A person standing on a second floor balcony drops keys to a friend standing below the balcony. The keys are dropped from a height of 10 feet. The height in feet of the keys as they fall is given by the functionh(t)=−16t2+10, where t is the time in seconds since the keys were dropped.

The friend catches the keys at a height of 4 feet. Find the elapsed time before the keys are caught.

Answers

Answer 1

Answer:

sqrt(3/8) = t

.61237 = t

Step-by-step explanation:

h(t)=−16t^2+10

Let h(t) = 4

4 =−16t^2+10

Subtract 10 from each side

4-10 =−16t^2+10-10

-6 = -16 t^2

Divide by -16

-6/-16 = t^2

3/8 = t^2

Take the square root of each side

sqrt(3/8) = sqrt(t^2)

sqrt(3/8) = t

.61237 = t

We only take the positive since time is not negative


Related Questions

Don't forget! If you multiply or divide by a negative number, you must
flip the inequality symbol!

I need help with these 2 and ignite the 5 and 6 it’s the question number

Answers

Answer:

c > 20

make a number line that starts with the number 16 and ends with 22.

on the number 20 circle it (don't fill in the circle).

then draw an arrow to the right on top of the circle that you circled.

Step-by-step explanation:

What is the solution to this inequality?
[tex]x \div 12 + 3 \leqslant 7[/tex]

Answers

x/12 + 3 < 7

Subtract 3
x/12 < 4

Multiply by 12
x < 48

Check:
Let x = 0 which is less than or equal to 48

0/12 + 3 < 7
0 + 3 < 7
3 < 7 :)

Label the chart with the correct place value. hundredths tenths thousandths

Answers

Answer:

1020000is a hundredth tenths thousands

PLEASE HELP

Find the number of edges on this solid

Answers

Answer:

8

Step-by-step explanation:

count the number of solid-black lines.

Peyton, Nathan and Alexandra sold their stuffies for a fundraising event.
Peyton sold two more than four times the stuffies Nathan.
Alexandra sold half as many stuffies as Peyton.
Each stuffie was sold for $2.50. Together they fundraised $130.
How many stuffies did each person sell?

Answers

Answer:

p = 30, n = 7, a = 15

Step-by-step explanation:

Let's say that p is the amount of stuffies Peyton sold, n is the amount of stuffies Nathan sold, and a is the amount of stuffies Alexandra sold.

Peyton sold two more than four times the stuffies Nathan sold.

This means that: p = 2 + 4n (n = (p-2)/4)

Each stuffie was sold for $2.50. Together they fundraised $130.Alexandra sold half as many stuffies as Peyton.

This means that: a = p/2

Each stuffie was sold for $2.50. Together they fundraised $130.

This means that: 2.50p + 2.50n + 2.50a = 2.50(p + n + a) = 130

We can make the equation in terms of p by substituting a and n.

2.50(p + n + a)

= 2.50(p + (p-2)/4 + p/2)

= 2.50(4p/4 + (p-2)/4 + 2p/4)   [Make the p's have a denominator of 4]

= 2.50((4p + p - 2 + 2p)/4)

= 2.50((7p-2)/4)

= 5/2 * (7p-2)/4

= 5(7p-2)/8

= (35p-10)/8 = 130

35p-10 = 1040

35p = 1050

p = 30

n = (30-2)/4

  = 7

a = 30/2

  = 15

Find the width of the rectangular prism which has Surface area of 10 CM2, length of 2cm and height of 1 cm

Answers

Answer:

width is 1 cm

Step-by-step explanation:

The SA of a rectangular prism is SA = 2(lw + wh + hl)

We are given the length, the height, and the SA, and we need to find the width. So we plug in the known values into this equation:

10 = 2(2w + w + 1*2)

10 = 2(3w+2)

10 = 6w+4

6=6w

w=1

We can check the answer by plugging in all the values into the equation:

10 = 2(2*1+1*1+1*2)

10 = 2(5)

10 = 10

3/4 part of a rope is 150m. find the length of 7/10 part of the rope
Please help ASAP with step by step explanation.

Answers

Answer:

140m

Step-by-step explanation:

3/4 = .75

x/.7 = 150/.75

multiply both sides by .7

x = 150/.75 * .7

x = 140m

What Value of X satisfies this equation?

