The question is incomplete. The full question is below.
The path of a particular punt follows the quadratic function
[tex]h(x)=\frac{-1}{8}(x-25)^{2}+50[/tex]
where h(x) is the height of the ball in yards and x corresponds to the horizontal distance in yards. Assume x=0 corresponds to midfield (the 50 yards line). For example, x=20 corresponds to the punter's own 30 yard line, whereas corresponds to the other team's 30 yard line.
a. Find the maximum height the ball achieves.
b. Find the horizontal distance the ball covers. Assume the height is zero when the ball is kicked and when the ball is caught.
Answer: a. Maximum height = 50
b. Horizontal distance = 40
Step-by-step explanation: A quadratic function has its maximum or minimum point on its vertex.
When the function is negative, function has a maximum point.
The quadratic function h(x) is written in vertex form, meaning the coordinate of vertex is explicit in the function.
General vertex form: [tex]f(x)=A(x-h)^{2}+k[/tex]
A is vertical scaling parameter
(h,k) are the coordinates of vertex
So, the quadratic function for the height for the ball:
[tex]h(x)=\frac{-1}{8}(x-25)^{2}+50[/tex]
shows its vertex:
(h,k) = (25,50)
a. The maximum height the ball achieves the maximum value corresponds to the y-axis, which means, maximum height is 50 yards.
b. Horizontal distance is when h(x)=0, so:
[tex]\frac{-1}{8}(x-25)^{2}+50=0[/tex]
[tex]\frac{-1}{8}(x-25)^{2}=-50[/tex]
[tex](x-25)^{2}=400[/tex]
[tex]x^{2}-50x+625=400[/tex]
[tex]x^{2}-50x+225=0[/tex]
Solving quadratic equation:
[tex]x_{1}=\frac{50+\sqrt{1600} }{2}[/tex] = 45
[tex]x_{2}=\frac{50-\sqrt{1600} }{2}[/tex] = 5
When ball is kicked, it is in position 5. When is caught, is position 45. So, distance the balls covers is 40 yards.
Hello Please Answer Quickly:
Answer:
17 1/30
Step-by-step explanation:
Answer:
The answer is 1/6.
53/6 is the largest and -26/3 is the smallest.
What is the equation of the line that is perpendicular to and has the same y-intercept as the given line
Answer:
y = 5x + 1
Step-by-step explanation:
Visually you can see the slope is -1/5, perpendicular just means opposite inverse so -1/5 becomes 5. Line crosses the y-intercept at point (0, 1).
y = mx + b
y = 5x + 1
Answer:
C.
Step-by-step explanation:
Just took the test
Estimate the total of 3,933+790+3,528+1,830 by adding the numbers and then rounding the result to the thousands place.
Answer:
The answer to your problem is 10000
Answer: 11,000
Step-by-step explanation:
Rounding to the nearest thousand first gives us,
4,000+1,000+4,000+2,000=11,000.
I need help with this :/
Answer:
Plz mark me brainliest!!!!
Step-by-step explanation:
0
90
180
270
380
how can I do this someone explain me
Answer: Converse: If the candy has 350 calories, the candy is chocolate, False. There is another 350 calorie candy.
Inverse: If the candy does not have 350 calories, the candy is not chocolate. True In this case, the evidence in the chart supports this. The inverse is not always true.
Contrapositive: If the candy does not have 350 calories, the candy is not chocolate. True The evidence in the chart supports this statement, and the Contrapositive is generally considered a logical equivalent of the original.
Step-by-step explanation:
You need to have a basic frame for converting the original statement to the other forms such as
Original: If P, then Q
Converse: If Q, then P Just reverse the parts
Inverse: If not P then not Q In the same order, make both negative, add "not"
Contrapositive: If not Q then not P Reverse the order of the original and make both negative.
Please help me on this question ASAP if you do ill give you brainliest!
Answer:
7. 2/3 8. 1 1/13 9. 1 3/5 10. 1 17/19 11. 1 16/19 12. 22.63 13. 4 20/39 14.2 16 /145 15. 1 25 /62
Step-by-step explanation:
The management of Hartman Rent-A-Car has allocated $2.52 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $18,000 each, intermediate-size cars cost $27,000 each, and full-size cars cost $36,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)
Answer:
The number of compact cars = x = 30 cars
The number of intermediate-sized car = y = 60 cars
The number of full-size cars purchased = z = 10 cars
Step-by-step explanation:
Let us denote:
the number of compact car = x
the number of intermediate-sized car = y
the number of full-size cars purchased = z
The total number of cars to be purchased is 100.
