A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground. t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Answers

Answer 1

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

Answer 2

The time will be t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

What is Function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable the dependent variable.

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum.

We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground.

The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

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Related Questions

35.
What is the equation of the line that is
parallel to y = 4x + 3 and passes through
the point (2,6)?

HELP! answer if you can!​

Answers

Hi there! :)

Answer:

[tex]\huge\boxed{y = 4x - 2}[/tex]

Given line with an equation of y = 4x + 3

Parallel lines contain equivalent slopes, so a parallel line to the given equation would contain a slope of m = 4.

Plug in the coordinates of the point given, along with the slope into the equation y = mx + b where:

m = slope

y = y-coordinate of point

x = x-coordinate of point

Solve for the 'b' value, or y-intercept:

y = mx + b

6 = 4(2) + b

6 = 8 + b

b = -2

Rewrite the equation as slope-intercept form:

y = 4x - 2

Answer:

When you see the word "parallel", you know the new line will have the same slope.

parallel to y = 4x + 3

So, the new line will have a slope of 4

"Indicate the region where y≥ 4x + 3

Plot y= 4x + 3 by finding the points that make it true. For example, (y = 0, x = 3/4), (y = 2, x = 2) and so on.

y = 4x + b

b is the y intercept ( point y when x = 0)

Insert new coefficients:

+2 = 4(0) + b

b = +2

y = 4 + 2

[tex] \: [/tex]

it has rained on the 6th of january twice in the last 20 years calculate the probability that it will rain on the 6th january next year​

Answers

There is obviously an infinite amount of probabilities in which it will rain on the 6th of January

But 50/50, because just because it happened other times doesn’t mean it’ll happen again

Hope this helped ♥︎

Find the measure of b

Answers

Answer:

b = 76°

Step-by-step explanation:

According to the inscribed angles proposition, the measure of an inscribed angle in a semicircle is said to be 90°.

Therefore, in the figure given, m<a = 90°

b = 180° - (90° + 14°) => sum of angles in a triangle.

b = 180° - 104°

b = 76°

Ahmad has some files.
He gave 3/5 of the files and had 14 files left.

How many files did he have at first?​

Answers

Answer:

The answer is 35

Step-by-step explanation:

Let the number of files he had be x

He gave 3/5 of the files

That's

3/5x

After that he still had 14 files left which means when we subtract 14 from the original files we should get 3/5 of the original files

So we subtract 14 from the original number of files

That's

x - 14

We equate the two statements

that's

[tex] \frac{3}{5} x = x - 14[/tex]

Multiply through by 5

[tex]5 \times \frac{3}{5} x = 5x - 70[/tex]

We have

3x = 5x - 70

3x - 5x = 70

-2x = - 70

Divide both sides by -2

We have the final answer as

x = 35

Therefore he had 35 files at first

Hope this helps you

Answer:

35 files

Step-by-step explanation:

gave=3/5

left=2/5 = 14f

had= 5/5

2/5=14

5/5

5×14÷2 = 35

3/4a−16=2/3a+14 PLEASE I NEED THIS QUICK and if you explain the steps that would be geat:) Thank youuuuuuu

Answers

Answer:

360

Step-by-step explanation:

3/4a - 16 = 2/3a + 14               ⇒ collect like terms 3/4a - 2/3a = 14 + 16               ⇒ bring the fractions to same denominator9/12a - 8/12a = 30                  ⇒ simplify fraction1/12a = 30                               ⇒ multiply both sides by 12a = 30*12a = 360                                   ⇒ answer

Emily's family loves to work together in the garden.They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden. How many vegetable plants do they have?

Answers

50 plants total, 40% are vegetables

40% = 40/100 = 0.40

40% of 50 = 0.40*50 = 20

Answer: There are 20 vegetable plants

If we did not write the equation 5x=21, instead we wrote it 21=5x,
we would get a different solution.
O True
O False

Answers

True we would get a different solution

Answer:

Step-by-step explanation:

5x = 21 and 21 = 5x are identical relationships, and so the solution would be the same in both cases.  (Commutative Property:  order of addition/subtraction is immaterial)

I NEED HELP PLEASE :(

Answers

Answer:

7/8

Step-by-step explanation:

power of 1/2 is the same as square root.

