A basketball is thrown with an initial upward velocity of 30 feet per second from a height of 6 feet above the ground. The equation h=-16t^(2)+30t+6 models the height in feet t seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?

Answers

Answer 1

For this case we have the following equation:
h = -16t ^ (2) + 30t + 6
We substitute the value of h = 10 in the equation:
10 = -16t ^ (2) + 30t + 6
Rewriting we have:
0 = -16t ^ (2) + 30t + 6-10
0 = - 16t ^ (2) + 30t - 4
We look for the roots of the polynomial:
t1 = 0.144463904
t2 = 1.730536096
"the ball passes its maximum height, it comes down and then goes into the hoop". Therefore, the correct root is:
t = 1.730536096
Answer:
It goes into the hoop after:
t = 1.73 seconds

Related Questions

Write the equation of the perpendicular bisector of CD.
A) y = -x + 6
B) y = x + 1 2
C) y = 1 2 x + 6
D) y = -x + 1 2

Answers

You haven't provided the coordinates of C and D, therefore, I cannot provide an exact solution. However, I'll tell you how to solve this problem and you can apply on the coordinates you have.

The general form of the linear equation is:
y = mx + c
where:
m is the slope and c is the y-intercept

1- getting the slope:
We will start by getting the slope of CD using the formula:
slope = (y2-y1) / (x2-x1)
We know that the line we are looking for is perpendicular to CD. This meas that the product of their slopes is -1. Knowing this, and having calculated the slope of CD, we can simply get the slope of our line

2- getting the y-intercept:
To get the y-intercept, we will need a point that belongs to the line.
We know that our line passes through the midpoint of CD.
Therefore, we will first need to get the midpoint:
midpoint = ([tex] \frac{x1+x2}{2} , \frac{y1+y2}{2} [/tex])

Now, we will use this point along with the slope we have to substitute in the general equation and solve for c.

By this, we would have our equation in the form of:
y = mx + c

Hope this helps :)

Answer:

The answer is A.) y= -x+6

Step-by-step explanation:

If you choose one card from a standard deck, what is the probability that the card is either red or a king?

Answers

[tex] |\Omega|=52\\
|A|=\underbrace{26}_{\text{red}}+\underbrace{4}_{\text{king}}-\underbrace{2}_{\text{red king}}=28\\\\
P(A)=\dfrac{28}{52}=\dfrac{7}{13}\approx54\% [/tex]

Answer:

C) 7/13

Step-by-step explanation:

An apple pie with a circumference of 28.26 inches is cut into 6 equal-sized pieces. Two pieces of the pie are eaten. What is the area of the pie that is left? Select the correct answer. Use 3.14 for π.

Answers

C = πd
d = C / π
d = 28.26 / 3.14
d = 9 in

but r = d/2 = 9/2 = 4.5 in

A = π r^2
= 3.14 x (4.5^2)
= 3.14 x 20.25
= 63.585

divided into 6 equal
so 63.585 / 6 = 10.5975

but ate 2, so there are 4 pieces left
4 x 10.5975 = 42.39

answer
the area of the pie that is left is 42.36 in^2

hey user!!

your answer is here...

we know that circumference of circle = πd

given the circumference of the apple pie = 28.26 in.

therefore πd = 28.26 in.

==> 3.14 × d = 28.26 in.

==> d = 28.26/3.14

==> d = 9 in.

the diameter of the apple pie is 9 in.

therefore radius of the apple pie = 9/2 = 4.5 in.

area of the apple pie = πr²

== 3.14 × 4.5 × 4.5

= 63.585 in²

it's divided into 6 equal parts and two pieces are eaten. so the area of leftover pie = 63.585/6 × 4

= 63.585/3 × 2

= 21.195 × 2

= 42.39 in²

cheers!!

Solve equation -6/7m=-84

Answers

The first step for solving this equation is to determine the defined range.
[tex] \frac{-6}{7m} [/tex] = -84, m ≠ 0
Multiply both sides of the equation by 7m.
-6 = -588m
Now switch the sides of the equation.
-588m = -6
Divide bot sides of the equation by -588.
m = [tex] \frac{1}{98} [/tex], m ≠ 0
Lastly,, check if the solution is in the defined range (it is) to find your final answer.
[tex]m = \frac{1}{98} [/tex]
Let me know if you have any further questions.
:)

To solve the equation -6/7m = -84, multiply both sides by the reciprocal of -6/7, which is -7/6. The solution is m = 98.