Hence:
x + y + z = 100...........Equation 1
If Hartman purchases twice as many compacts as intermediate-size cars
y = 2x
So: x + 2x + z = 100..........Equation 2
= 3x + z = 100
z = 100 - 3x
Compacts cost $18,000 each, Intermediate-size cars cost $27,000
Full-size cars cost $36,000 each.
Assume that the entire budget will be used.
Hence,
x × $18,000 + y × $27,000 + z × $36,000 = $2,520,000.
18000x + 27000y + 36,000z = $2,520,000.....Equation 4
Substitute 100 - 3x for z and y = 2x in Equation 4
18000x + 27000(2x) + 36,000(100 - 3x) = $2520000
18000x + 54000x + 3,600,000 -108000x = $2520000
72000x -108000x + 3,600,000 = $2,520,000
= $3,600,000 - $2,520,000 = 108000x - 72,000x
$1,080,000 = 36,000x
Divide both sides by $36,000
x = $1080000/36000
x = 30
From the above:
y = 2x
y = 2 × 30
= 60
z = 100 - 3x
= 100 - 3 × 30
= 100 - 90
= 10
Therefore,
The number of compact cars = x = 30 cars
The number of intermediate-sized car = y = 60 cars
The number of full-size cars purchased = z = 10 cars
4) 41 25h+6
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3210 12 3 4 5 6 7 8 9
Step-by-step explanation:
buena suerte con todo....
Seven friends bought pizza. Each friend pitched in the same amount. If the pizza came to a total of $14.49, how much did each friend pay?
Answer: 7p = $14.49
Step-by-step explanation: BRAINLIEST MEEE
Which scales are equivalent to 1 inch to 1 foot?
Select all that apply.
A. 1 to 12
B. 1/12 to 1
C. 100 to 0.12
D. 5 to 60
E. 36 to 3
F. 9 to 108
Answer:
A, B, D, F
Step-by-step explanation:
solve equation with variable on both sides
2(3r-4)=4r=3
Step-by-step explanation:
your problem can't have two equal however if you mean 2(3r-4)=4r + 3 its equal to 11/2. but if you mean 2(3r-4)=4r(3) its equal to -4/3
what is the answer? pls help
Answer:
for the line to have a constant slope, the difference of every y- ordinate with the last ordinate has to be equal
to check this, we will use the following formula
y4 - y3 = y2 - y1
if both the LHS and the RHS are equal, the slope is constant and is irregular otherwise
5 - 8 = 7 - 3
-3 = 4
LHS ≠ RHS
Since LHS is not equal to RHS, the slope is NOT constant and hence keeps increasing or decreasing irregularly
Therefore, option 4 (Not a line) is correct
Answer:
it is not a constant line
Step-by-step explanation:
each x value increases by 1, but the y values are all over the place and are in no order.
Janine opens a savings account with a deposit of $850. The account pays 1.75% interest,
compounded daily. What is the first day's interest? Round to the nearest cent.
Answer:?????
Step-by-step explanation:
At pizza express it takes 6 cups of cheese to make 15 pizzas. At perfect pizza it takes 4 cups of cheese to make 6 pizzas. If the number of pizzas,y,is proportional to the cups of cheese,x, which pizza place has a larger constant of proportionality?
Pizza Express has a larger constant of proportionality than Perfect Pizzas because 1.6 > 1.5
15/6 6/4
Simplify
5/3 > 3/2
PE: 5/3 or 1.6
PP: 3/2 or 1.5
I had this on my math test
The actual volumes of quart-size jars of Hellmann's mayonnaise are uniformly distributed from 31.58 to 32.51 fluid ounces. Find the standard deviation in volumes of quart-size Hellmann's mayonnaise jars (in fluid ounces). NOTE: There are 32 fluid ounces in a quart.
Answer:
0.27
Step-by-step explanation:
The standard deviation of a uniform distribution is:
σ² = (b − a)² / 12
σ² = (32.51 − 31.58)² / 12
σ² = 0.0721
σ = 0.268
Rounded to the hundredths place, the standard deviation is 0.27.
To solve this question, we use concepts of the uniform probability distribution.
Using this, we get that the standard deviation in volumes of quart-size Hellmann's mayonnaise jars is of 0.2685 fluid ounces.
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
The actual volumes of quart-size jars of Hellmann's mayonnaise are uniformly distributed from 31.58 to 32.51 fluid ounces.
This means that [tex]a = 31.58, b = 32.51[/tex]
Find the standard deviation in volumes of quart-size Hellmann's mayonnaise jars (in fluid ounces).
[tex]S = \sqrt{\frac{(32.51 - 31.58)^2}{12}} = 0.2685[/tex]
Thus, the standard deviation is of 0.2685 fluid ounces.
