The path of a skateboarder can be modeled by the equation (x – 4)2 = –4(y – 9), where distance is in feet and air resistance is insignificant. If the skateboarder makes a jump from a ramp at x = 0, what is her maximum height and how far is she horizontally from the end of the ramp when she lands?
Maximum height 4 feet; horizontal distance 12 feet
Maximum height 5 feet; horizontal distance 10 feet
Maximum height 9 feet; horizontal distance 12 feet
Maximum height 9 feet; horizontal distance 10 feet

Answers

Answer 1

Answer:

Maximum height 9 feet; horizontal distance 10 feet

Step-by-step explanation:

First, let's get the distance out of they way

When the skateboard lands, her height will be at 0 feet, so y has to equal 0

(x - 4)² = -4(0 - 9)

(x - 4)² = -4(-9)

(x - 4)² = 36

Square root both sides

√(x - 4)² = √36

x - 4 = 6

Note that x - 4 = -6 is also possible

Add 4 to both sides

x - 4 = 6

 + 4  + 4

x = 10

Note that x = -2 is also an answer. but not valid

To find the max height

Remember our zeros? x = -2, x = 10

The number in the middle would be 4

Plug 4 in place of the x in the original equation

(4 - 4)² = -4(y - 9)

(0)² = -4(y - 9)

0 = -4(y - 9)

You can divide both sides by 4

0/4 = (-4(y - 9))/4

0 = y - 9

+ 9    + 9

y = 9

Vertex is (4,9); or in other words, 9 feet is the max height


Related Questions

someone plz help me plzzzzzzz

Answers

Answer:

Step-by-step explanation:

30÷2/5 = 75

75

Draw a possible function that satisfy the given domain and range

Answers

9514 1404 393

Answer:

  see attached.

Step-by-step explanation:

Your graph demonstrates a possible function, but it has the domain and range swapped.

__

The domain is the horizontal extent, so your line must end at x=-9 on the left and x=6 on the right.

The range is the vertical extent, so the function must extend from -4 at the bottom to +8 at the top.

The attachment shows a linear function with those characteristics.

Which of these represent the statement, "36 is 4 times as many as 9"?

Answers

Answer:

36=4*9

Step-by-step explanation:

Help me with this lol

Answers

Answer:

here are answers of 21 22,23,24

Step-by-step explanation:

11 ,21,15,9

7. Yin's cellphone plan costs $30 a month. She used 22.5 hours in May
What was her cost per minute?

Answers

Answer:

CPM = ~$0.02

Step-by-step explanation:

[tex]22.5 Hours = 1350Minuets\\\frac{30}{1350} = 0.0(2)\\[/tex]

Which of the following is the probability that a blue marble will NOT be selected from a bag containing 9 red marbles, 6 blue marbles, 7 green marbles, and 11 yellow marbles if one is selected randomly?

Answers

Answer:

The chance of 18.18 percent.

Step-by-step explanation:

9 red marbles

6 blue marbles

7 green marbles

11 yellow marbles

9+6+7+11=33

33 total marbles.

The chance of getting red marbles of the 33 is 27.27

The chance of getting blue marbles of the 33 is 18.18

The chance of getting green marbles of the 33 is 21.21

The chance of getting yellow marbles of the 33 is 33.33

please solve the following equations?​

Answers

Answer:

I only solved the first equation

a) x = 30

Step-by-step explanation:

a) [tex]log_4(2log_3(1+log_2(1+3log(x/3)))) = 1/2\\4^{1/2} = 2log_3(1+log_2(1+3log(x/3)))\\(2^{2})^{1/2} = 2log_3(1+log_2(1+3log(x/3)))\\\\2 = 2log_3(1+log_2(1+3log(x/3)))\\\\\\1 = log_3(1+log_2(1+3log(x/3)))\\\\\\\\3^1 = 1+log_2(1+3log(x/3))\\3 -1 = log_2(1+3log(x/3))\\\\2 = log_2(1+3log(x/3))\\\\\\2^2 = 1+3log(x/3)\\4 -1 = 3log(x/3)\\\\3 = 3log(x/3)\\\\\\1 = log(x/3)\\10^1 = x/3\\x = 30[/tex]

solve the equation for y and then graph it. 9y-x=18

Answers

Answer: 2+ x/9

graphed

x  y

0 2

9 3

Step-by-step explanation:

