Sports. The path of a particular punt follows the quadratic function where is the height of the ball in yards and corresponds to the horizontal distance in yards. Assume corresponds to midfield (the yard line). For example, corresponds to the punter's own yard line, whereas corresponds to the other team's 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.
Answers
The question is incomplete. The full question is below.
The path of a particular punt follows the quadratic function
\(h(x)=\frac{-1}{8}(x-25)^{2}+50\)
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: \(f(x)=A(x-h)^{2}+k\)
A is vertical scaling parameter
(h,k) are the coordinates of vertex
So, the quadratic function for the height for the ball:
\(h(x)=\frac{-1}{8}(x-25)^{2}+50\)
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:
\(\frac{-1}{8}(x-25)^{2}+50=0\)
\(\frac{-1}{8}(x-25)^{2}=-50\)
\((x-25)^{2}=400\)
\(x^{2}-50x+625=400\)
\(x^{2}-50x+225=0\)
Solving quadratic equation:
\(x_{1}=\frac{50+\sqrt{1600} }{2}\) = 45
\(x_{2}=\frac{50-\sqrt{1600} }{2}\) = 5
When ball is kicked, it is in position 5. When is caught, is position 45. So, distance the balls covers is 40 yards.
Related Questions
Maria bought apples(a) for $2.32 per pound and bananas(b) for $1.65. She spends $31.42. Write the equation for this situation.
Answers
Answer:
$31.42-(2.32+1.65)
Step-by-step explanation:
In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=". The word equation and its cognates in other languages may have subtly different meanings; for example, while in English, any equality is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Last season Emily soccer team how to win loss ratio of 9 to 12 and Grant soccer team how to win loss ratio of 10 to 15 who’s team has a higher ratio of wins to losses use complete sentences to explain your reasoning
Answers
The Emily soccer team has the higher ratio of wins to losses.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Ratio of win to loss of Emily soccer team = 9 : 12
Ratio of win to loss of Grant soccer team = 10 : 15
9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60
10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60
If 60 games are losses, then 45 games are wins for Emily soccer team.
If 60 games are losses, then 40 games are wins for Grant soccer team.
Higher ratio is for Emily soccer team.
Hence higher ratio of wins to losses is for Emily soccer team.
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A computer is regularly priced at a store for $400. Over a holiday
weekend, the store offers a 20% discount. How much money would you
save if you bought the computer over the weekend? Show all work or
explain how you got your answer. (2 points: 1 point for correct answer, 1
point for correct work or explanation). *
Answers
Answer:
$80
Step-by-step explanation:
400 times 20%= 80
400-80= 320
the cost of the computer on the weekend costed 320, so you save $80
Answer:
80$
Step-by-step explanation:
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answers
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
Please refer to the photo for the solution!
Elijah wants to purchase two shirts that are on the discount rack at his favorite clothing store. The original price of one shirt is $19.99, and the original price of the other shirt is $22.59.
If both shirts are marked 60% off the original price, how much will Elijah pay for the two shirts before taxes?
F $17.03 G $21.29 H $25.55 J $42.58
Answers
She will pay $25.54 for both shirts.
$19.99 times .60=$11.99
$22.59 times .60=$13.55
$11.99+$13.55=$25.54
I hope it helps if it does mark me as Brainliest pls thank you!
If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.What is the volume in cubic centimetres?
Answers
Answer:
4192.4 cm³
Step-by-step explanation:
x = length of one side
x² = area of one side
There are 5 sides because it's an open top.
5(x²) = 1300
x² = 1300/5 = 260
x = √260 = 16.12
Volume = x³ = 16.12³ = 4192.4 cm³
write y-5=(4/3)(x-6) into a point intercept form
Answers
The equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.
The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form of a line can be converted to the slope-intercept form of a line, y = mx + b, where b is the y-intercept.
The equation y - 5 = (4/3)(x - 6) can be rearranged into the point-slope form of a line by isolating the y-term and simplifying: y - 5 = (4/3)(x - 6)y - 5 = (4/3)x - 8y = (4/3)x - 3
Now, we have the point-slope form of the line with slope 4/3 and y-intercept -3.
To convert this to the slope-intercept form of a line, we simply rearrange the equation to solve for y:y = (4/3)x - 3 This is the slope-intercept form of the line, where the slope is 4/3 and the y-intercept is -3.