Answers

Answer:

x=0

Step-by-step explanation:

4 ( 2.5) ^x = 4

Divide each side by 4

4/4 ( 2.5) ^x = 4/4

( 2.5) ^x = 1

Take the log of each side

log  ( 2.5) ^x =  log (1)

x log ( 2.5) = log 1

x log (2.5) = 0

Divide each side by log (2.5)

x = 0

NEED HELP; What is the value of x?

X/8=6/12

A. 3
B. 5
C. 4.
D. 0.5

Answers

Answer:

the answer is 4

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x=4
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The graph shown is a scatter plot:
Which point on the scatter plot is an outlier?

Answers

Answer:

D is the outlier

Step-by-step explanation:

An outlier is a point that is far from the other points

We can draw a line that roughly represents an equation for the points

A,B ,C are all near the line

D is not along the line

Find the quotient.the fraction
8 1/3 divided by 4 1/2​

Answers

Answer:

[tex]8 \frac{1}{3} \div 4 \frac{1}{2} = \frac{50}{27} = 1.851 = 1 \frac{23}{27} [/tex]

find the difference (2m+3)-(7m-5)

Answers

Answer:

- 5m + 8

Step-by-step explanation:

Given:

(2m + 3) - (7m - 5)

If you want to find the differences between two values, it means you are to subtract

(2m + 3) - (7m - 5)

This means subtract (7m - 5) from

(2m + 3)

Step 1: Open parenthesis

(2m + 3) - (7m - 5)

= 2m + 3 - 7m + 5

Group like terms

= 2m - 7m + 3 + 5

= - 5m + 8

Or

= 8 - 5m

Mary has a rectangular driveway. She measures it and finds out it is 14 1/4 feet long by 17 1/2 feet wide. She wants to know how many square feet of paint she will need to completely cover the driveway.

Answers

Answer:

253.75 square feet

253 feet is the answer

Here is some information about a holiday.
7 night holiday
$340 per person
8% discount if you book before 31 March

On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.

Answers

Answer:

$625.6

Step-by-step explanation:

Information about the holiday:

7 night holiday

$340 per person

8% discount if you book before 31 March

Number of people Naseem booked the holiday for = 2

Date of booking of the holiday = 15 February

Total cost of the holiday per person = cost per person - discount before March 31

= $340 - 8% of $340

= 340 - 8/100 * 340

= 340 - 0.08 * 340

= 340 - 27.2

= $312.8

Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person

= 2 * $312.8

= $625.6

What is the slope of the line shown below?

Answers

Answer:

The answer is C

Step-by-step explanation:

1-(-7)=8

9-(-3)=12

8/12=2/3

can someone please help for brainlest

Answers

Answer:125√3:6

Step-by-step explanation:

A cylinder with a radius of 6cm and height of 15 cm has a cylindrical cut out of the
middle of it with a radius of 5 cm.
Find the volume of the cylinder that remains, rounded to the nearest whole number.

Answers

Answer:

[tex]V = 518cm^3[/tex]

Step-by-step explanation:

Given

[tex]h = 15cm[/tex]

[tex]R = 6cm[/tex]

[tex]r =5cm[/tex]

Required

The volume of the remaining cylinder

Before the cut-out, the cylinder has a volume (V) of:

[tex]V = \pi R^2h[/tex]

After the cut-out, the cylinder has a volume of:

[tex]V = \pi [R^2 -r^2]h[/tex]

So, we have:

[tex]V = 3.14* [6^2 -5^2]*15[/tex]

[tex]V = 3.14* [36 -25]*15[/tex]

[tex]V = 3.14* 11*15[/tex]

[tex]V = 518cm^3[/tex]

which statement would be true if you evaluate the expression 18x (365x12)
a. the solution is 3 times as small as 6x(365x12)
b. the solution is 6 times as small as (365x12)
c. the solution is 3 times as large as 6x(365x12
d. the solution is 3 times as large as 6x(365+12)

Answers

Answer:

c. the solution is 3 times as large as 6x(365x12)

Step-by-step explanation:

c. the solution is 3 times as large as 6x(365x12)

QUICK I NEED HELP! I WILL MARK BRAINLIEST!