Find the value of 2xy+3yz −xyz, when x=2, y=−2and z =4

Answers

Answer:

-8-24+16

-16

Step-by-step explanation:

Hope it helps you

The answer you are looking for is -16

Question 8 of 10
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark ( as the fraction bar if necessary.

Answers

Answer:

2/4 or 1/2

Hope this helps!

The slope of the line that passes through (-2, -3) and (2, -1) will be 1/2.

What is the slope?

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the points are (-2, -3) and (2, -1). Then the slope of the line is calculated as,

m = (- 3 + 1) / (-2 - 2)

m = 2/4

m = 1/2

The slope of the line that passes through (-2, -3) and (2, -1) will be 1/2.

More about the slope link is given below.

https://brainly.com/question/3605446

#SPJ7

-4 2/3 • 1 4/5
Help me with this

Answers

the answer is -42/5 :D

can't type because im lazy

Evaluate the expression when c=12 and d=112.

3(14+c2)+2d

Enter your answer as a mixed number in simplest form in the box.

Answers

Answer:

698 or 338

Step-by-step explanation:

3*(14+[tex]c^{2}[/tex]) +2d

3*(14+[tex]12^{2}[/tex])+2*112 = 42+3*[tex]12^{2}[/tex]+224

42+3*144+224 = 42+432+224 = 698

3*(14+12*2)+2*112

3(14+24)+2*112 = 3*38+224 = 114+224 = 338

Answer:Substitute the value of the variable into the expression and simplify.

698

Step-by-step explanation:

PLEASE HELP!!!!!
will mark brainliest!!!!!

Answers

Answer:

(-9,-6) ,(-3,0),(-2,1),(4,7)(6,9)

Answer:

x = -9 —> f(x) = – 6

x = -3 —> f(x) = 0

x = -2 —> f(x) = 1

x = 4 —> f(x) = 7

x = 6 —> f(x) = 9

Step-by-step explanation:

x = -9 —> f(x)= x+3 —> f(-9)= -9+3 = -6 —> f(x) = – 6

x = -3 —> f(x)= x+3 —> f(-3)= -3+3 = 0 —> f(x) = 0

x = -2 —> f(x)= x+3 —> f(-2)= -2+3 = 1 —> f(x) = 1

x = 4 —> f(x)= x+3 —> f(4)= 4+3 = 7 —> f(x) = 7

x = 6 —> f(x)= x+3 —> f(6)= 6+3 = 9 —> f(x) = 9

I hope I helped you^_^


Junie bought bananas at the store on Monday. She bought four
and twenty-two hundredths pounds of bananas. How do you
write this number in decimal form?

Answers

Answer:

4.22

Step-by-step explanation:

twenty-two hundredths = .22

Answer:

22

Step-by-step explanation:

In the year 2008, a person bought a new car for $26500. For each consecutive year
after that, the value of the car depreciated by 12%. How much would the car be worth
in the year 2010, to the nearest hundred dollars?

Answers

Answer:

$20500

Step-by-step explanation:

26500-(.12*26500)=23320 For 1 year

23320-(.12*23320)=$20521.60 For 2 years

1/16 1/14 1/2 1/6 1/50 1/30 1/8 1/40 1/20 1/5 1/100 1/625 1/25 1/45 1/125 1/12 1/32 1/7 1/28 1/24 1/64 1/11 1/4 1/21

Determine which fractions in the list can be written as terminating decimals.
List these fractions in order from greatest to least.