√(49/64) = 7/8 since 7/8 * 7/8 = 7*7/8*8 = 49/64

(t)What is the difference between
{2, 3} and {{2, 3}}?

Answers

[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3

[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]

Solve for y
4x + 7y +5

Answers

To find the slope, m, of the line represented algebraically by the given linear equation in two variables: 4x = 7y + 5, first put the given equation in the slope-intercept form of the equation of a straight line, i.e., y = mx + b, as follows:

4x = 7y + 5 (Given)

4x - 5 = 7y + 5 - 5

4x - 5 = 7y + 0

4x - 5 = 7y

7y = 4x - 5 since equality is symmetric, i.e., if a = b, then b = a.

(7y)/7 = (4x - 5)/7

(7/7)y = (4x)/7 - 5/7

(1)y = (4/7)x- 5/7

y = (4/7)x - 5/7

From the last step above, the given equation is now in the slope-intercept form of the equation of a straight line: y = mx + b, i.e., y = (4/7)x - 5/7; therefore, we can now see by observation, that the slope of the line is m = 4/7 which means that the line has a positive slope, i.e., it's > 0, which means that if the line were to be constructed on a Cartesian coordinate system, it would slope upward from left to right and would intersect the y-axis at the point (0, -5/7).

Barry has been watching the geese that live in his neighborhood. The number of geese changes each week. n f(n) 1 56 2 28 3 14 4 7 Which function best shows the relationship between n and f(n)? f(n) = 28(0.5)n f(n) = 56(0.5)n−1 f(n) = 56(0.5)n f(n) = 112(0.5)n−1

Answers

Answer:

B. f(n) = 56(0.5)^n-1

Step-by-step explanation:

 First, You have to find out the starting population, if you look at the problem you see the population starts at 56

f(x) = 56

Second, you know that the population goes down 50% each week so it has a decay of 0.5

f(x) = 56(0.5)

 Third,  you need to add the exponent of n to make it exponential.  But, if you just add n then the the population would be 28 on week 1 which is incorrect. To fix that you make the exponent n-1 so when you are on week 1 it doesn't become 28 but it stays on 56, and on week 2 it's 28, ect

f(x) = 56(0.5)^n-1

Maurice needs 45 exam review books for the students in his math class. The local bookseller will sell him the books at $3 each. He can also purchase them over the internet for $2 each plus $35 for postage. How much does he save by accepting the better offer?

Answers

Answer: he will save $42.50

Step-by-step explanation:

45÷3=15

45÷2+35=57.50

57.50-15= $42.50

To make a net from a container, you start by cutting one of the seams along the edge where the two sides meet. If you wanted to make a different net for the container, what would you do differently?

Answers

Answer:

I would not separate the same edges when making a second net. Also,  I would make sure that the result cannot be rotated or flipped so that it is the same  as the first.

Step-by-step explanation:

A taxi cab company charges a flat rate of $2.00 per trip plus $0.25 per mile of the trip. If m is the number of miles traveled on a particular trip, interpret the following expressions: a) 0.25m b) 2.00 + 0.25m

Answers

Answer:

b) 2.00 + 0.25m

Step-by-step explanation:

2.00per trip and $0.25 per mile = 2.00 + 0.25m

Answer:

see below

Step-by-step explanation:

a) 0.25m

This is the cost of the mileage alone

The cost is 25 cents per mile times m miles

b) 2.00 + 0.25m

This is the total cost of the trip

There is a 2 dollar flat rate fee plus the cost of the miles

2 dollars plus m miles at 25 cents per mile

An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)? (2 points) PLEASE HELP ASAP 30 POINTS!!!!!!! need full explanation and work

Answers

Answer:

299.99 miles

Step-by-step explanation:

Since the plane traveled due west,

The total angle is 49.17 + 90

Represent that with θ

θ = 49.17 + 90

θ = 139.17.