Thus, the equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.
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do the following: a) find the real and imaginary parts, and sketch each with a stem plot. b) find the magnitude and phase, and sketch each with a stem plot. g
Answers
a) To find the real and imaginary parts of a complex number, we can use the equation z = x + iy, where x is the real part and y is the imaginary part.
To sketch a stem plot, we need to plot the real part on the x-axis, and the imaginary part on the y-axis. For example, for the complex number z = 4 + 3i, the real part is x = 4 and the imaginary part is y = 3. Therefore, the stem plot would be (4, 3).
b) To find the magnitude and phase of a complex number, we can use the equation z = |z|e^(iθ), where |z| is the magnitude and θ is the phase. To sketch a stem plot, we need to plot the magnitude on the x-axis, and the phase on the y-axis. For example, for the complex number z = 4 + 3i, the magnitude is |z| = 5 and the phase is θ = arctan(3/4). Therefore, the stem plot would be (5, arctan(3/4)).
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Rewrite the expressions without the absolute value sign. |x+12| , if x>−11
Answers
Answer: The absolute value of a number is its distance from 0 on the number line. For any real number x, the absolute value of x is defined as:
|x| = x if x >= 0 |x| = -x if x < 0
In the given expression, |x+12|, we need to consider the condition that x > -11. If x > -11, then x+12 > 1. Since x+12 is positive, we can remove the absolute value sign and the expression becomes x+12.
So, the given expression |x+12| can be rewritten without the absolute value sign as x+12 when x > -11.
Hope this helps! <3
When conducting a two-sided test of significance, the value of the parameter under the null hypothesis is not plausible and will not be contained in a 95% confidence interval when: A. The p-value is less than or equal to 0.05 B. The p-value is greater than 0.05. C. There is no relationship between the p-value and the con fidence interval.
Answers
The value of parameter under null hypothesis which is not plausible , will not be contained in a 95% confidence interval when (a) p value is less than or equal to 0.05 .
The "P Value" is the probability of observing a test statistic as extreme or more extreme than the one computed from the sample data, assuming the null hypothesis is true.
When the p value is less than equal to 0.05 , it indicates that the observed test statistic is statistically significant at the 5% level of significance, means that the null hypothesis will be rejected.
Therefore , the parameter value that is assumed under the null hypothesis is not plausible and is not likely to be in a 95% confidence interval.
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The given question is incomplete , the complete question is
When conducting a two-sided test of significance, the value of the parameter under the null hypothesis is not plausible and will not be contained in a 95% confidence interval when
(a) The p-value is less than or equal to 0.05
(b) The p-value is greater than 0.05.
(c) There is no relationship between the p-value and the confidence interval.
Hello everyone-SOLVING nonlinear system of equations- ALGEBRA 1
Answers
The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.
To solve the nonlinear system of equations:
Equation 1: \(y = -x^2 + 7\)
Equation 2: y = 2x + 4
We can equate the right sides of both equations since they both represent y.
\(-x^2 + 7 = 2x + 4\)
To simplify the equation, we can rearrange it to be in the standard quadratic form:
\(x^2 + 2x - 3 = 0\)
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
(x + 3)(x - 1) = 0
From this equation, we get two possible solutions:
x + 3 = 0 => x = -3
x - 1 = 0 => x = 1
Now, we substitute these x-values back into either equation to find the corresponding y-values.
For x = -3:
y = 2(-3) + 4
y = -6 + 4
y = -2
For x = 1:
y = 2(1) + 4
y = 2 + 4
y = 6
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A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is A 100 + 1.96 0.5(0.5) 432 100 + 1.645 0.5(0.5) 432 100 + 1.96 0.231(0.769) 432 0.231 +1.96 0.231(0.769) 432 0.231(0.709) 0.231 +1.6451 432
Answers
Answer:
The 95% confidence interval is \(0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}\)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
A random sample of 432 voters revealed that 100 are in favor of a certain bond issue.
This means that \(n = 432, \pi = \frac{100}{432} = 0.231\)
95% confidence level
So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).
Confidence interval:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}\)
The 95% confidence interval is \(0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}\)
What is the area of a square with h=3in l=5in w=6in
Answers
Answer:
30in
Step-by-step explanation:
Length x Width = Area
Solve the inequality and enter your solution as an inequality in the box below,
using "<=" for sor">=" for 2 if necessary.