Answers

Answer:None

Step-by-step explanation:

Excel tells me that all of the numbers have terminating decimals.  One might ask for a definition of what is considered terminating.  Is 1/14=

0.0714285714285714000000000 going too many places before concluding it is not terminating?

X                               1/X

16 0.0625000000000000000000000

14 0.0714285714285714000000000

2 0.5000000000000000000000000

6 0.1666666666666670000000000

50 0.0200000000000000000000000

30 0.0333333333333333000000000

8 0.1250000000000000000000000

40 0.0250000000000000000000000

20 0.0500000000000000000000000

5 0.2000000000000000000000000

100 0.0100000000000000000000000

625 0.0016000000000000000000000

25 0.0400000000000000000000000

45 0.0222222222222222000000000

125 0.0080000000000000000000000

12 0.0833333333333333000000000

32 0.0312500000000000000000000

7 0.1428571428571430000000000

28 0.0357142857142857000000000

24 0.0416666666666667000000000

64 0.0156250000000000000000000

11 0.0909090909090909000000000

4 0.2500000000000000000000000

21 0.0476190476190476000000000

solve each problem using picturesand using a number sentence involing division

Answers

Answer:

Sorry, but I'm not seeing the question to solve.

Did you mean to attach any pictures?

Helppppppppppppponnmammam

Answers

Answer:

xd

Step-by-step explanation:

1*41*4*4*

PLEASE HELP!!!!

Given A and B, use your knowledge of sets to determine which one of the following numbers is not in
AUB.
A = {-10, 8, 12, 26, 29}
B = {-8, - 1,5, 26, 36}


A.18
B. -10
C. 26
D. 36
E. None of the above

Answers

Answer:   A.  18

===========================================================

Explanation:

The set A U B represents the list of items that are either in set A, set B or both sets at the same time. The "U" is the union symbol.

Set A U B looks like this

A U B = {-10, 8, 12, 26, 29,   -8, - 1,5, 26, 36}

I basically started with set A, then tacked on the stuff in set B shown in bold.

From here, we toss out the duplicate item 26 and we can optionally sort the set

A U B = {-10, -8, -1, 5, 8, 12, 26, 29, 36}

We see that the number 18 is not in this final set, which is why choice A is the answer.

--------------------

Put another way: the number 18 is neither in set A nor set B, so it cannot be in set A U B.

Something like -10 is in set A, so it's going to be in set A U B as well. We can rule out choice B for this reason. Choices C and D follow a similar idea as choice B.

e. If a basketball player made 72 out of 85 free throw attempts, how many could she expect to make and 200 attempts

Answers

Answer:

170

Step-by-step explanation:

72/85=.85

.85x200=170

170 out of 200 attempts

5x-3y=20 line perpendicular

Answers

Answer:

y=(-3/5)x

Step-by-step explanation:

5x-3y=20

-3y=-5x+20

y=(5/3)x-(20/3)

perpendicular lines have opposite reciprocal slopes

Answer:

Perpendicular line is y = -3/5 x - 20/3

Step-by-step explanation:

First subtract 5x to move it to the other side. Now you have -3y = -5x + 20 . Next divide -3 on both sides to get y by its self. Now you have

y = 5/3 x - 20/3.

To find the perpendicular line, just remember that slope will be opposite. Look at the graph, I did for you above.⤴⤴⤴

Hope this helped :)

Help please (I have to write something so that I can post a question) ​.

Answers

Step-by-step explanation:

answers: -9

the ground

^^^^^^^^^^^

PLS HELP ME UNDERSTAND THIS quUESTION!!

Answers

Answer:

-2 11/35

GOOD LUCK!!

30 points!

Paul has
$20000
to invest. His intent is to earn
9%
interest on his investment. He can invest part of his money at
6%
and part at
10%
interest. How much does Paul need to invest in each option to make a total of 9%
return on his
$20000
?

