URGENT! TIMED QUESTION, WILL GIVE BRAINLIEST!
The height of a punted football is modeled by the following quadratic function:
h(t) - -5t2 . 40
where the height is measured in meters after t seconds.
+
a. How many seconds will it take the ball to hit the ground?
c. What is the maximum height of the ball?
Answers
Answer:
Step-by-step explanation:
Part a
When the ball hits the ground it has covered the height of zero meters so we replace h(t) with zero
[tex]h(t)=-5t^2+40t\\0=-5t^2+40t\\40t-5t^2=0\\5t(8-t)=0\\5t=0 \ \ \ , \ \ \ 8-t=0\\t=0 \ \ \ , \ \ \ t=8\\[/tex]
So it will take 8 seconds for the ball to hit the ground we another value
t = 0 seconds is when the ball was thrown and after 8 seconds the balls hits the ground
Part c
The ball reaches its maximum height when the velocity is zero.
So as this functions represents the displacement of the ball h(t) we differentiate it to get the velocity equation, so we differentiate h(t) with respect to t.
[tex]v=-10t+40[/tex]
so now we replace the velocity which is v with a zero because the ball reaches its maximum height when the velocity is zero.
[tex]0=-10t+40\\10t=40\\t=40/10\\t=4[/tex]
so now we insert the value of t = 4 into the equation of h(t) to get the height.
[tex]h(t)=-5t^2+40t\\h(4)=-5(4)^2+40(4)\\h(4)=-80+160\\h(4)=80\\[/tex]
so the maximum height of the ball is 80 meters.
Part d
The y-intercept of the graph is zero, and it represents that there is no initial height covered by the ball or the ball is actually thrown from already a height of x meters, as we can see from the equation the y-intercept is zero which means the height covered by the ball is 0 meters when time is zero.
So the point is actually at the Origin (0 , 0).
Part e
We can see that the origin (0 ,0) and (8,0) are the x-intercepts of the graph as solved from part A
We can see that the stationary point or the maximum point is at (4,80) which means the maximum height of the ball is 80 meters when the time is 4 seconds as solved in part C
Graph attached.
Related Questions
PLEASE HELP IM TIMED!
Answers
Answer:
B
Step-by-step explanation:
The length of a rectangle is 3 inches less than its width the area of the rectangle is 18 in.² what are the dimensions of the rectangle
Answers
Answer:
w=6 in
l=3 in
Step-by-step explanation:
let w = width and length be 'w-3'
Two sides of w and two sides of (w-3) equal 18 sq in
18=2(w)+2(w-3)
18=2w+2w-6
4w=24
w=6
The width of rectangle is, 6 in.
And, Length of rectangle is 3 in.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The length of a rectangle is 3 inches less than its width
And, the area of the rectangle is 18 in.²
Now, We know that;
Area of rectangle = Length × Width
Let the width of rectangle = x
Hence, Length of rectangle = x - 3
Thus, We get;
Area of rectangle = Length × Width
18 = x (x - 3)
18 = x² - 3x
x² - 3x - 18 = 0
x² - (6 - 3)x - 18 = 0
x² - 6x + 3x -18 = 0
x(x - 6) + 3 (x - 6) = 0
(x - 6) (x + 3) = 0
x = 6 , x = - 3
But dimensions are not negative.
Hence, We get;
x = 6
Thus, the width of rectangle = 6 in.
Hence, Length of rectangle = x - 3
= 6 - 3 = 3 in.
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Solve the system of linear equations by multiplying.
{−2x + 2y =4
{−4x + 8y =24
Answers
Answer:
The solution set is (2,4).
Step-by-step explanation:
Given that:
−2x + 2y =4 Eqn 1
−4x + 8y =24 Eqn 2
Multiplying Eqn 1 by -2
-2(-2x+2y=4)
4x-4y= -8 Eqn 3
Adding Eqn 2 and 3
(-4x+8y)+(4x-4y)=24-8
-4x+8y+4x-4y=16
4y=16
Dividing both sides by 4
[tex]\frac{4y}{4}=\frac{16}{4}\\y=4[/tex]
Putting y=4 in Eqn 1
-2x+2(4)=4
-2x+8=4
-2x=4-8
-2x=-4
Dividing both sides by -2
[tex]\frac{-2x}{-2}=\frac{-4}{-2}\\x=2[/tex]
Hence,
The solution set is (2,4).
Can someone rewrite the following equation into slope-intercept form ?
6x-7y=3
Answers
Work out: 6x-7y=3
Subtract x to isolate y
-7=-6x+3
Dived -7 to both sides to isolate y
Y=6/7-3/7
True or False: -10 > -65
Help plz
Answers
Answer:
True
Step-by-step explanation:
on a number line -10 is further right than -65.