To solve the equation -6/7m = -84, we need to isolate the variable m on one side of the equation. We can do this by performing the inverse operation of what is currently being done to m. Since m is being divided by -6/7, we can multiply both sides of the equation by the reciprocal of -6/7, which is -7/6, to cancel out the division on the left side.

The steps to solve the equation are:

Multiply both sides of the equation by -7/6:

-7/6 * (-6/7m) = -7/6 * -84

The left side simplifies to m, and the right side becomes m = 98.

So, the solution to the equation is m = 98.

determine the qotient of 7,684 and 78

Answers

Hello!

To determine the quotient of 7684 and 78, you'll need to divide 7684 by 78 or 7684/78.

You can do this by dividing 7684 by 78 in a calculator. Once you've done so, your quotient or answer, rounded to the nearest tenth, will be...

98.5

I hope this helps

Final answer:

The quotient of 7,684 and 78 is 98 with a remainder of 60, determined through long division.

Explanation:

To determine the quotient of 7,684 and 78, follow these steps:

Set up the division problem using long division with 7,684 as the dividend and 78 as the divisor.

Divide 78 into the first two digits of the dividend (76), which does not go evenly. Move to the first three digits (768).

Divide 78 into 768 to begin finding the quotient. 78 goes into 768 approximately 9 times because 78 x 9 = 702.

Subtract 702 from 768 to get a remainder of 66 and bring down the next digit from the dividend, which is 4, forming 684.

Divide 78 into 684. It goes 8 times because 78 x 8 = 624.

Write 8 next to the 9 in the quotient to update the quotient to 98 and subtract 624 from 684 to get a new remainder of 60. Since there are no more digits to bring down from the dividend, 60 is the final remainder.

The quotient is 98 with a remainder of 60.

what is the work for 34,992 divided by 81

Answers

34992/81 or 81*x=34992 = 432

Q is directly proportional to r. q is 76 when r is 20. work out q when r is 45.

Answers

q α r
q=kr
thus
k=q/r
when r=20, q=76
hence
k=76/20=
q=76/20r
when r=45 the value of q will be:
q=76/20×45
q=171

Answer:

q=171

Step-by-step explanation:

Hello there!

In this explanation k is constant and it means that q is some constant amount bigger than r.

q=kr

76=k×20

76÷20=k

k= 3.8

q=3.8r

q=3.8×45

q=171

Olly drank 1/2 of a 16 fluid ounce bottle of juice how many cups of juice are left in the bottle explain

Answers

If Olly drank 1/2 of 16 fluid ounces, then what the question really means is that Olly drank 8 fluid ounces.

Remember the conversion: 8 fluid ounces = 1 cup. Since Olly drank 8 fluid ounces, then using the conversion, we can tell that Olly drank 1 cup of juice.

The total number of cups of juice that are left in the bottle are 8x.

What is division?

Division is a process of splitting a number into two or more equal parts.

Given is that Olly drank 1/2 of a 16 fluid ounce bottle of juice.

Assume that 1 fluid ounce of bottle can fill {x} cups. So, we can write -

16 fluid ounce bottle of juice can fill {16x} cups.

So, 1/2 x 16 fluid ounce of juice will fill {1/2 x 16x} cups.

{1/2 x 16x} cups

8x cups

Therefore, the total number of cups of juice that are left in the bottle are 8x.

To solve more questions on division, visit the link below-

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james just bought a large container of ice cream the label says that there are 16 servings of ice cream write a formula to help james determine the number of grams on one serving of ice cream x=number of grams of ice cream in the container y=number of grams per serving

Answers

The correct formula that must be used is y=x/16. Variable 'x' represents the total mass of ice cream in the container. Mass of ice cream per serving is represented by the variable 'y'. The total mass of ice cream is divided by sixteen to determine the number of grams per serving.

Final answer:

To determine the number of grams per serving of ice cream, use the formula y = x / 16, where x is the total number of grams in the container and y is the number of grams per serving.

Explanation:

To determine the number of grams per serving of ice cream, we can set up a formula using the variables x and y. Since the container has 16 servings of ice cream, the total number of grams in the container can be represented as 16y (16 servings multiplied by the number of grams per serving).

So, the formula to determine the number of grams per serving (y) is: y = x / 16

For example, if the total number of grams in the container (x) is 800g, then the number of grams per serving (y) would be 800g / 16 = 50g.

The cost for groceries was $11.20 before sales tax. How much was the total cost of groceries after the 5% sales tax was charged?

