The equation of the parabola that models the movement of the football is y = -2x² + 5x + 12. The time at which the ball hits the ground is x = 4 seconds.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
a. We know that the general form of the quadratic equation is y = ax² + bx + c, where a, b, and c are constants.
We are given three points that the football passes through: (1, 15), (2, 14), and (3, 9).
We can substitute these points into the quadratic equation and solve for a, b, and c.
For the first point, we have: 15 = a(1)² + b(1) + c
For the second point, we have: 14 = a(2)² + b(2) + c
For the third point, we have: 9 = a(3)² + b(3) + c
Solving this system of equations using elimination gives us:
a = -2
b = 5
c = 12
Therefore, the equation of the parabola that models the movement of the football is y = -2x² + 5x + 12.
b. To find the time at which the ball hits the ground, we can set the value of y equal to 0 and solve for x.
y = -2x² + 5x + 12
0 = -2x² + 5x + 12
-12 = -2x² + 5x
-2x² + 5x - 12 = 0
We can use the quadratic formula to solve for x:
x = (-5 +/- √(5² - 4(-2)(-12)))/(2(-2))
x = (-5 +/- √(25 + 96))/(-4)
x = (-5 +/- √(121))/(-4)
x = (-5 +/- 11)/(-4)
Therefore, x = 4 or x = -3/2.
The time at which the ball hits the ground is x = 4 seconds.
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A 3-ounce serving of tuna provides 21 g of protein use equivalent ratios to find how many grams of protein are in 9 ounces of tuna! Explain
Answer: 63 grams of protein in 9 ounces of tuna
Step-by-step explanation: To find how many grams of protein are in 9 ounces of tuna, we can use equivalent ratios.
We know that a 3-ounce serving of tuna provides 21 grams of protein.
Let's set up a ratio:
3 ounces of tuna: 21 grams of protein
To find out how many grams of protein are in 9 ounces of tuna, we can set up a proportion:
3 ounces of tuna / 21 grams of protein = 9 ounces of tuna / x grams of protein
To solve for x, we can cross-multiply:
(3 ounces of tuna)(x grams of protein) = (9 ounces of tuna)(21 grams of protein)
3x = 189
Dividing both sides of the equation by 3:
x = 63
Therefore, there are 63 grams of protein in 9 ounces of tuna.
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PRE CAL
f(x)=x^3+x^2+4x+4
Solve with Synthetic division and find all zeros of the function
True or false: given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.
A 90% confidence interval will have a width of 2.36 which is false.
What is a confidence interval?Let μ be the mean, σ be the standard deviation, n be the ample size, and z be the z-score. Then we have
Confidence interval = μ ± z (σ / √n)
A sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points.
We know that the z-score for 90% of the confidence interval is 1.645. Then we have
Confidence interval = μ ± z (σ / √n)
Confidence interval = 2.1 ± 1.645 (0.7 / √10)
Confidence interval = 2.1 ± 0.364
For positive sign, then the width will be
⇒ 2.1 + 0.364
⇒ 2.46
A 90% confidence interval will have a width of 2.36 which is false.
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At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
Answer:
21
Step-by-step explanation:
Write an expression for 4 snacks at n pence each
To start the school year, a teacher spends $54.35 in school supplies for her classroom. During the course of the year, she will restock her supplies and will spend $22 each time she restocks the supplies. The expression below describes this situation.
22x + 54.35
In this expression, what is the coefficient and what does it describe?
A.) x, which describes the number of times she restocks her supplies
B.) 22, which describes the amount she spends each time restocking her supplies
C.) 22x, which describes the total amount she spends each time she goes to the store
D.) 54.35, which describes the amount she originally spends on supplies
If in one year a city recorded a total of 97 rainy, how many of the days did it not rain?
1 year = 365 days
365 -97 = 268
it did not rain 268 days
what would be the maximum value for f(x) = −5x2 + 9
Monica ramirez works at the hospital as a nursing assistant. she works 15 hours per week and earns $8.50 per hour. what is monica's straight-time pay for each week?
Answer:
$127.50
Step-by-step explanation:
Given: Monica ramirez works at the hospital as a nursing assistant. She works 15 hours per week and earns $8.50 per hour.
To find: Monica's straight-time pay for each week.
Solution:
Monica earns $8.50 per hour.
Monica works for 15 hours per week.
To find the straight-time pay for each week, we need to multiply the per hour cost with the total number of hours she had worked in a week.
So, the straight-time pay for each week can be calculated as:
[tex]=15\times8.50=127.50[/tex].
Therefore, the straight-time pay for each week is $127.50
write a percent between 25percent and 50 percent then write it as a decimal and as a fraction in simplest form
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ? Enter your answer in the box.