Answer:
True -10 is closer to 1 the -65
Step-by-step explanation:
pls help!!!
A diagram using arrows to show how to get from one statement to the next is called a _________.
Answers
Step-by-step explanation:
an arrows digram also known as an activity networkchart he
Answer:
auxiliary line
Step-by-step explanation:
Did I plot these coordinates right? If so, are they congruent?
Answers
In an xy-coordinate system, Line l has a slope of –3. If the points (2, 16) and (5, t) are on Line l, what is the value of t?
A.17
B.15
C.25
D.7
Answers
See attachment for math work and answer.
The value of t is 7 and the coordinate is (5, 7). Therefore, option D is the correct answer.
Given that, in an xy-coordinate system, line l has a slope of -3. If the points (2, 16) and (5, t) are on line l.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)
Now, substitute m=-3, (x1, y1)=(2, 16) and (x2, y2)=(5, t) in slope formula, we get
-3 =(t-16)/(5-2)
⇒ -3 =(t-16)/3
⇒ t-16=-9
⇒ t=7
The value of t is 7 and the coordinate is (5, 7). Therefore, option D is the correct answer.
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Can someone pls help me!!!
Answers
Answer:
10 i believe
Step-by-step explanation:
Clara buys an item with a normal price of $24, but saves $6 by using a coupon. For what percentage off is this coupon?
Answers
Answer:
She saved 25%
Step-by-step explanation
(100 * 6) /24 = 25
If the value of y varies directly with x, which function represents the relationship between x and y when y= 16/5 and x = 20?
Answers
Not sure if this is the answer but this is what I got
Answer: y= 4/25 x
Kaley's family drove to DisneyLand for spring break. Her mom and dad shared the driving duties for a total of 24 hours. Her mom drove 75 miles per hour, and her dad drove 60 miles per hour. If they drove a total of 1,710 miles, how many hours did each person drive for?
Answers
Answer:
Mom drove for 18 hours.
Dad drove for 6 hours.
Step-by-step explanation:
Given that:
Number of hours for the driving duty = 24 hours
Speed at which the mom drove = 75 miles per hour
Speed at which the dad drove = 60 miles per hour
Total distance driven by both of them = 1710 miles
To find:
Number of hours for which each person drive for ?
Solution:
Let number of hours driven by dad = [tex]x[/tex] hours
Let number of hours driven by mom = (24 - [tex]x[/tex]) hours
Let us have a look at the formula for Distance in terms of Speed and Time.
[tex]Distance = Speed \times Time[/tex]
Distance traveled by Mom = [tex]75 \times x =75x \ miles[/tex]
Distance traveled by dad = [tex]60(24-x) =144-60x[/tex] miles
As per question statement:
[tex]75x+1440-60x=1710\\\Rightarrow 15x=1710-1440\\\Rightarrow 15x = 270\\\Rightarrow x = 18\ hours[/tex]
So, Mom drove for 18 hours.
Dad drove for 6 hours.
A customer at a store paid $42 for 4 pairs of pants and 3 shirts. At the same store, a second customer paid $2 more for 1 pair of pants and 7 shirts. The price of each pair of pants is the same, and the price of each shirt is the same. Which system of equations can be used to find the price in dollars of each pair of pants, x, and each shirt, y?
Answers
Answer:
The system of Equations:
4x + 3y = 42
x + 7y = 44
Step-by-step explanation:
Let the price in dollars of
each pair of pants = x
each shirt = y
A customer at a store paid $42 for 4 pairs of pants and 3 shirts.
Hence:
4 × x + 3 × y = $42
4x + 3y = 42
At the same store, a second customer paid $2 more for 1 pair of pants and 7 shirts.
This means he, paid $42 +$2 = $44
Hence:
1 × x + 7 × y = 44
x + 7y = 44
The system of equations can be used to find the price in dollars of each pair of pants, x, and each shirt, y is
4x + 3y = 42.... Equation 1
x + 7y = 44..... Equation 2
Help!!!!!!!!!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
y is 130° too because it's an alternative angle love
Answer:
X=130
Y=130
Step-by-step explanation:
I know this because x is the same as 130 and the congruent angle is the same as well. Hope this helps
Frieda paid $132 for groceries for her family. This was 1 1/8 as much as she paid for the previous time she shopped. How much did Freda pay on her previous shopping trip
Answers
Answer:
$117.33
Step-by-step explanation:
1 1/8 = 1 + 1/8 = 8/8 + 1/8 = 9/8
She paid 9/8 what she paid the last time.
Let the amount she paid last time equal x.
$132 is 9/8 of x.
