The height of a ball in feet is modeled by
[tex]y = - 16x {}^{2} + 72x[/tex]
where X is the time in seconds after the ball is hit. How long is the ball in the air?
(May I also get steps on how to solve these kind of questions please?)
![The Height Of A Ball In Feet Is Modeled By [tex]y = - 16x {}^{2} + 72x[/tex]where X Is The Time In Seconds](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/jHxKQlEFKTSPA7f9Yp7VoDIdibmO5jfz.jpeg)
Answers
The value of time of the ball in the air is,
⇒ 4.5 seconds
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The height of a ball in feet is modeled by the equation,
y = - 16x² + 72x
where, x is the time in seconds after the ball is hit.
Hence, For time of the ball in the air, we can plug y = 0 in above equation.
y = - 16x² + 72x
0 = - 16x² + 72x
Solve for x;
- 16x² + 72x = 0
- 4x (4x - 18) = 0
This gives,
4x = 18
x = 18/4
x = 4.5 seconds
Thus, The value of time of the ball in the air is,
⇒ 4.5 seconds
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Related Questions
Which system of equation can represent the equation?
Answers
The logarithmic property of base change given that
logx (b) = logc (b) / logc (x)
Therefore, the same property applies to this problem and the correct expression for this question is:
y1 = log (x + 3) / log 4
y2 = log (2 + x) / log2
What best describes the expression y over 3?
A. 3 more than some number
B. Some number times 3
C. Some number divided by 3
D. 3 less than some number
Answers
A represents addition, y + 3
B represents multiplication, y * 3
D represents subtraction, y - 3
The median and interquartile range of a set of data is shown. Write a set of data consisting of seven values for the pair of measures.
Median: 5 Interquartile Range: 5
Answers
If the IQR is 5, we then know that the difference between y and r is 5.
Let's find the 1st and 3rd quartiles. Focusing on the 1st 3 numbers, we see that the 1st quadrant is y; focusing on the last 3 numbers, we see that the 3rd quadrant is r. The IQR is r-y = 5. Just supposing that y were 4, r would be 9:
x 4 y 5 q 9 s
We could arbitrarily let x = 3, y = 4, q = 5 and s = 9: 3 4 4 5 5 9 9.
We must check this!
What is the median? Since there are 7 numbers here, we take the middle number (5) as the median. This agrees with the problem statement.
Next, we find Q1 and Q3. Q1 is the number between 3 and the 2nd 4, and is 4. Q3 is 4+5, or 9, because the IQR is 5. This agrees with the problem statement.
A student attempted to generate an equivalent expression using the distributive property, as shown below:
6(m + 3) = 6m + 3
What was the mistake made?
A. 6 was not multiplied by m
B. Incorrect sign was used for the first term
C. Incorrect sign was used for the second term
D. 6 was not multiplied by 3
Answers
Look at them one at a time
Choice A
The result of multiplying 6 and m together (which is what you are supposed to do is 6m). This step is correct.
Choice B
There are no minus signs anywhere, either outside or inside the brackets, B is incorrect. Minus signs cannot be manufactured out of thin air. You need a reason.
Choice C
Same as B.
D is the correct answer. Both sides of a plus or minus sign have to be multiplied by what is outside the brackets. The plus sign cannot be destroyed unless you started out with something like
6 ( 4m + 3m) which = 24m + 18m = 42m But you could have combined like terms in the beginning.
6 * 7m = 42m
.
which is a ABBC pattern?
Answers
Answer:
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Step-by-step explanation:
Need Help ASAP..GIVING 15 POINTS TO WHO ANSWERS.IF YOU COPY AND NOT ANSWER YOU WILL GET REPORTED
The original price for a clothes washer and dryer is $999. Which coupon is a better deal? A) SAVE 20% ON ANY WASHER/DRYER COMBO B) SAVE $200 ON ANY WASHER/DRYER COMBO C) SAVE $75 PLUS 5% OFF ON ANY WASHER/DRYER COMBO D) SAVE $50 PLUS 20% OFF ON ANY WASHER/DRYER COMBO
Answers
A small Learning Center holds 24 less students than the larger Learning Center. Together the learning centers hold seventy-two students. How many students does each Learning Center hold?
Answers
L=Large
72=(L-24)+s
48=L+s
By this point, the “-24” no longer affects the equation. L=s for the purpose of division.
48/2
24=s
Now we know s=24.
The “-24” is now important in finding the value of L. We find the inverse of “-24”, +24.
s+24=48
s= 24 students
L= 48 students
The larger Learning Center can hold 48 students and the smaller Learning Center can hold 24 students.
Explanation:The key to solving this problem is to first express it as two linear equations. Let's denote the number of students the small Learning Center holds as S and the number of students the larger Learning Center holds as L.
The problem provides us with two facts:
The small Learning Center holds 24 less students than the larger one, we can express this as: S = L - 24.Together, both Learning Centers hold seventy-two students, so we can express this as: S + L = 72.Now, we can solve these two equations simultaneously.
Substitute S from the first equation into the second: (L - 24) + L = 72, simplify to: 2L = 96
Thus, L = 48. This means the larger Learning Center can hold 48 students. Substitute L=48 into our first equation to find S: S = 48 - 24 = 24. So, the small Learning Center can hold 24 students.