Represent the sides as

A = 170

B = 150

C = unknown

Since, θ is opposite side C, side C can be calculated using cosine formula as;

C² = A² + B² - 2ABCosθ

Substitute values for A, B and θ

C² = 150² + 170² - 2 * 150 * 170 * Cos 139.17

C² = 22500 + 28900 - 51000 * Cos 139.17

C² = 51400 - 51000 (−0.7567)

C² = 51400 + 38,591.7

C² = 89,991.7

Take Square Root of both sides

C = 299.9861663477167

C = 299.99 miles (Approximated)

Hence, the distance between the plane and the airport is 299.99 miles

-4 = BLANK - 9 what is BLANK

Answers

Answer:

5

Step-by-step explanation:

Let be blank be a

-4=a-9

-4+9=a

9-4=a

a=5

Proof:

-4=a-9

-4=5-9

-4=-4

Hope this helps ;) ❤❤❤

The value of BLANK in the given expression is 5.

To solve the equation "-4 = BLANK - 9",

Isolate the variable on one side of the equation.

To do this, we can add 9 to both sides of the equation:

-4 + 9 = BLANK - 9 + 9

This simplifies to:

5 = BLANK

So the value of BLANK is 5.

To solve the equation "-4 = BLANK - 9",

We can add 9 to both sides of the equation to isolate the variable.

This gives us the solution of BLANK = 5.

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16. Acme car rental agency charges a fee of $29 per day plus $0.15 per
mile. Travel Ease car rental agency charges $20 per day plus $0.25 per
mile. For a one-day trip, what mileage would make the two rates equal?

Answers

Answer:

90 miles

Step-by-step explanation:

0.15x + 29 = y ---- acme car agency

0.25 x + 20 = y ---- travel ease agency

0.15x + 29 = 0.25x + 20

9 = 0.1x

x = 90

A company ships coffee mugs using boxes in the shape of cubes. The function g(x) = gives the side length, in inches, for a cube with a volume of x cubic inches. Suppose the company decides to double the volume of the box. Which graph represents the new function?

Answers

Answer:

The graph is attached below.

Step-by-step explanation:

The volume of the box containing the coffee mugs is,

[tex]V=x^{3}[/tex]

Then the function representing the side length, in inches, for the box is:

[tex]g(x)=x[/tex]

Now, it is provided that the company decides to double the volume of the box.

That is, the new volume will be:

[tex]V_{n}=2x^{3}[/tex]

Then the side length, in inches, for the box will be:

[tex]g_{n}(x)=\sqrt[3]{2x^{3}} =\sqrt[3]{2}x[/tex]

Then the graph representing the function, formed using the following points is:

[tex]x\ \ \ \ \ \ \ \ \ g_{n}(x)\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\0\ \ \ \ \ \ \ \ \ \ \ 0\\1\ \ \ \ \ \ \ \ \ \ \ 2^{1/3}[/tex]

Answer:

c

Step-by-step explanation:

Which expressions are equivalent to -2y-8+4y−2y−8+4yminus, 2, y, minus, 8, plus, 4, y ? Choose all answers that apply: Choose all answers that apply: (Choice A) A -2(y+4)+4y−2(y+4)+4yminus, 2, left parenthesis, y, plus, 4, right parenthesis, plus, 4, y (Choice B) B 4(-2+y)-2y4(−2+y)−2y4, left parenthesis, minus, 2, plus, y, right parenthesis, minus, 2, y (Choice C) C None of the above

Answers

Answer:

C. None of the above. The correct expression is  2(y-4)

Step-by-step explanation:

Given the expression -2y-8+4y, we are to find the equivalent expressed is which other expression is similar to it. This can be expressed as shown below;

Step 1: Collect the like terms of the expression

= -2y-8+4y

= (-2y+4y)-8

Step 2: Sum up the terms in parenthesis:

=  (-2y+4y)-8

= 2y-8

Step 3: factor out the common terms

= 2y-8

= 2(y-4)

Hence the equivalent expression is 2(y-4).