-2(5x + 1) > 48
Answer here
Answers
Answer:
x < -5
Step-by-step explanation:
-2(5x + 1) > 48
Divide by -2, remembering to flip the inequality
-2/ -2(5x + 1) < 48/-2
5x +1 < -24
Subtract 1 from each side
5x+1-1 < -24-1
5x < -25
Divide by 5
5x/5 < -25/5
x < -5
A test of significance uses evidence provided by sample data to assess whether a claim about a ___________ is supported or refuted.
Answers
Answer:
parameter
Step-by-step explanation:
Given: Line segment AC and line segment BD intersect at O.
Prove: ZAOB ZCOD
Since line segment AC and line segment BD intersect at O, ZAOB is supplementary to ZBOC and ZBOC is supplementary to
ZCOD by the linear pair theorem.
Which statement and reason best completes the proof?
ZCOD.
ZCOD.
By the congruent supplements theorem, ZAOB
By the substitution property of equality, ZAOB
By the congruent complements theorem, ZAOBZCOD.
By the subtraction property of equality, ZAOB ZCOD.
Answers
By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Given: Line segment AC and line segment BD intersect at O.
Prove: ∠AOB ≅ ∠COD
By the supplementary angles property, the equations are given as,
∠AOB + ∠BOC = 180° .....1
∠BOC + ∠COD = 180° ....2
By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.
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Answer: By the congruent complements theorem
Step-by-step explanation: I took the test
Solve this equation: -72 + 12 - 2.x = 23 + 13.2
Answers
Answer:
x =-48.1
Step-by-step explanation:
-72 + 12 - 2.x = 23 + 13.2
Combine like terms
-60 -2x = 36.2
Add 60 to each side
-2x -60+60 = 36.2+60
-2x = 96.2
divide by -2
-2x/-2 = 96.2/-2
x =-48.1
Answer:
\( = - 48.1\)
Step-by-step explanation:
\( - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1\)
hope this helps
brainliest appreciated
good luck! have a nice day!
Pamela is 5 years younger than Jiri. The sum of their ages is 81. What is Jiri's age?
Answers
Pamela is 5 years younger mean
Mean Jiri is old 5 years, take number of Jiri age minus Pamela age.
-> J-5=P
The sum mean plus
P+J=81
Use substitution for the equation 1 to find the answer.
(J-5) +J=81
2J-5=81
2J=86
J=43
Answer: Jiri is 43 years old
Step-by-step explanation:
Let x be the age of Pamela, and (x+5) be the age of Jri
Expression
x+(x+5)=81
Expand paranthesis
x+x+5=81
Combine like terms
2x+5=81
Subtract 5 on both sides
2x+5-5=81-5
2x=76
Divide 2 on both sides
2x/2=76/2
x=38
Since we've set Jiri's age as (x+5), we need to substitute the value of x
x+5=38+5=43
Hope this helps!! :)
Please let me know if you have any questions
What are three non-collinear points, so I can write them down for my daughter for her study guide
Answers
Answer:
point A, point D and point E are Non-colinear points
\(A,D\text{ and E }\rightarrow Non-\text{ collinear points}\)Explanation:
Collinear points are points that lie on the same line. Any two or more points that lie on the same straight line are collinear point.
Non-collinear points are the opposite of collinear points, they are points that do not lie on the same line.
From the diagram attached to the question;
point D and point A does not lie on the same line, so they are Non-collinear points.
point E also does not lie on the same line as either point D or point A.
So;
point A, point D and point E are Non-colinear points
\(A,D\text{ and E }\rightarrow Non-\text{ collinear points}\)The ratio of the sides of two cylinders is 4:7. What is the ratio of their surface areas?
Answers
Answer:
Step-by-step explanation:
idont understand
Determine the shaded area
Answers
The shaded area is 40 square centimeters.
What is the triangle?
A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is οne οf the basic shapes in geοmetry and is used in many fields οf mathematics and science. The three sides οf a triangle may have different lengths, and the three angles may alsο have different measures.
Tο determine the shaded area, we need tο find the area οf the trapezοid and the area οf the triangle and then subtract the area οf the triangle frοm the area οf the trapezοid.
