/3,1)
d=\(\sqrt{(2-\frac{5}{3} )^{2}+(\frac{7}{2} -1)^{2} } =\sqrt{(\frac{1}{3} )^{2} +(\frac{5}{2}) ^{2} } \\=\sqrt{\frac{1}{9}+\frac{25}{4} } =\sqrt{\frac{229}{36} } =\frac{\sqrt{229} }{6}\)
Therefore we found the distance between two points to be \(\sqrt{229}\)/6 units.
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) Find the average gold medal winnings of those NOCs who have been
awarded fewer than ten bronze medals.
Count the number of those NOCs that have been awarded ten or more
silver medals.
This question requires the construction and interpretation of a pie chart based
on the data throughout this task.
a) Create a suitable and fully labelled pie chart to show the total medal
winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games.
Interpret the pie chart produced in Question 8a). Discuss two probable
justifications for the behaviour of the data.
Answers
a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:
Obtain the data for the medal winnings of the Top 10 NOCs
Find the average gold medal winnings of those NOCs who have beenawarded fewer than ten bronze medals.?Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)
Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option
Add a title and labels to the chart to show the NOCs and their corresponding medal winnings
b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:
Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.
Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.
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I’ll give brainliest if correct!
Question 16 of 43
For the data set 9, 13, 14, 15, 15, 18, the mean is 14. What is the mean
absolute deviation?
O A. The mean absolute deviation is 14.
O B. The mean absolute deviation is 12.
O C. The mean absolute deviation is 2.
D. The mean absolute deviation is 6.
Answers
Answer:
C. The mean absolute deviation is 2.
Step-by-step explanation:
In order to find the mean absolute deviation, follow the following steps:
Find the absolute distance of each data from the mean. Add the distances so obtained Divide the sum by no of given data to get the mean absolute deviation.Let's work it out.
STEP: 1
|9 - 14| = 5
|13 - 14| = 1
|14 - 14| = 0
|15 - 14| = 1
|15 - 14| = 1
|18 - 14| = 4
STEP: 2
5 + 1 + 0 + 1 + 1 + 4 = 12
STEP: 3
Mean Absolute deviation \( =\frac{12}{6}= 2\)
help please, asap. i need this done
Answers
Answer:
2
Step-by-step explanation:
15/3=5
25/5 = 5
10/2 = 5
Answer:
2
Step-by-step explanation:
You have to find the "pattern."
for 15 and 3, you have to divide 15 by 5 and thats 3.
for 25 and 5, 25/5 is 5, so 10/5 is 2.
please help me it's ,due, by 30 minutes please help me.
Answers
Step-by-step explanation:
I hope its helped ! studied well.
Answer:
a: The tape diagram represents the story because there’s 5 boxes representing the 5 weeks and x-2 in each box since x represents the amount Andre’s neighbor will pay him weekly to mow the lawn. This all equals 40 because that’s how much money he has to save.
B: Andre’s neighbor pays him 10 dollars each week to mow the lawn.
Step-by-step explanation:
b: For this part you have to make an equation combining all the five weeks which would be 5x-10. Then you would make it equal 40 because that’s how much he needs to save 5x-10=40. The you solve to find x by adding 10 to both sides of the equation and get 5x = 50. Then if you divide 5 on both sides you get 10!
You can check you work by plugging in 10 as x into the diagram.
Multiplying a number by its reciprocal always results in a product of 1. What number must be multiplied by 4 5/8 to create a product of 1?
Answers
First, turn 4 5/8 into an improper fraction.
4 = 32/8
(The fraction bar is basically division)
32/8 + 5/8 = 37/8
Now, flip it to find the answer.
6/37
That is the answer.
Hope I helped
In ASTU, mZS = (6x – 15)°, mZT = (2x − 2)°, and
mZU = (4x – 7)º. What is the value of x?
Answers
Answer:
x = 17
Step-by-step explanation:
all three expressions should be added together and set equal to 180 degrees
6x - 15 + 2x - 2 + 4x - 7 = 180
now combine like terms
12x - 24 = 180
add 24
12x = 204
x = 204/12
x = 17
Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
Answers
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
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to 2z√44z - 2√11z³, if x > 0?
Answers
Simplifying the expression would give 2√11z ( 2z - z²)
What are surds?Surds are known as values in square root that cannot be simplified into whole numbers or integers
Given the expression:
2z√44z - 2√11z³
Find the factors of 44;
= 11 × 4
Substitute into the expression;
2z√4 × 11z - 2√11z³
Find the square root of 4 and leave that if 11, because it does not have a perfect square root
2z × 2√11z - 2√11z³
4z√11z - 2√11z³
Now, let's find the common factor
2√11z ( 2z - z²)
Simplifying the expression gives 2√11z ( 2z - z²)
Thus, simplifying the expression would give 2√11z ( 2z - z²)
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Evaluate the expression 4*4*4 ÷ (7 − 3) × 2. (4 points)
Answers
4^3/(4)*2
64/(4)*2
64/8
= 8
Can some body please help me with #12 pleassssssse T^T
Answers
Demitrius deposited $41.67, which was 60% of his paycheck.
Using this, we can make an equation.
If x is the amount of his paycheck,
\(0.6x=41.67\)
\(x=69.45\)
The value of the paycheck was $69.45.
Hope this helps.
頑張って!
Write a linear equation to describe the number pattern that starts with 3 and continues with positive odd integers.
Answers
In order to have a linear equation, you have to write an equation like
\(y=mx+q\)
The sequence has to start with 3, so we must choose \(q=3\), because this guarantees that when \(x=0\) we have
\(y=0\cdot m + 3 =3\)
Now, \(m\) must be even. In fact, if \(m\) is even, \(mx\) will always be even for every possible \(x\), and \(mx+3\) will be odd.
So, for example, you might choose
\(y=2x+3\)
Which will produce the following sequence:
\(\begin{array}{c|c}x&f(x)\\0&3\\1&5\\2&7\\3&9\end{array}\)
and so on
Find the values of x and y so that the quadrilateral is a parallelogram.
