5. During a game of golf, Kayley hits her ball out of a sand trap. The height of the golf ball is modeled by the
equation h=-16r² + 20 - 4, where h is the height in feet and is the time in seconds since the ball was hit.
Find how long it takes Kayley's golf ball to hit the ground.
a. Write the equation that you are trying to solve.
b. Solve the equation by factoring.

Answers

Answer 1

Answer:

(a) [tex]\sf -16r^2+20r-4=0[/tex]

(b)  r = 1,  r = 1/4

Step-by-step explanation:

Given equation:   [tex]\sf h=-16r^2+20r-4[/tex]

where:

h = height (in feet)t = time (in seconds)

Question (a)

The ball will hit the ground when h = 0

[tex]\sf \implies-16r^2+20r-4=0[/tex]

Question (b)

To factor [tex]\sf -16r^2+20r-4=0[/tex]

Divide both sides by 4:

[tex]\sf \implies-4r^2+5r-1=0[/tex]

Swap signs:

[tex]\sf \implies 4r^2-5r+1=0[/tex]

Split middle term:

[tex]\sf \implies 4r^2-4r-r+1=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\sf \implies 4r(r-1)-(r-1)=0[/tex]

Factor out common term (r - 1):

[tex]\sf \implies (4r-1)(r-1)=0[/tex]

Therefore:

[tex]\sf \implies (4r-1)=0 \implies r=\dfrac14[/tex]

[tex]\sf \implies (r-1)=0 \implies r=1[/tex]


Related Questions

320 people attended a rock concert how much money was taken?

rock concert £6 per person

Answers

Answer:

320 x 6 euros = 1920 Euros

Step-by-step explanation:

Simple multiplication :)

Hope this helps

Answer:

£1,920

Step-by-step explanation:

Multiply 320 by 6


320 • 6 = 1,920

And your answer will be 1,920


I hope it helps! Have a great day!

Muffin ^^

Express the trig ratios as fractions in simplest terms.

Answers

Answer:

See below

Step-by-step explanation:

[tex]\cos M=\frac{adjacent}{hypotenuse}=\frac{56}{70}=\frac{4}{5}\\\\\sin L=\frac{opposite}{hypotenuse}=\frac{56}{70}=\frac{4}{5}[/tex]

Hence, both ratios are equal to each other

Hi I just need quick answers !

Answers

Question 1: Perimeter of baseDefinition of Perimeter: is the of the side lengths

         ⇒ Perimeter = 10 + 10 + 10 + 10 = 40 ft

Question 2: Find the slant height Definition of Slant Height:  is the distance measured along a lateral face from the base to the center along the "center" of the face

        To understand the slant height, look at the diagram I attached

       Slant height: 13 ft

Question 3:  Find the Lateral AreaDefinition of Lateral Area: Area of the non-base faces only

         ⇒ Lateral Area = 4 * (Area of Triangle)

                                    = [tex]4*(\frac{1}{2} *10 * 13) = 4 * 5* 13 = 260ft^2[/tex]

                                    = 260 ft^2

Question 4: Area of Base

       Area of Base = 10 * 10 = 100ft^2

Question 5: Surface AreaDefinition of Surface Area: sum of the areas of surfaces of the figure

        Surface Area = Area of Base + Lateral Area

                               = 100 + 260 = 360 ft^2

Hope that helps!

The angle \theta_1θ 1 ​ theta, start subscript, 1, end subscript is located in Quadrant \text{III}IIIstart text, I, I, I, end text, and \sin(\theta_1)=-\dfrac{\sqrt{3}}{2}sin(θ 1 ​ )=− 2 3 ​ ​ sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, square root of, 3, end square root, divided by, 2, end fraction .

Answers

So the answer is 4 I’m right u wrong ok I’m tell the truth trust me I got 5 hearts this morning

i need help with this i don't know how to do it.​

Answers

Answer:

1935 were supporting the home team

Step-by-step explanation:

Since there are 4,500 people attending the game, we must find 43% of that. Doing this, we need to multiply 43% or .43 by 4,500.

After solving, you should get 1,935. There were 1,935 people supporting the home team.

each row in the table below shows one possible set of angle measurements for this drawing

find the missing angle measurements​

Answers

Applying the definitions of angles on a straight line and vertical angles, the missing angle measurementts are given in the table atached below.

What are Angles on a Straight Line?

Angles found on a straight line equals 180 degrees.

What area Vertcial Angles?

Vertical angles are congruent angles that lie directly opposite each other.