Answers

Answer:

go a head what can i help you with

Answer:

Step-by-step explanation:

[tex]y_A = 9x -3x - 4 \\y_A = 6x - 4\\\\y_B = 12x - 4\\\\y_C = 5x + x - 4\\y_C = 6x -4[/tex]

Standard equation of a line with slope, m and y - intercept b is y = mx + b.

Clearly. for  the second equation has a different coefficient for x.

a ) The coefficient for x , is the slope of the line.

     Though the y - intercept for each equation is same = - 4.

    For example :

  Expression A = 2 , when x = 1

  Expression B = 8 , when x = 1

  Expression C = 2 , when x = 1

b) From above :

        [tex]y_A \ and \ y_C \ are \ the \ same \ expression.[/tex]

c) Expression A and  C are equivalent because the coefficient of x

    is the same  for A and  C.

 

Find angle N and arc NQ. See the image below.

Answers

Answer:

Angle N=32

Arc NQ=106

Step-by-step explanation:

Angle N is a inscribed angle of Arc MP so that means Angle N measures 32.

Angle NPQ is a inscribed angle of Arc NQ so that means Arc NQ is twice the measures of NPQ so

Arc NQ=106

The function f is defined by f(x) = (x − 2) 2 − 3 for x > −2. The function g is defined by g(x) = 2x+6 x−2 for x > 2. Find fg(7).

Answers

Answer:

[tex]fg(7)=143.95[/tex]

Step-by-step explanation:

We are given that

[tex]f(x) = (x -2)^2 -3[/tex] for x > −2

[tex]g(x) = 2x+6x^{-2}[/tex] for x > 2

We have to find fg(7)

[tex]fg(7)=f(g(7))[/tex]

[tex]=f(2(7)+6(7)^{-2})[/tex]

=[tex]f(14+\frac{6}{49})[/tex]

=[tex]f(\frac{692}{49})[/tex]

692/49>-2

fg(7)=[tex](\frac{692}{49}-2)^2-3[/tex]

=[tex]146.95-3[/tex]

Hence, [tex]fg(7)=143.95[/tex]

plzz help 100 points
Part B
What is the measurement of angle G? Part C
Let the variable c represent the measurement of angle C. Use the measurement of angle G to write an equation that you can use to solve for c. Part D
What is the measurement of angle C?

Answers

Finishing the angles of the smaller triangle if E is 90 and F is 30 then G needs to be 180-90-30 = 60 degrees.

Angles G and C are supplementary angles which need to equal 180 degrees

Angle c = 180-g = 180-60 = 120

Angle c = 120 degrees.

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then Δ EGF

∠ G = 180° - (90 + 30)° = 180° - 120° = 60°

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

c and g are adjacent angles and sum to 180° , then

c + g = 180° , that is

c + 60° = 180° ( subtract 60° from both sides )

c = 120

That is ∠ C = 120°

An excursion group of four is to be drawn from among 5 boys and 6 girls.
Find :
a. the number of ways of choosing the excursion group if the group :

i. Is to be made up of an equal number of boys and girls.
ii. Is to be either all-boys or all-girls.
III. Has no restriction on its composition.
b. Whatis the probability that a random choice of numbers from the group will result in 3 boys and 1 girl.​

Answers

Answer:

Because you are recounting people several times. Say for example, let us number those people

{1,2,3,4} for the four girls and {1,2…7} for the boys.

One possible combination by your way is to fix one boy and girl each, say

{1,1} and then choose the remaining people. Let this combination be, for the sake of the example, {1,1,2,2,3}. This is a valid combination.

Now, when you fix another combination of a boy and a girl, say {1,2}, you could get the same combination as before because one the combinations while choosing the three remaining people would be {1,2,3}.

A correct way would be to choose  girls and then choose 5− boys for 1≤≤4

So we get ∑4=1(4)(75−)=441

Answer:

We need group of 4 out of group of 5 + 6 = 11 people.