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A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the boat in still water, if it covers 70 km with the current in 3.5 hours?
(its not 20 i tried)
Answers
r + c = speed with current
r - c = speed against current
3.5(r + c) = 70
r + c = 20
c = 20 - r
4(r + c) = distance from pier to pier
5(r - c) = distance from pier to pier
4(r + c) = 5(r - c)
4(r + 20 - r) = 5(r - 20 + r)
80 = 10r - 100
180 = 10r
18 = r
The speed in still water is 18 km/hour
find the value of this expression if x= -6 and y=1. xy^2/-7
Answers
Hope it's right
x=-6
y=1
xy^2/-7
substitute the values;
-6*1/-7 = 6/7 = 0.857
Which of the following is a statistical question?
A.
How much money is in Althea's pocket?
B.
How tall is the tallest building in the United States?
C.
What is the temperature in the refrigerator?
D.
What were the grades on the history final exam?
Answers
which expression is equivalent 121x^2-64y^2 ?
Answers
What is the size of the angle in the shaded triangle marked by the arrow
Answers
find the missing dimension. use the scale factor 5:8
Answers
5 : 8
1.5 : x
[tex]5x = 12 \\ x = 2.4[/tex]
Answer : Actual length = 2.4m
Question 15
5 : 8
x : 20
[tex]8x = 100 \\ x = 12.5[/tex]
Answer : Actual length = 12.5m
Hope this helps. - M
The diameter of a circular placemat is 15 inches. Devon wants to sew a border of lace around the placemat. If the lace he wants is sold by the foot, how many feet of lace will he need to purchase?
Answers
Answer: 47 feet
Determine which function has the greatest rate of change over the interval [0, 2].
Answers
Rate of change of [tex]a[/tex]:
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of [tex]a[/tex]:
[tex]m= \frac{y_{2}-y_{1}}{x_2-x_1} [/tex]
[tex]m= \frac{4-1}{2-0} [/tex]
[tex]m= \frac{3}{2} [/tex]
[tex]m=1.5[/tex]
The average rate of change of the function [tex]a[/tex] over the interval [0,2] is 1.5
Rate of change of [tex]b[/tex]:
Here the end points are (0,0) and (2,2)
[tex]m= \frac{2-0}{2-0}[/tex]
[tex]m= \frac{2}{2} [/tex]
[tex]m=1[/tex]
The average rate of change of the function [tex]b[/tex] over the interval [0,2] is 1
Rate of change of [tex]c[/tex]:
Here the end points are (0,-1) and (2,0)
[tex]m= \frac{0-(-1)}{2-0}[/tex]
[tex]m= \frac{1}{2} [/tex]
[tex]m=0.5[/tex]
The average rate of change of the function [tex]c[/tex] over the interval [0,2] is 0.5
Rate of change of [tex]d[/tex]:
Here the end points are (0,0.5) and (2,2.5)
[tex]m= \frac{2.5-0.5}{2-0} [/tex]
[tex]m= \frac{2}{2} [/tex]
[tex]m=1[/tex]
The average rate of change of the function [tex]d[/tex] over the interval [0,2] is 1
We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.
Answer:
what the other guy said
Step-by-step explanation:
What conclusions can you make about numbers in scientific notation with negative exponents?
Answers
0.16+0.45 eaqkesbnnn
Answers
If you were supposed to add 0.16 and 0.45, the correct answer would be 0.61.
Short answer: 0.61 || 61/100
Why?
When you're adding two decimals, as long as it doesn't have a whole number, you can just add down like so.
1
0.16
+ 0.45
_______
0.61
In fraction form, it is 61/100, because we have the decimal number, and put it to how long it is. (hundred[th])
Hope this helped you! ♥
Mrs. Sloan is purchasing 3.4 pounds of trail mix that costs $4.25 per pound. How much change will Mrs. Sloan receive if she gives the cashier $20.00.
a. $14.45 b. $5.55 c. $12.55 d. $7.45
Answers
multiply number of pounds purchased by price per pound
= 3.4 pounds * $4.25 per pound
= $14.45 total cost
STEP 2:
subtract total cost of purchase (step 1) from amount she gave cashier ($20.00)
= $20.00 - $14.45
= $5.55 amount received back from cashier
ANSWER: (B) $5.55 received back
Hope this helps! :)
what Is 12 divided by 1/3
Answers
When you divide something by a fraction, it’s easier to think of multiplying its opposite, or reciprocal.
THIS IS SUPER EASY I NEED HELP
Answers
[tex]2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]
Answer: [tex]\left(\dfrac{1}{2}\right)^5=\dfrac{1}{32}[/tex]
(1/2) x (1/2) x (1/2) x (1/2) x (1/2)
The answer is .03125 or 1/32
triangle ABC is similar to Triangle d e f if the perimeter of a triangle ABC is 24 in what is the perimeter of triangle d e f a b c has one length of 9 inches and d e f has one length of 6 in
Answers
24/1.5 = 16
triangle DEF has a primeter of 16 inches
triangle ABC is similar to Triangle XYZ.