Lines can be parallel, perpendicular or have no relationship at all.
The equation of the line is: [tex]\mathbf{y = -3x + 14}[/tex]
First, we calculate the slope of: [tex]\mathbf{y = \frac x3 - 1}[/tex]
A linear equation is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where:
m represents the slope
So, by comparison:
[tex]\mathbf{m = \frac 13}[/tex]
From the question, we understand that the required line is perpendicular to [tex]\mathbf{y = \frac x3 - 1}[/tex]
This means that, the slope (m2) of the required line is:
[tex]\mathbf{m_2 = -\frac 1m}[/tex]
So, we have:
[tex]\mathbf{m_2 = -\frac 1{1/3}}[/tex]
[tex]\mathbf{m_2 = -3}[/tex]
The equation of the line is:
[tex]\mathbf{y = m_2(x - x_1) + y_1)}[/tex]
Where:
[tex]\mathbf{(x_1,y_1) = (4,2)}[/tex]
So, we have:
[tex]\mathbf{y = -3(x - 4) + 2}[/tex]
Open bracket
[tex]\mathbf{y = -3x + 12 + 2}[/tex]
[tex]\mathbf{y = -3x + 14}[/tex]
Hence, the equation of the line is: [tex]\mathbf{y = -3x + 14}[/tex]
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If a car with an average speed of 50 miles per hour travels for 30 minutes, how far will it have gone?
Which graph represents the system of inequalities?
y+32x>−3
y−5≤−6x
Rewrite the systems of inequalities in slope-intercept form, and then graph the lines using the respective inequalities. The shaded area that overlaps will represent the solution to these systems of inequalities.
Explanation:In order to determine a graph that represents the system of inequalities, y+32x > -3 and y-5 ≤ -6x, you will need to write the systems of inequalities in mathematical terms, known as slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Firstly, let's rewrite the first inequality as y > -32x - 3. This inequality suggests that y is greater than -32x - 3, therefore the area above the line will be shaded.
Next, the second inequality is rewritten as y ≤ 6x + 5. This suggests y is less than or equal to 6x + 5, thus the area below the line will be shaded.
Remember, when creating the graph, a solid line should be used for ≤ symbol and a dashed line for the > symbol. The overlapping region of the two inequalities on the graph is the solution to the system of inequalities.
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what is the volume of a cube with 1/2 inch sides
Answer:
the answer is 1/8
Step-by-step explanation:
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation. What is the scale factor of the dilation?
Answer: Its option C. (4)
Step-by-step explanation: You're welcome you dirty cheaters.
Icket sales tickets for a high school play are $3.00 each for students and $4.00 each for all others. find the total money collected from ticket sales if 315 student tickets are sold out of a total of 518 tickets
315 x 3 = 945
518 - 315 = 203
203 x 4 = 812
945 + 812 =1757
So the answer is $1,757 total
The total money collected from ticket sales for the high school play, with 315 student tickets sold at $3.00 each and 203 other tickets sold at $4.00 each, is $1,757.00.
To find the total money collected from ticket sales, we need to calculate the revenue from both student tickets and tickets sold to others. We know that 315 student tickets were sold at a price of $3.00 each, and the remaining tickets sold to others were at a price of $4.00 each. Since a total of 518 tickets were sold, the tickets sold to others amount to 518 - 315 = 203 tickets.
Revenue from student tickets = 315 tickets imes $3.00 per ticket = $945.00
Revenue from other tickets = 203 tickets imes $4.00 per ticket = $812.00
Total revenue from ticket sales = Revenue from student tickets + Revenue from other tickets = $945.00 + $812.00 = $1,757.00
Therefore, the total money collected from ticket sales is $1,757.00.
Two consecutive even integers have a sum of 42 . find the integers.
If two consecutive even integers have a sum of 42. The integers are 20 and 22.
What is an integer?it is defined as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc.
It is given that, two consecutive even integers have a sum of 42.
The difference between two even numbers is 2.
Suppose two consecutive even integers are x , (x+2)
x + (x+2) = 42
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
2x +2 = 42
2x =42-2
2x = 40
x = 20
The two consecutive even integers are,
x =20
x+2 = 20 +2 =22
Thus, if two consecutive even integers have a sum of 42. The integers are 20 and 22.
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Randy and Susie Moser are newlyweds. Randy drives their car to his job, twenty-seven miles away from home, each day. If Randy and Susie are both twenty, what premiums would they pay for bodily injury and property damage insurance in the amount of 50/100/10?
The weight of 10 identical samples of a substance is 0.1 pound, what is the weight of 100 samples
If the cost of a pound of nails increased from $2.29 to $2.48. what is the percent of the increase to the whole number percent?