Answers

$11.76 I looked up the problem for you it gives you the right answer hope I helped!!

hey can you please help me posted picture of question

Answers

The correct answer for the problem shown in the figure atttached is the last option (option D), which is shown below:

D.(-x-9i)(x-9i)

If you want to verify that the option D.(-x-9i)(x-9i) is the correct answer, you can apply the distributive property to (-x-9i)(x-9i).

Therefore, when you apply the distributive property, you obtain that the result is:

-x²-81

The graph attached shown this equation, which is a parabola.

The answer is D... looked it up tbh

WHAT ARE THE THREE DIFFERENT TYPES OF ANGLES!!!!!!??

Answers

Hello there, and thank you for asking your question here on brainly.

Answer: The three different types of angles are an acute angle, which is an angle that is an angle that measures from 1° to 89°. A right angle, that specifically measures to 90°. Finally, an obtuse angle that measures from 91° to 179°. An angle that also measures 180° is a straight line, and is called a straight angle.

Hope this helped you! ♥

Final answer:

The three different types of angles are acute angles, right angles, and obtuse angles.

Explanation:

The three different types of angles are:

Acute angle: An acute angle is an angle that measures less than 90 degrees. For example, if you have an angle that measures 60 degrees, it would be considered an acute angle, since it is less than 90 degrees.

Right angle: A right angle is an angle that measures exactly 90 degrees. It forms a perfect square corner, like the angle formed by the corner of a book or the corner of a piece of paper.

Obtuse angle: An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. For example, if you have an angle that measures 120 degrees, it would be considered an obtuse angle, since it is more than 90 degrees but less than 180 degrees.

a plane takes off at an angle of elevation of 15 degrees and travels in a straight line for 3,000 meters. What is the height of the plane above the ground at this instant?

Answers

SOH CAH TOA tells you the sine function of an angle gives the ratio of opposite side to the hypotenuse of the right triangle.
Sin = Opposite/Hypotenuse
In this problem, the angle is 15°, the hypotenuse is 3000 m and we want to find the length of the opposite side (the height above the ground).

sin(30°) = height/(3000 m)
Multiplying by 3000 m, we get
height = (3000 m)*sin(30°) = 1500 m

The height of the plane at that instant is ...
1500 m

Q 5 please whats are the coordinates

Answers

Remember that to rotate a point 180° clockwise or anticlockwise, we need to apply the following rule: [tex](x,y)[/tex]⇒[tex](-x,-y)[/tex]. In other words, the new coordinates of the point will be the negative coordinates of the point before the rotation.

[tex](-10,-3)[/tex]⇒[tex][-(-10),-(-3)][/tex]⇒[tex](10,3)[/tex]

We can conclude that the coordinates of the point after a 180° clockwise rotation are: (10,3)

The answer to your question would be the fourth option which is (10,3).

Solution:
(x,y)►(-x,-y)
Substitute:
(-10,-3)►(-(-10),-(-3))
=(10,3)

So the coordinates of the 180° clockwise rotation are (10,3).

The International Space Station orbits approximately 250 miles above the surface of the Earth. If the station makes 16 orbits per day, what is the linear velocity, in miles per hour, of the International Space Station? Round the answer to the nearest whole number. Use the following information: radius of Earth ≈ 3,960 miles and 1 mile = 5,280 feet.

Answers

The station orbits 250 miles above the surface of earth.
So, the radius of the orbit with respect to the center of Earth will be = r = 250 + 3960 = 4210 miles

Angular velocity = w =16 orbits per day = 16 x 2π radians per day

w = 32π radians per day
w = 32π/24 radians per hour = 4π/3 radians per hour

Linear speed = v = r w

v = 4210 x 4π/3 miles per hour

v = 17,635 miles per hour

The International Space Station has a linear velocity of approximately 17,625 miles per hour when orbiting Earth at an altitude of 250 miles above the surface and completing 16 orbits per day.

To find the linear velocity of the International Space Station (ISS), we first calculate the circumference of its orbit around the Earth. The radius of the Earth is given as approximately 3,960 miles, and the ISS orbits about 250 miles above the surface. Therefore, the total distance from the center of the Earth to the ISS is 3,960 miles + 250 miles = 4,210 miles.

The formula for the circumference (C) of a circle is C = 2yr, where y represents pi (approximately 3.1416), and r is the radius of the circle. Substituting the values, we get C = 2 * 3.1416 * 4,210 miles = 26,437.792 miles.