AB=9.7, BC=9.6, AC=15.1
YZ=118.8, Find XZ
triangle ABC is similar to Triangle XYZ.
AB=9.7, BC=9.6, AC=15.1
YZ=118.8, Find XZ
Answers
Since the triangles are similar, the ratio of their angles is the same. This means the ratio of BC to YZ will be the same as the ratio of AC to XZ; using this to set up a proportion,
9.6/118.8 = 15.1/x
Cross multiply:
9.6*x = 118.8(15.1)
9.6x = 1793.88
Divide both sides by 9.6:
9.6x/9.6 = 1793.88/9.6
x = 186.8625
Two numbers multiply to be -15 and adds to be 2 what are the numbers?
Answers
[tex]x + y = 2 \\ x \times y = - 15[/tex]
[tex]x + y = 2 \\ x = 2 - y[/tex]
Substitute that into
[tex](2 - y) \times y = - 15 \\ 2y - {y}^{2} = - 15 \\ {y}^{2} - 2y - 15 = 0 \\ (y - 5)(y + 3) = 0 \\ y = 5[/tex]
Substitute that into
[tex]x = 2 - 5 \\ x = - 3[/tex]
Answer : The two numbers are 5 and - 3.
Hope this helps. - M
Plzz help me
Match the system of the equation to the number of solutions.
y = 5
2x - 2/3y = 10
1. No solutions
2. One solution
3. Infinite solutions
Answers
They have different slopes and therefore must have one solution.
a window cleaner charges a call out fee of £3 plus 25p per square metre of glass cleaned. a front window in a butcher's shop measures 3.5 m by 6 m. how much does it cost to get 2 of these windows cleaned?
Answers
Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer: Sample Adventure Beach Cruise Ski A 73 4 18 3 B 71 6 22 1 Which of the following inferences can be made based on the data?
Most members prefer a beach vacation.
Most members prefer a cruise vacation.
More members prefer a cruise vacation and a ski vacation than a beach vacation.
More members prefer a beach vacation and a cruise vacation than an adventure vacation.
Answers
There are a total of 18+3+22+1=44 people that prefer a cruise or ski vacation, while 4+6=10 people that prefer a beach vacation.
Answer:
More members prefer a cruise vacation and a ski vacation than a beach vacation.
Step-by-step explanation:
Of the 3,558 people impaired drivers killed in 2009 (not counting the drivers themselves) death were preventable
Answers
Final answer:
The preventable nature of deaths caused by impaired driving, emphasizing the impact of alcohol and other risky behaviors on driving safety.
Explanation:
Each day in the United States, over 8 people are killed and 1,161 injured in crashes reported to involve a distracted driver, highlighting a significant public health concern. There is a noted problem with young drivers getting into serious automobile accidents, contributing to many preventable deaths.
It has been estimated that 35 percent of all U.S. early deaths in 2000 could have been avoided by changing just three behaviors, with alcohol being a significant contributing factor to risky behavior on the roads.
In 2014, alcohol-impaired driving fatalities accounted for 9,967 deaths, which is 31% of overall driving fatalities, underscoring the critical need for improved driving safety measures and individual behavior changes to reduce these numbers.
the number of people who attended the spring festival is 799 more than 8 thousands. how many people attended the festival?
Answers
In this question, we are given the information about total number of people but in word equation.
We are given that, 799 more from 8 thousand attend the festival.
When we are given more, we add the number to the number from which it is more.
Here, we will add 799 to 8,000 in order to calculate total number of people who attended the festival
Thus, total number of people who attended the festival = 8,000 people + 799 people = 8,799 people.
PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!!!
Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following data table.
Weight of elk antler pairs at Mount St Helens NVM:
{34, 34, 30, 30, 30, 28, 28, 26}
Weight of elk antler pairs at Rocky Mountain NP:
{40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the mean and MAD for each area of collection.
(c) Calculate the means-to-MAD ratio for the two areas of collection.
(d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain
Answers
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= {4, 4, 0, 0, 0, 2, 2, 4}
RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= {4, 2, 0, 0, 0, 0, 2, 4}
Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
A) The two line plots are attached.
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= {4, 4, 0, 0, 0, 2, 2, 4}
RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= {4, 2, 0, 0, 0, 0, 2, 4}
Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
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what number must you add to complete the square? x2-20x=17
A. 100
B. -10
C.-100
D. 10
Answers
Answer:
The number is 100
A is correct
Step-by-step explanation:
Given: [tex]x^2-20x=17[/tex]
We need to make completing square at left side.
Rule: We add a number " take half of the coefficient of x and then square it"
Coefficient of x = 20
Half of 20 = 10
Square of 10 = 100
So, we will add 100 both sides make completing square.
Now we make completing square to add 100
[tex]x^2-20x=17[/tex]
Add 100 both sides
[tex]x^2-20x+100=17+100[/tex]
Now we will factor left side perfect square
[tex]a^2-2ab+b^2=(a-b)^2[/tex]
[tex](x-10)^2=117[/tex]
[tex](x-10)^2[/tex] is completing square or perfect square.
Hence, The number is 100