Answer:

A and B

Step-by-step explanation:

On Khan Academy its right.

what is this equation in simplest form? 9x + 26 + 7x - 17 = 2x + (-3x) + 5x

Answers

Answer:

4x+3=0 or x=-3/4

Step-by-step explanation:

9x+26+7x-17=2x-3x+5x

arrange all numbers with coefficient x at one side let's say the left hand side and constant or real numbers at the right hand side in doing that we get

9x+7x-2x+3x-5x=17-26

12x=-9

(12x)/3=-9/3

4x=-3

x=-3/4

sloving polynomial (2x+8)(-3y-4)​

Answers

Answer:

Step-by-step explanation:

2x ( -3y - 4) + 8 ( -3y - 4 )

= -6xy - 8x - 24y - 32

Hope this helps

plz mark as brainliest!!!

Answer:

Step-by-step explanation:

Use FOIL method

(2x + 8)(-3y -4) = 2x*(-3y) + 2x*(-4) + 8*(-3y) + 8*(-4)

                       = -6xy - 8x - 24y - 32

What is the constant term for 4x-2y+3

Answers

Answer:

Step-by-step explanation:

3 is the constant term.

Constant term is the term without any variables

Answer:

3

Step-by-step explanation:

The constant number is the number that has no variable and just a number.

1A-MATH
Diviwuetalls
2 Exercise 7:
Your ansv
Type you
The three angles in a triangle are labeled A, B and C.
A = 2x
B= 3x
C=4x
Private coi
1) calculate X
2) find the actual angle of B
3) find the exterior angle to B

Answers

Answer:

Value of x = 20°

Angle B = 60°

Exterior angle to B = 300°

Step-by-step explanation:

Given:

Angles of triangle.

A = 2x

B = 3x

C = 4x

We know that,

A + B + C = 180°

2x + 3x + 4x = 180°

9x = 180°

x = 20°

Value of x = 20°

Angle B = 3x

Angle B = 3(20°)

Angle B = 60°

Exterior angle to B = 360° - 60°

Exterior angle to B = 300°

what is -7 + 11 - 14 + 3 + 12​

Answers

Answer:

5

Step-by-step explanation:

Answer:

5 (Follow PEMDAS left—>right)

Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many laps must Kellyn jog to meet her goal?

Answers

Answer:

She needs to jog 7 laps to make sure she covers at least 7.5 miles

Step-by-step explanation:

Kelly's goal is to complete 7 1/2 miles which in decimal form is: 7.5 miles.

Each lap around the park is 1 1/5 miles, which in decimal form is written as: 1.2 miles

Then, to find how many laps she needs to complete we do the quotient:

7.5/1.2 = 6.25

which means that she needs a quarter of a lap more than 6 laps, so she needs to go for 7 laps to meet the goal

Shape 1 and shape 2 are plotted on a coordinate plane which statement about the shapes is true?
DA Shape 1 and shape 2 are not congruent.
B A translation will prove that shape 2 is congruent to shape 1.
C. A rotation and a translation will prove that shape 2 is congruent to shape 1
OD. A reflection a rotation, and a translation will prove that shape 2 is congruent to shape 1

Answers

Answer:

The answer is D. A reflection, a rotation and a translation will prove that shape 2 is congruent to shape 1.

what is the range and domian of y=(x-4)

Answers

The answer is 8 because 4 over 4 up for y

Please help i need help answering these math problems i listed below

Answers

Answer:

Step-by-step explanation:

1) (-13)* .......(-13) for 35 times = (-13)³⁵

2) (2/3) *  ...... * (2/3) for 4 times = (2/3)⁴

3)(-3.1)* ......(-3.1) for 4 times = (-3.1)⁴ = 92.2531

Anna is planting in her garden the package says she needs to use 4 punds od fertilizer for 120 sqft the area of annas yard is 180 how much fertilizer is needed for the 180 sqft garden

Answers

Answer:

6 pounds

Step-by-step explanation:

The area of Anna's garden = 180 square feet

From the question, we know that:

120 square ft = 4 pounds of fertilizer

180 square ft = y

Cross Multiply

120 × y = 4 × 180

y = 4 × 180/120

y = 720/120

y = 6 pounds

Therefore, the amount of fertilizer that is needed for Anna's 180 square feet garden is 6 pounds.