A similar example is given at https://brainly.com/question/15855314
What is the domain of this function?
Domain = inputs = x = { 1 , 2 , 3 }
Range = outputs = y = { 2 , -1 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Need Help please i will mark brainliest when it lets me
Answer:it’s the second one
Step-by-step explanation:
Answer:
the 2nd one
Step-by-step explanation:
I asked my brother and he said it was that one
I need your help! there’s a photo above ^^
Answer:
1. c 2. No, its not the original figure. Its 270 degree turn.
Step-by-step explanation:
Answer:
1.) C 2.) choice d flipped left to right.
Identify all the numbered angles that are congruent to the given angle.
Justify your answers.
Answer/Step-by-step explanation:
The reasons for the stated numbered angles that are congruent to the given angles are written in the parentheses as follows:
7. <7 ≅ 65° (alternate interior angles)
<4 ≅ 65° (corresponding angles)
<1 ≅ 65° (vertical angles)
8. <4 ≅ 51° (alternate interior angles)
<5 ≅ 51° (corresponding angles)
<7 ≅ 51° (vertical angles)
9. <1 ≅ 120° (corresponding angles)
<3 ≅ 120° (alternate angles)
Anyone have the guided notes answers from this point up to the unit test ? Geometry A
Answer:
vvhcfggfcc
Step-by-step explanation:
ccgvvhhh I don't I need more points buddy
What is the slope of the line that passes through points (-3,5) and (11,5)
Answer:
slope = -3/14
Step-by-step explanation:
y1 - y2 / x1 - x2
They gave you one value, two total coordinates
5-5 = 1
-3 - 11
-14
1/-14
y=1/-14 + b
11= 1/-14(-3) + b
11 = -3/14 + b
17 + 14
b = 15 3/14
Which expression represents the total volume of the two storage spaces
Answer:
S^3+12
Step-by-step explanation:
The big block shows three s then you have to simplify that with 12ft^3
The expression that represents the total volume of the two storage spaces is s³+ 12
What is the total volume?The total volume of the two storage spaces is the sum of the smaller storage space and the larger storage space.
Volume = width x height x length.
Volume of the larger storage space = s x s x s = s³
The total volume of the two storage spaces = s³+ 12
To learn more about the volume of a cuboid, please check: https://brainly.com/question/26406747
Determine the mode of the following data set:
21, 45, 44, 21, 40, 67, 93
Answer:
21 is the mode
Step-by-step explanation:
a mode is the number in a set that occurs the most and 21 is the number that appeared the most in this set
The record low temperature in Pittsburgh, PA is -22°F. The record high is 103°F. What is the difference in the record high and the record low temperatures?
Answer:
The difference in the record high and the record low temperatures is 125°F
Step-by-step explanation:
Given a quantity T that varies in time, say T1 and T2, being T1 the initial value and T2 the final value.
The change or difference between the final and the initial values is:
T=T2-T1
The record low temperature in Pittsburgh, PA is T1=-22°F while its record high is T2=103°F
The difference is:
T=103°F - (-22°F)
Note both negative signs multiply to produce a positive sign, and a sum instead of a subtraction:
T=103°F + 22°F = 125°F
The difference in the record high and the record low temperatures is 125°F
The statement "If a = 6, then 6 = a." illustrates which property?
Answer
Symmetric law
Step-by-step explanation:
This means that even if you swap the numbers the answer stays the same.
HOPE IT HELPED
HAVE A GOOD NIGHT/DAY
please help :D I understand them but I need someone to check them :)
what are the coordinates of (4,-3) after a translation 3 units right and 6 units up
Answer:
(7,3)
Step-by-step explanation:
How can you estimate the area of a irregular figure?
Answer: To find the area of irregular shapes, the first thing to do is to divide the irregular shape into regular shapes that you can recognize such as triangles, rectangles, circles, squares and so forth... Then, find the area of these individual shapes and add them up!
Answer:
and that how you estimate the area of an irregular figure
Can you help plz I need this
Answer:
110 square cm
Step-by-step explanation:
Answer:
i think it's c. 110 cm
Step-by-step explanation:
hope you pass your test ;)
You had planned to go out for pizza with your friends Saturday night. You’ve all gathered at your place but when you’re about to leave, it starts to snow heavily, so you decide to have a pizza party at your place. The pizza delivery guy shows up with your order much sooner than you expected. The bill is $133.32. How much would you tip him? Explain your reasons for deciding how much to tip.
Answer:
$20
Step-by-step explanation:
the delivery guy show up early and that guy deserve 20bucks