Second Row:

m∠LGK = 45° (given in the diagram)

m∠IGH = 35° (given in the table)

m∠KGJ = m∠IGH (vertical angles)

m∠KGJ = 35°

m∠JGI = 180 - m∠KGJ (angles on a straight line)

m∠JGI = 180 - 35 = 145°

m∠HGL = 180 - m∠LGK - m∠IGH (angles on a straight line)

m∠HGL = 180 - 45 - 35 = 100°

Third Row:

m∠LGK = 45° (given in the diagram)

m∠HGL = 97° (given in the table)

m∠KGJ = 180 - m∠HGL - m∠LGK (angles on a straight line)

m∠KGL= 180 - 97 - 45 = 38°

m∠JGI = 180 - m∠KGJ (angles on a straight line)

m∠JGI = 180 - 38 = 142°

m∠IGH = m∠KGL (vertical angles)

m∠IGH = 38°

Thus, applying the definitions of angles on a straight line and vertical angles, the missing angle measurementts are given in the table atached below.

Learn more about straight line and vertical angles on:

https://brainly.com/question/14362353

Find the arc length of a central angle of 36° in a circle whose radius is 2 inches.

Answers

Answer:

y

Step-by-step explanation:

bc I told u to ..............

Given the function f(x)=3-2x^2, find k such that f(k)=-3

Answers

Answer:

k = ±√3

Step-by-step explanation:

Given :

f(x) = 3 - 2x²f(k) = -3

To find the value of k, we need to equate both the functions to find the value of x such that it is equal to the value of k.

⇒ 3 - 2x² = -3⇒-2x² = -6⇒ x² = 3⇒ x = ±√3

We already set a relation before, which is :

x = kTherefore, k = ±√3

A group of coins is shown below. What is the probability and it's compliment of randomly selecting a nickel?

Answers

Answer:

Please post the full question.

Step-by-step explanation:

I am trying to help, but the question is missing some key info.

Please dont delete, as when he posts the full thing, I will reply to this answer with the answer and explanation.

NEED ANSWERS TO THESE PAGES!!!!!

Answers

1. B
2. C
3. B
4. 0.045p +p
5. A
6. B

Evaluate each algebraic expression.

3w + 4 ; w = 1/4, 7, -2

Answers

Check my attached work for answer
Hope it helps, let me know if you have questions!:

Please help me with this please and thank you

Answers

Answer:

L bozo

Step-by-step explanation:

ur whole life is an L

need it ASAP If a graph shows intersecting lines that represent a system of equations, how many solutions does that system of equations have?
Infinite solutions
No solution
Two solutions
One solution

Answers

Answer: Well, the answer really depends. But here are a few ways you can figure this out.

Step-by-step explanation:

If the two lines intersect once, then they have one solution.

If they intersect twice there are two solutions

If the lines never intersect, there are no solutions

And if the lines are identical, meaning that their equation is exactly the same. There are infinite solutions.

A solution with systems of equations is determined by the point of intersection. Your answer is the point of intersection

I hope this is helpful! : )

Answer:

no s

Step-by-step explanation:

What is the scale factor of this dilation?

Answers

Answer:

I am not sure but I thing it is -2.

Step-by-step explanation:

Hope it helps! (Please mark brainliest if it does!)

1.6667

Step-by-step explanation:

the lengths are the same on both sides which makes the triangles equilateral

therefore the scale=5/3

=1.6667

Does the graph represent a function? Why or why not?

Answers

Yes, because there are no x repeats (passed vertical line test).

What is the measure of \angle D∠Dangle, D?

Answers

Answer:

135⁰

Step-by-step explanation:

As in cyclic quadrilateral sum if opposite angles is equal to 180⁰

Explain the error and solve with correct step.

-5x + 9 - 9x < 21

-4x + 9 < 21

-4x < 12

x > -3

Answers

i don’t know i have a feeling it has to do something with the -4

help me solve please show steps

Answers

There can be several possibilities and causes

y>2x-1

Then line will be dashed and solution region to be shaded.

y<2x-1

Same like before

y≤2x-1

Solid line should be done and shading the solution region

y≥2x-1

Same like before

y=2x-1

A straight line and no shading

Credit: Mister Brainly

There can be several possibilities and causes:

y>2x-1

Then line will be dashed and solution region to be shaded.

y<2x-1

Same like before

y≤2x-1

Solid line should be done and shading the solution region

y≥2x-1

Same like before

y=2x-1

A straight line and no shading

A grain silo has a cylindrical shape. Its radius is 8ft, and its height is 36ft. What is the volume of the silo?

Use the value 3.14 for[tex]\pi[/tex], and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.