21. Which of the following is an identity? a) sin (a) cos (a) = (1/2) sin(2 a) b) sin a + cos a = 1 c) sin(-a) = sin a d) tan a = cos a / sin a

Answers

Answer:

A

Step-by-step explanation:

[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]

[tex] \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) [/tex]

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The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,224.00 for 264 square feet, what is the size of a kitchen that costs $3,824.00? A. 239 square feet B. 256 square feet C. 7,648 square feet D. 63,096 square feet 5/8 divided by 11/9 divided by 1/4= Which number is in the 3rd position after ordering indescending order. V220,-10, V100, 11.5 In what ways did cross-cultural interactions drive change in the pre-1200 world f(x) = x+ bx + 5 In the given function, b is a constant. If f(1) = 0, what is the value of f(3) ? A ________ pay plan pays for individual performance based on performance appraisal ratings. A) piece-rate B) merit-based C) employee stock ownership D) profit-sharing E) gainsharing Too Young, Inc., has a bond outstanding with a coupon rate of 7 percent and semiannual payments. The bond currently sells for $951 and matures in 23 years. The par value is $1,000. What is the company's pretax cost of debt? Approximately how many calories are in one gram of carbohydrates? The paragraph contains several sentence fragments. Decide if the selection in bold needs to be revised or if it is correct as is.Near the Normandy coast of northern France, the village of Bayeux houses a remarkable treasure. The Bayeux Tapestry may be found in itsown museum in the former Great Seminary of Bayeux. Also known as the Tapestry of Queen Matilda or the Cloth of the Conquest. This tapestryis unusual. Because it is a very long, narrow strip of linen measuring 70 meters by 50 centimeters. The tapestry is actually an embroidery ofWilliam the Conqueror's invasion and conquest of England in 1066. It consists of fifty-one scenes and depicts more than 1,500 figures.Including warriors, horses, other animals, ships, castles, weapons, and other objects. Latin words are embroidered on the scenes. To explainwhat is taking place at each stage of the invasion and battle.Which option below would be an acceptable revision of the selection in bold?a. No revision is necessary.b. It consisted of fifty-one scenes and depicting more than 1,500 figures.Oc Consisting of fifty-one scenes and depicting more than 1,500 figures.d. Therefore, it consists of fifty-one scenes and depicting more than 1,500 figures. Combine like terms to simplify the expression: -5.55-8.55c+4.35c name four points that are not coplanar Celine is Drakes granddaughter. Her age is 4 years greater than of Drakes age. If Celine is 28 years old, how old is Drake? Ms. Canton has a book case. On three of the shelves there are the same amount of books. On another shelf there are four of her favorite books. Write an expression to represent all of the books in Ms. Canton's book case. Explain your answer What protective items should you wear when using benedicts solution? Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32 angle with the ground. The second tree is 16 feet long. What is the approximate angle, x, that the second tree makes with the ground? A 0.6 B 35.0 C 39.0 D 58.0 435Q2.2.51. The scale factor of the dilation that takes P to Qis2. The scale factor of the dilation that takes to PisBlank 1:Blank 2:Helppppp!! *LAST QUESTION, PLEASE ANSWER I NEED HELP* What will be the new volume of the prism if a scale factor of 2.5 is applied to the dimensions? Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9 } A= {1, 2, 3, 4} and B= {4, 5, 6, 7}. Draw the Venn diagram of A B. Answer with full explanation and diagram will be marked as brainliest for sure!!! Convert .23 Kiloliters to literswhats the answer? 165145x =Please Help!!!!