First, let's find the area οf the trapezοid:
The height οf the trapezοid is 10 cm (the distance between the twο parallel bases), and the length οf the twο parallel bases are 8 cm and 16 cm. Therefοre, the area οf the trapezοid is:
A = (b1 + b2)h / 2
A = (8 cm + 16 cm) x 10 cm / 2
A = 120 cm²
Next, let's find the area of the triangle:
The base of the triangle is 16 cm, and the height is 10 cm. Therefore, the area of the triangle is:
A = bh / 2
A = 16 cm x 10 cm / 2
A = 80 cm²
Finally, we can determine the shaded area by subtracting the area of the triangle from the area of the trapezoid:
Shaded area = 120 cm² - 80 cm²
Shaded area = 40 cm²
Therefore, the shaded area is 40 square centimeters.
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please answer it i have 10 min
Answers
a) The inequality that models this situation is given as follows: 90 + 4p + 45 ≥ 625.
b) The minimum number of pages that she must read in each of these four weeks is given as follows: 123 pages.
How to define the inequality?Menal has to read the 625 pages of the book in six weeks, with the divisions given as follows:
First week: 90 pages.Remaining four weeks: p pages each week, for a total of 4p.Fifth week: 45 pages.Then the inequality is defined as follows:
90 + 4p + 45 ≥ 625.
(as if she desires, she can read more than 625 pages).
Then the inequality is solved similarly to an equality, isolating the variable p to obtain a range of values, as follows:
135 + 4p ≥ 625
4p ≥ 490
p ≥ 490/4
p ≥ 122.5.
Rounding up, the minimum number of pages that she must read per week is of 123 pages.
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Work out the length of x. Give your answer rounded to 3 significant figures. 13.3 mm 5.5 mm The diagram is not drawn accurately. X = 0 mm x
Answers
Step-by-step explanation:
Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.
To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.
Perimeter = 13.3 mm + 5.5 mm + X mm
The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.
To find X, we can subtract the sum of the known sides from the perimeter:
X mm = Perimeter - (13.3 mm + 5.5 mm)
Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.
What is the length of the indicated side of the triangle?
Answers
9514 1404 393
Answer:
15 m
Step-by-step explanation:
The area of the square attached to the third side is the sum of the areas of the other squares:
81 m² +144 m² = 225 m²
The side length is the square root of this:
? m = √(225 m²) = 15 m
The length of the indicated side is 15 m.
4^-5 as a fraction? Imma lil stuck on this, can you help asap
Answers
Answer:
1/1024
Step-by-step explanation:
4 to the power of -5 is 0.0009765625, which in fraction form is 9765625/10000000000. Simplifying that turns it into 1/1024
1/1024
Explanation:
This is one of the laws of exponents:
a^-n = 1/a^n
Any number with a negative exponent is equal to the fraction of 1 over the number to the exponent but positive. Therefore:
4^-5=1/4^5
4^-5=1/1024
I hope this helps!
Find the final value if £3500 is invested for 6 years at 6.9% p.a.
Final value = £
Answers
= Answer:
Step-by-step explanation:
interest= 3500 * 6 * 6.9* 1/100
= 4949
Final value = £ 3500 + 1449
= 4949
Principal=P=3500
Time=T=6years
Rate of interest =R=6.9
Interest be I
\(\\ \sf\longmapsto I=\dfrac{PRT}{100}\)
\(\\ \sf\longmapsto I=\dfrac{3500(6)(6.9)}{100}\)
\(\\ \sf\longmapsto I=\dfrac{144900}{100}\)
\(\\ \sf\longmapsto I=1449\)
Now
Final value=3500+1449=4949
Tessellations
Determine whether the given figure tessellates the plane.
a. yes
b. no
Please select the best answer from the choices provided
Answers
Answer:
B. No
Step-by-step explanation:
I calculated it logically
PLEASE HELP WITH MARK BRAINLIEST
What is the value of w?
Answers
Answer:
26
Step-by-step explanation :
73 - 47 = 26 brainliest?
find the area of a rectangle with a length of 10 inches and a width of 4 inches
Answers
Answer:
40 in²---------------------
Formula for area of a rectangle with dimensions l and w is:
A = lwSubstitute 10 for l and 4 for w:
A = 10*4A = 40 in²how many 5 letter code words can be formed from the letters of the word MATRICES
Answers
113
Hope this helped you- have a good day bro cya)