Answers

The volume of a silo cylinder with radius of 8 feet and height of 36 feet is 7235 feet cube.

Volume of a cylinder

The volume of a cylinder can be calculated as follows;

Volume = πr²h

where

r = radiush = height

Therefore,

r = 8 ft

h = 36 ft

volume = 3.14 × 8² × 36

volume = 3.14 × 64 × 36

volume of the silo = 7234.56

Therefore, the volume of the cylindrical silo is 7235 ft³

learn more on volume here: https://brainly.com/question/27270919

What is the measurement of < F

Answers

Answer:

Option C - 65°

Step-by-step explanation:

Since the side lengths of this triangle are equal this triangle is an isosceles:

Because the triangle is an isosceles the base angles are equal so

∠G = ∠F = 65°

hello! this is an isosceles triangle, meaning that two sides are congruent.
angle g and angle f are also congruent so angle f is 65 degrees

1) 3x + 6 - 2 + 5x
2) a bicycle is originally priced at 80$. The store owner gives a discount and the bicycle is now 60$. What percent discount was taken off?

Answers

Answer: ✨4(2+1)✨

Step-by-step explanation: ✨3+6−2+53x+6−2+5x3+4+53✨

Answer:

4(2x + 1)

---->

Step-by-step explanation:

1:    3x + 6 - 2 + 5x = 4(2x + 1)

2:    Orignal Cost=80

Discounted Cost=60

Discount=80-60=20

Discount%=(20/80)*100=25%

Which of the following equations would describe the graph shown below?

Answers

Answer:

2

Step-by-step explanation:

WHOEVER ANSWERS THE QUESTION FIRST WILL GET 15 POINTS!!!!!

Answers

Answer:

b

Step-by-step explanation:

the answer is b

in the problem you can put the expression into a calculator and you will get the answer 3

in option b, y+2=3 bc a variable is always equal to one so your basically adding 1+2 which is equal to 3

I HOPE I HELPED A BIT<3

2x(5x-2)+(3x-0.5)*2=2x+3+10x-5+2x+3
Find X
(give step by step)

Answers

Answer:

x = 1.348331477 and 0.148331477

Step-by-step explanation:

TEPS USING THE QUADRATIC FORMULA2x(5x−2)+(3x−0.5)2=2x+3+10x−5+2x+3Use the distributive property to multiply 2x by 5x−2.10x2−4x+(3x−0.5)×2=2x+3+10x−5+2x+3Use the distributive property to multiply 3x−0.5 by 2.10x2−4x+6x−1=2x+3+10x−5+2x+3Combine −4x and 6x to get 2x.10x2+2x−1=2x+3+10x−5+2x+3Combine 2x and 10x to get 12x.10x2+2x−1=12x+3−5+2x+3 Subtract 5 from 3 to get −2.10x2+2x−1=12x−2+2x+3Combine 12x and 2x to get 14x.10x2+2x−1=14x−2+3Add −2 and 3 to get 1.10x2+2x−1=14x+1Subtract 14x from both sides.10x2+2x−1−14x=1Combine 2x and −14x to get −12x.10x2−12x−1=1Subtract 1 from both sides.10x2−12x−1−1=0Subtract 1 from −1 to get −2.10x2−12x−2=0This equation is in standard form: ax2+bx+c=0. Substitute 10 for a, −12 for b, and −2 for c in the quadratic formula, 2a−b±b2−4ac​​.x=2×10−(−12)±(−12)2−4×10(−2)​​Square −12.x=2×10−(−12)±144−4×10(−2)​​Multiply −4 times 10.x=2×10−(−12)±144−40(−2)​​Multiply −40 times −2.x=2×10−(−12)±144+80​​Add 144 to 80.x=2×10−(−12)±224​​Take the square root of 224.x=2×10−(−12)±414​​The opposite of −12 is 12.x=2×1012±414​​Multiply 2 times 10.x=2012±414​​Now solve the equation x=2012±414​​ when ± is plus. Add 12 to 414​.x=20414​+12​Divide 12+414​ by 20.x=514​+3​Now solve the equation x=2012±414​​ when ± is minus. Subtract 414​from 12.x=2012−414​​Divide 12−414​ by 20.x=53−14​​The equation is now solved.

x=514​+3​x=53−14​​

Help Needed. Please.....!

Answers

Answer:

1  7/8

Step-by-step explanation:

You just have to subtract 2 from 1/8.

What is the equation of the line passing through (0,2), with a slope of 5?