Given the ISS makes 16 orbits per day, we can calculate the daily distance traveled by multiplying the circumference of a single orbit by the number of orbits: 16 orbits/day * 26,437.792 miles/orbit = 423,004.672 miles/day.

To find the velocity in miles per hour (mph), we divide the daily distance by the number of hours in a day: 423,004.672 miles/day y 24 hours/day = 17,625.195 mph. Rounding to the nearest whole number, we get a linear velocity of approximately 17,625 mph.

can someone plz help me!!!

Answers

6√25, ∛27, √64, ∛64

6*5, 3, 8, 4

30, 3, 8, 4

∛64 > ∛27> √ 64 > 6√25

what is a multiple of 6,9,18 between 61 and 107

Answers

There are two possible answers: 72 and 90.

We can find the answer by looking at the largest number among the three of them: 18. The only multiples of 18 between 61 and 107 are 72 and 90. We can check that both numbers are also multiples of 6 and 9:

90 : 6 = 15
90 : 9 = 10

72 : 6 = 12
72 : 9 = 8

Which of the following is a reason people sometimes use mean or median to misrepresent the “average” of a set of data?

a.

In many data sets, the mean and median are always similar.

b.

In most data sets, the mean and median are always different.

c.

The median is meaningless but is often confused with the mean.

d.

In data sets with outliers, either the mean or median can be used to make the data set appear more favorable to their agenda.

Answers

Answer: In data sets with outliers, either the mean or median can be used to make the data set appear more favorable to their agenda.

Step-by-step explanation:

We know that the "mean" is the "average" we used where we need to add up all the numbers and then divide by the number of elements where as the "median" is the "middle" value in the list of numbers.

The mean and median would not affected by outlying data points within data sets. Thus, the median is often used when a data set has outlying data points that could influence the mean and thereby misrepresent the middle of the data set.

The correct reason people sometimes use mean or median to misrepresent the “average” of a set of data is " In data sets with outliers, either the mean or median can be used to make the data set appear more favorable to their agenda. '

Which graph models the equation y = 3.5x?

Answers

C is your answer

slope is 3.5
x = 0, y = 0
x = 1, y = 3.5
x = 2, y = 7
x = 4, y = 10

Answer: the answer is c

Step-by-step explanat

System of equations help?

Answers

The soluions are approximately x ∈ {0.5, 7.8}.

APLZ HELP ASAP INSCRIBED QUADRILATERALS

Answers

For any inscribed quadrilateral, the sum of each pair of opposite angles must add up to 180. In this case, B + A = 180, and similarly, E + R = 180. Therefore,
74 + R = 180
R = 106 degrees

(Similarly, if we had to solve for B, B + 92 = 180, and B = 88 degrees.)

The opposite angles in any inscribed quadrilateral are supplementary.
∵ ∠E + ∠R = 180°
∴ ∠R = 180 - ∠E = 180° - 74° = 106°

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.

Answers

Residual. Bc that diff between observed y and predicted y.

Marty correctly answers 36 questions on his science test. There are 50 questions on the test. Find the percent of the questions Marty answers correctly.

Work Pls
Thx

Answers

All you have to do is divide the score by how many questions there are.

Score = 36
Total = 50

36 ÷ 50 = 0.72

0.72 = 72%

Answer = 72%

Hope this helped :)

The percent of the questions Marty answers correctly is 72 percent.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Marty correctly answers 36 questions on his science test.

There are 50 questions on the test.

Percentage of correct answers = Number of correct answers/Total number of questions ×100

= 36/50 ×100

= 0.72×100

= 72%

Therefore, the percent of the questions Marty answers correctly is 72 percent.

To learn more about the percentage visit:

brainly.com/question/24159063.

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the circumference of a circle is 37.68 what is the radius

Answers

the main formula for finding circumference is c=2piR
circumference//37.68=2(3.14)r =6.28 now divide 6.28 by both sides which will give you 6 therefore the radius is 6

Laura is completing a craft project that involves covering only the lateral surface of a cylindrical container with fabric. The cylinder has a height of 16.8 in. and a radius of 14.6 in. To the nearest square unit, how much fabric does she need for this project? Use a calculator.

Answers

The answer is 1561 in^2
The lateral surface area formula of a cylinder is LA = 2 pi r h

We are given
r=14.6 in
h=16.8 in
pi=3.14

LA = 2 * 3.14 * 14.8 * 16.8 about 1561 in^2

Answer:

1,541

Step-by-step explanation:

Which diagram shows the most useful positioning of a rectangle in the first quadrant of a coordinate plane? Answers are in the pictures.