The answer is provided in the image attached.
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A group of n students is assigned seats for each of two classes in the same classroom. how many ways can these seats be assigned if no student is assigned the same seat for both classes?
The number of ways the seats can be assigned is equal to n factorial (n!).
Explanation:The number of ways the seats can be assigned is given by the permutation formula. Since there are n students and 2 classes, each student can be assigned a seat in the first class in n ways. After that, there are (n-1) seats left and (n-1) students remaining to be assigned seats in the second class. Therefore, the total number of ways to assign seats is n * (n-1) * (n-2) * ... * 1, which is equal to n factorial (n!).
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how do you solve 5x^2+30x=10
Jeremy ate p pieces of pizza. Brandon ate 5 less pieces than Jeremy. Write an expression to represent the total amount of pizza eaten by both boys.
What is the equation of a line perpendicular to the line y=(4/9)x-2 that passes through the point (4,3)?
a. y= -(4/9)x-2
b. y= (9/4)x+6
c. y= -(9/4)x+12
d. y= -(9/4)x-12
(pls explain solution!!)
To find the equation of a line perpendicular to y=(4/9)x-2 that passes through the point (4,3), we need to determine the slope of the original line and then find the negative reciprocal of that slope. The equation of the perpendicular line is y = -(9/4)x + 12.
To find the equation of a line perpendicular to y=(4/9)x-2 that passes through the point (4,3), we need to determine the slope of the original line and then find the negative reciprocal of that slope. The original line has a slope of 4/9, so the perpendicular line will have a slope of -9/4. Using the point-slope form of a line, we can plug in the slope and the given point to find the equation of the perpendicular line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Plugging in the values, we get:
y - 3 = -(9/4)(x - 4)
Simplifying the equation, we get:
y = -(9/4)x + 12
Therefore, the equation of the line perpendicular to y=(4/9)x-2 that passes through the point (4,3) is y = -(9/4)x + 12.
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The equation below represents the fact that your driving rate (the distance divided by the time in hours) must be less than or equal to 65 mph by law. if you drive for 2.5 hours, what is the maximum distance you can drive and still be within the law
Mariana averaged 7474 on her first three history exams. the first score was 7777. the second score was 77 less than the third score. what did she score on the second and third exams
Write a reciprocal function with asymptotes x=4 and y=-9.
Final answer:
To write a reciprocal function with asymptotes x=4 and y=-9, the function is f(x) = -9/(x-4).
Explanation:
To write a reciprocal function with asymptotes x=4 and y=-9, we need to find the equations of the vertical and horizontal asymptotes.
For the vertical asymptote, the equation is x=4. This means that the function approaches infinity as x approaches 4 from the left or right.
For the horizontal asymptote, the equation is y=-9. This means that the function approaches -9 as x approaches infinity or negative infinity.
Therefore, the reciprocal function with these asymptotes is:
f(x) = -9/(x-4)
Final answer:
To create a reciprocal function with asymptotes x=4 and y=-9, the function can be expressed as y = 1/(x-4) - 9. This form ensures a vertical asymptote at x=4 and a horizontal asymptote at y=-9.
Explanation:
To write a reciprocal function with asymptotes x=4 and y=-9, you need to include factors that will create these asymptotes in the function's equation. A reciprocal function generally has the form y = a/(x-h) + k, where (h, k) represents the horizontal and vertical shifts to create the asymptotes x=h and y=k. In this case, we have:
y = 1/(x-4) - 9
This function has a vertical asymptote at x=4 because as x approaches 4, the denominator approaches 0 causing the function to approach infinity. The horizontal asymptote at y=-9 occurs because as x goes to infinity, the value of 1/(x-4) approaches 0, and the entire function approaches -9.
Which is larger 1 meter or 105 centimeters?
What is the cosine of angle a?
a. 8/17
b. 15/8
c. 15/17
d. 8/15
Consider the following conditional statement. If a + 1 = b, then b > a. A. Create a pair of values for a and b in which the numerical relationship shown in the given conditional statement is true. In your final answer, include the values of the variables and proof of truth. B. Is it possible to create a pair of values for a and b in which the numerical relationship shown in the given conditional statement is false? Use complete sentences to explain your answer.
In mathematics, creating values for a and b satisfying a given conditional statement involves fulfilling the logical relationships between the variables. It is impossible to violate the logical connection established by the initial condition of the statement.
A: Let's choose a=2 and b=3. If a+1=b, then 2+1=3, which is true. So, a=2 and b=3 satisfy the given conditional statement.
B: It is not possible to create a pair of values for a and b where the numerical relationship shown in the given conditional statement is false. This is because the statement is a logical consequence of the initial condition a+1=b.