6%: ?

10%: ?

Answers

Step-by-step explanation:

0,06x + 0,1(20000-x) = 0,09(20000)

0,06x + 2000 - 0,1x = 1800

-0,04x = -200

x = -200 /(-0,04)

x = 5000

therefore,

for 6% interest => total invest =$5000

for 10% interest => total invest = $15000

Screenshoting my answer because brainly somehow thinks there are bad words...

show your work” below and solve the given equation for x showing all your steps.
3.5(6 – x) + 14 = 7 – 1.5(5x + 16)
please make the steps as clear as you can for brainliest!

Answers

Answer:

x=-13

Step-by-step explanation:

21-3.5x+14=7-7.5x-24

21+14-3.5x=7-24-7.5x

35-3.5x=-17-7.5x

35+17=3.5x-7.5x

52=-4x

-4. -4

x=-13

I need help with question 20

Answers

20 because 10+10=20 and 20+20=40 and 20+40=60

Answer:

20 feet

Step-by-step explanation

Here's what you know.

Perimeter-60 feet

width is 10 feet less than the length.

If the length is 20, the width has to be 10. 20+10+10+20 equals 60. Hope this helps-Brainliest plz

write the factors of 20 that are not also factors of 12​

Answers

5 & 10 and 20 are factors of 20 that are also not factors of 12

Hope this helped you- have a good day bro cya)

The factors of 20 that are not also factors of 12​ are 5 and 10.

What is a factor?

A factor exists as a number that divides the assigned number without any remainder. The factors of a digit can either be positive or negative. The factors of any number exist as finite.

To estimate the factors of 20 and 12

To estimate the factors of 20

Find the prime factors of 20 are 2, 2, and 5.

Multiply the prime factors of 20 are 4, 10.

Adding prime factors 2, 5

Add 1 and the number 20 itself 1, 20.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

To estimate the factors of 12

Find the prime factors of 20 are 2, 2, and 3.

Multiply the prime factors of 12 are 4, 6.

Adding prime factors 2, 3

Add 1 and the number 20 itself 1, 12.

The factors 12 are 1, 2, 3, 4, 6, and 12.

Therefore, 5 and 10 factors of 20 that are not also factors of 12​.

To learn more about prime factors refer to:

https://brainly.com/question/340559

#SPJ2

Complete the table of values

Answers

Answer:

x = 0 —> y = 0 —> ( 0 , 0 )

x = 1 —> y = – 2 —> ( 1 , – 2 )

x = 5 —> y = – 10 —> ( 5 , – 10 )

x = -3 —> y = 6 —> ( -3 , 6 )

Step-by-step explanation:

x = 0 —> y = -2x = -2(0)=0

x = 1 —> y= -2x = -2(1) = -2

x = 5 —> y = -2x = -2(5) = -10

x = -3 —> y = -2x = -2(-3) = 6

I hope I helped you^_^

De enero a junio, 46200 inmigrantes solicitaron la ciudadanía. Durante este mismo período el año pasado, se postularon 120000 inmigrantes. ¿Cuál es el porcentaje de disminución?

Answers

Usando el concepto de porcentaje, se encuentra que el porcentaje de disminución es de 61.5%.

El porcentage de disminución es la disminución multiplicada por 100% y dividida por la cantidad inicial.

Disminución de 120000 imigrantes para 46200 imigrantes, entonces:

[tex]P = \frac{(120000 - 46200)}{120000} \times 100\% = 61.5\%[/tex]

El porcentaje de disminución es de 61.5%.

Un problema similar es dado en https://brainly.com/question/24547889


About how many years did it take to pay off this account if...
Principal = $1582
Rate = 2.5%
Interest = $79.10
Answer:
years

Answers

Answer:

2 years

Step-by-step explanation:

Simple Interest=P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

so with the givens, 79.10=1582*0.025*x

79.10/(1582*0.025)=x

x=2 years

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