Answers

use this one and that will be useful

me thinks you do not have to deal with all the other stuff. you jus tuse "a" for the height and "b" with the width

A diagram that shows the most useful positioning of a rectangle in the first quadrant of a coordinate plane is: D. diagram D.

What is a quadrant?

In Mathematics and Euclidean Geometry, a quadrant is the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a coordinate plane or cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Quadrant 1: both x and y are positive.Quadrant 2: x is negative while y is positive.Quadrant 3: both x and y are negative.Quadrant 4: x is positive while y is negative.

In this scenario, we can logically deduce that the coordianetes of this rectangle can be easily calculated by using diagram D;

Length, b = |b - 0| = b

Width, a = |0 - a| = a

Read more on quadrant here: brainly.com/question/2551599

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There are 9 different colors of paint to choose from. Out of the 9 colors, how many ways can 4 different colors be chosen?

Answers

This is the concept of combination, the number of ways 4 different color can be chosen from 9 different colors will be:
9C4
=(9!)/(4!(9-4)!)
=362,880/(24×120)
=362,880/2880
=126
thus the number of ways is 126 ways

Answer:

Your answer would be 126 ways hopefully this helps!

A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?

1. Sydney’s pyramid will have the same surface area because the .5 in the expression for the area of the triangular faces will make up for the slant height being doubled.
2. Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
3. Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
4. Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.

30 POINTS

Answers

the surface area of a square pyramid with base length b and slant height x is
[tex]A=b^2+2bx[/tex]

note that b²=base area

so, if we say that her original pyramid's surface area is [tex]A_1=b^2+2bx[/tex], then the new one has a slant height of twice that, ie, we replace x with 2x and see what happens
[tex]A_2=b^2+2b(2x)[/tex]
[tex]A_2=b^2+4bx[/tex]
if we try to work [tex]A_1[/tex] back into there
[tex]A_2=b^2+2bx+2bx[/tex]
[tex]A_2=(b^2+2bx)+2bx[/tex]
[tex]A_2=A_1+2bx[/tex]

see our options
option 1 is wrong since the surface area increased by 2bx

option 2 is wrong since the surface area increased by 2bx, also we do use the slant height when finding surface area

option 3 is wrong because we got [tex]A_2=A_1+2bx[/tex] and not [tex]A_2=2(A_1)[/tex]

option 4 is correct since the new surface area is greater than the original by 2bx

answer is option 4

Answer:

Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.

Step-by-step explanation:

find the area of an isosceles triangle with base 20 and base angles 40 degrees

Answers

check the picture below.

make sure your calculator is in Degree mode.

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=20\\ h=y \end{cases}\implies A=\cfrac{1}{2}(20)(y)[/tex]

HELP ASAP

A rain barrel is full of water and used to water a garden. The rain barrel loses water at the rate of 2.5 gallons of water per minute. After seven minutes, the rain barrel contains 37.5 gallons.

D. What is the total number of minutes it will take to completely empty the rain barrel?

Answers

So, first let's refill the barrel to the top:
37.5 + 7*2.5 = 55
Now that it's full again, let's divide the total amount by the rate of water loss:
55/2.5 = 22
It will take 22 minutes to completely empty the rain barrel

The rain barrel, losing water at a rate of 2.5 gallons per minute, started with a volume of 55 gallons. It will take a total of 22 minutes to completely empty the barrel.

To calculate the total number of minutes it will take to completely empty the rain barrel, we must first establish how much water is being lost per minute and use that rate to determine how long it will take to empty the current amount of water in the rain barrel.

We know that the rain barrel loses water at a rate of 2.5 gallons per minute and after seven minutes, it contains 37.5 gallons. To determine the starting volume (V0) when the barrel was full, we can add the amount of water already used in seven minutes back to the current volume:

V0 = current volume + (rate of loss x time)V0 = 37.5 gallons + (2.5 gallons/minute x 7 minutes)V0 = 37.5 gallons + 17.5 gallonsV0 = 55 gallons

With a starting volume of 55 gallons and a loss rate of 2.5 gallons per minute, we can calculate the total time (T) to empty the barrel:

T = Total volume / Rate of lossT = 55 gallons / 2.5 gallons/minuteT = 22 minutes

Therefore, it will take a total of 22 minutes to empty the rain barrel completely.

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