9/8 x = 132
8/9 * 9/8 x = 132 * 8/9
x = 117.33
She paid $117.33
Please answer this please will give Brainliest
Answers
Answer:
y=1/3x+2
Step-by-step explanation:
The main rotor of a helicopter is spinning at a
constant rate. The rotor makes 80 revolutions every
12 seconds. At what rate, in revolutions per minute.
is the rotor spinning?
Answers
Answer:6.7
Step-by-step explanation: Just divide 80 by 12 you get 6.6 so round up
Find the sale price of the item. Round to the nearest cent if necessary. Original price: $75.00 Markdown: 34% The sale price is, in dollars, is $
Answers
The ages in years of right boys are. 14,14.5,12,11.5,15,13,20.5,13.5. what is the average age.
Answers
Answer:
to find the average you add all of the numbers together, and then divide by the amount of numbers you have. the numbers added is =114 and the amount of numbers is 8, 114/8= 14.25 years old
16.5 × 6.67 - 4.67 × 16.5
Answers
- (PEMDAS) if there are no parentheses then multiply first. so you would do 16.5•6.67 to get 110.055 and so the same with the -4.67•16.5 to get -77.055. now, you would subtract and your equation would now be 110.055-77.055=33. hope that helps some
Rewrite the division problem as multiplication:
Answers
Answer:
What is the problem??? If you didn't need an actual problem solved I said how to do it.
Step-by-step explanation:
You rewrite the division question as a multiplication question by flipping the second fraction over. Next, keep the first number, change the division to multiplication and then flip the second fraction over.
I hope this helps UwU
factor the expression using the GCF 8x+20y= ( x+ y)
Answers
9514 1404 393
Answer:
4(2x +5y)
Step-by-step explanation:
The variables x and y have no common factors. The coefficients 8 and 20 have a common factor of 4. So, the expression can be written ...
4(2x +5y)
You cell phone bill is $19.95 a month and $0.30 per text message. Your bill for last month was $94.95. How many text messages did you send or receive?
Answers
Answer:
Step-by-step explanation:
94.95-19.95= 74.00
74.00/ 0.30 = about 246 text messages
Answer:
250Step-by-step explanation:
Let the number of text messages be x.
We have following equation as per given:
19.95 + 0.30x = 94.950.30x = 94.95 - 19.950.30x = 75x = 75/0.30x =250Answer: 250 text messages
HELP IS THIS PROPORTIONAL RELATIONSHIP?!
Answers
Answer:
no it isn't
Step-by-step explanation:
Answer:
I am not fully sure but I think its not proportional
Step-by-step explanation:
ASAP help me with this question
Answers
the equation of the line is y = 3x - 5
Answer:
WOOF WOOF
Step-by-step explanation:
i love getting extra points :)
It costs Widgeco $2,000 to purchase a machine that produces widgets and $2.75 to produce each widget. If widgets are sold for $4.99 each, which of these represents the profit, P(w), received when Widgeco sells w widgets?
Answers
Answer:
C. P(w) = 2.24w - 2000Step-by-step explanation:
Starting point is - $2000 as this is spending
Income is calculated as:
-2.75w + 4.99w = 2.24wSo the profit formula is:
P(w) = 2.24w - 2000Correct option is C from below answer choices
The options are:
A . P(w) = 2.24w + 2,000 B. P(w) = 7.74w + 2,000 C. P(w) = 2.24w – 2,000 D. P(w) = 7.74w – 2,000
how do you solve for a missing measure on a triangle
Answers
To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.
You're welcome Have a nice night ✨Which street is parallel to 1st Ave?
A. 2nd Ave
B. Main Road
C. Central Ave
D. D Street
Answers
Answer:
i believe its the second ave
Parallel lines are those lines that are always the same distance apart and parallel lines do not intersect or meet each other.
The street that is parallel to 1st Ave is 2nd Ave.
What are parallel lines?Parallel lines are those lines that are always the same distance apart and parallel lines do not intersect or meet each other.
Example:
Line A and Line B have an angle of zero between each other.
This means Line A and Line B are parallel to each other.
We have,
Five streets:
1st ave
2nd ave
Central ave
D steet
Main road
Now,
Central Ave and the main road are parallel to each other.
1st Ave and 2nd Ave are parallel to each other.
D Street is perpendicular to 1st Ave and 2nd Ave.
Central Ave and Main Road are also perpendicular to 1st Ave and 2nd Ave.
We see that,
The street that is parallel to 1st Ave is 2nd Ave.
Thus,
The street that is parallel to 1st Ave is 2nd Ave.
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express 0.24 as a percent
Answers
Answer: 24%
Step-by-step explanation:
Answer: 0.24%
Step-by-step explanation: i hope this helps have a blessed day
distribute -14(-8y-11z) pls !!
Answers
Answer:
112y + 154z
Step-by-step explanation:
-14(-8y-11z) = 112y + 154z
Two minus makes one plus.