Answers

Answer:

y=mx+c

Finding the y-intercept by substituting the given points into the equation.

y=mx+c

2=5(0)+c

2-5=c

-3=c

Now, the equation is:

y=5x-3

what are the numbers for pie I need to know

Answers

Answer:

Pi is exactly [tex]3.1415926535897932384626433832795[/tex]

Pi is often used in mathematical expressions, calculating measurements, and finding circumference as well as volume.

65, 46, 78, 3, 87, 12, 99, 38, 71, 38

what is the median??

Answers

Answer:

median = 55.5

Step-by-step explanation:

Here we have 10 numbers which is an even number

then the median for the data set is the average of the two middle numbers

firstly ,we have to put the number of the set in order from least to greatest like this :

3 < 12 < 38 < 38 < 46 < 65 < 71 < 78 < 87 < 99

————————                     ————————-

As you can see the middle two numbers are : 46 and 65

Now, we calculate their average :

[tex]\large \text Median = \frac{46+65}{2}= 55.5[/tex]            

Tell whether each number is rational or irrational.0.121121112....

Answers

A rational number is any whole number or fraction that ends or repeats. An irrational number is a number that cannot be turned into a fraction.


It’s kind of hard to read the numbers because they’re to close but I hope that that helped you a little

Last one, I promise!!! ._.

19x+28=20x-53

Answers

Answer:

x = 81

Step-by-step explanation:

Given:

[tex]\displaystyle \large{19x+28=20x-53}[/tex]

Subtract both sides by 28:

[tex]\displaystyle \large{19x+28-28=20x-53-28}\\\displaystyle \large{19x=20x-81}[/tex]

Subtract both sides by 19x:

[tex]\displaystyle \large{19x-19x=20x-81-19x}\\\displaystyle \large{0=x-81}[/tex]

Add both sides by 81:

[tex]\displaystyle \large{0+81=x-81+81}\\\displaystyle \large{81=x}\\\displaystyle \large{\therefore x=81}[/tex]

Therefore, the solution is x = 81

Let me know if you have any questions!

[tex]{\boxed{\mathfrak{✿ฺSolution :}}} [/tex]

[tex] \bold{ 19x+28 = 20 x - 53 }[/tex]

[tex] \bold{ 19x+28 - 28 =20x - 53 - 28}[/tex]

[tex]\bold{ 19x = 20x - 81 }[/tex]

[tex]\bold{ 19x - 20x = 20x - 81 - 20x }[/tex]

[tex]\bold{ -x = - 81 }[/tex]

[tex]\bold{ \frac{ - x}{ - 1} = \frac{ - 81}{ - 1} }[/tex]

[tex] \bold{ x = 81 }[/tex]

Other Questions
What is one way in which the poem "The Jelly-Fish" by Marianne Mooreembodies Ezra Pound's rules of Imagism?A. It does not use descriptive words.B. It creates several images.C. It has an exact meter.D. It does not use excess words. UNIT 5: CEREAL BOX PROJECT / PORTFOLIO You have five employees. They work the following number of hours last week: 42, 26, 39, 12, 55. What is the median number of hours worked The volume of a cylinder is 48n cubic feet. Thearea of the base is 121 square feet.What is the height of the cylinder? The slope for 5 and 2 What is the SI (metric) unit of FORCE?A. meterB. newton There are 31 passengers split between 3 cars in the Metrolink. How many passengers per car? what is diversity in 200 words helpppp: Find the area of the parallelogram. Combine the sentences into one sentence. giving brainliest please help! 12.1 arithmetic sequences algebra 2 volume 2 answers What are ways to take advantage of the month to be a better Muslim? Today we call false accusations against a large number of people a mrs. vickers is covering her students work table with chalkboard paper. the table is a radius of 3.8 ft. How much paper will she need? WHO ANSWER'S THE FIRST WITH THE CORRECT ANSWER WILL GET FREE BRAINLIST!!!Michiko claims that to solve the system of linear equations 15x + 8y = 1 and 21x + 4y = -13, instead of multiplying the second equation by 2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct?A: Michiko is right for this system of linear equations, but her method will not work for other systems of linear equations.B: Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations.C: Michiko is wrong because her method will give the opposite of the correct value for x for any system of linear equations.D: Michiko is wrong because her method will give the opposite of the correct value for y for any system of linear equations. Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69^{\circ} with the ground. Whats the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary. Which expression is equivalent? Which expression is a prime polynomial?O A 8.37 - 9 + 12-2OB. 19 - yOC. I +9y2OD 3m + 9n Muhammad Ali donated millions of dollars to charity throughout his lifetime. He was one of the greatest boxers of all time. Quill