Part A

i)

2 boys and 2 girls:

5C2 * 6C2 = (5*4/2) * (6*5/2) = 150 ways

ii)

4 boys or 4 girls:

5C4 + 6C4 = 5 + 15 = 20 ways

iii)

No restrictions:

11C4 = (11*10*9*8)/(4*3*2) = 330 ways

Part B

Combination of 3 boys and 1 girl:

5C3*6C1 = (5*4/2)*6 = 60

Total number of ways is 330 (found above)

Required probability:

P(3 boys and 1 girl) = 60/330 ≈ 0.1818 = 18.18%

Can someone explain this to me please

Answers

Answer:

c. 36·x

Step-by-step explanation:

Part A

The details of the circle are;

The area of the circle, A = 12·π cm²

The diameter of the circle, d = [tex]\overline {AB}[/tex]

Given that [tex]\overline {AB}[/tex] is the diameter of the circle, we have;

The length of the arc AB = Half the the length of the circumference of the circle

Therefore, we have;

A = 12·π = π·d²/4 = π·[tex]\overline {AB}[/tex]²/4

Therefore;

12 = [tex]\overline {AB}[/tex]²/4

4 × 12 = [tex]\overline {AB}[/tex]²

[tex]\overline {AB}[/tex]² = 48

[tex]\overline {AB}[/tex] = √48 = 4·√3

[tex]\overline {AB}[/tex] = 4·√3

The circumference of the circle, C = π·d = π·[tex]\overline {AB}[/tex]

Arc AB = Half the the length of the circumference of the circle = C/2

Arc AB = C/2 = π·[tex]\overline {AB}[/tex]/2

[tex]\overline {AB}[/tex] = 4·√3

∴ C/2 = π·4·√3/2 = 2·√3·π

The length of arc AB = 2·√3·π cm

Part B

The given parameters are;

The length of [tex]\overline {OF}[/tex] = The length of [tex]\overline {FB}[/tex]

Angle D = angle B

The radius of the circle = 6·x

The measure of arc EF = 60°

The required information = The perimeter of triangle DOB

We have;

Given that the base angles of the triangles DOB are equal, we have that ΔDOB is an isosceles triangle, therefore;

The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex]

The length of [tex]\overline {OB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {FB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {OF}[/tex] = 2 × [tex]\overline {OF}[/tex]

∴ The length of [tex]\overline {OD}[/tex] = 2 × [tex]\overline {OF}[/tex] = The length of [tex]\overline {OB}[/tex]

Given that arc EF = 60°, and the point 'O' is the center of the circle, we have;

∠EOF = The measure of arc EF = 60° = ∠DOB

Therefore, in ΔDOB, we have;

∠D + ∠B = 180° - ∠DOB = 180° - 60° = 120°

∵ ∠D = ∠B, we have;

∠D + ∠B = ∠D + ∠D = 2 × ∠D = 120°

∠D = ∠B = 120°/2 = 60°

All three interior angles of ΔDOB = 60°

∴ ΔDOB is an equilateral triangle and all sides of ΔDOB are equal

Therefore;

The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex] = The length of [tex]\overline {DB}[/tex]  = 2 × [tex]\overline {OF}[/tex]

The perimeter of ΔDOB = The length of [tex]\overline {OD}[/tex] + The length of [tex]\overline {OB}[/tex] + The length of [tex]\overline {DB}[/tex] = 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] = 6 × [tex]\overline {OF}[/tex]

∴ The perimeter of ΔDOB = 6 × [tex]\overline {OF}[/tex]

The radius of the circle = [tex]\overline {OF}[/tex] = 6·x

∴ The perimeter of ΔDOB = 6 × 6·x = 36·x

f(x)=3(0.75)x exponential growth or exponential decay​

Answers

Answer:Exponential Decay


Explanation: It’s less than 1

Pls help me and thank you!

Answers

Answer:

Substitute your answer for Step 1 into the second equation to solve for Z.

Jada walks dogs to earn money. The points in this graph represent the total amount of money Jada earns based on the number of hours she walks dogs. Jada wants to purchase a new jacket that costs $32.

How many hours does Jada need to walk dogs to earn enough money to buy the jacket?


6 hours

7 hours

8 hours

9 hours

Answers

Answer:

8 hours

Step-by-step explanation:

In 4 hours she earns 16 dollars

Since this is proportional ( goes through zero), we can multiply by 2

8 hours = 32 dollars

Jada needs to walk the dog for, 8 hours.

4x8 = 32

Find the percentage decrease ???​

Answers

Step-by-step explanation:

Price of a book costing sh.250

reduced to sh.200

percentage decrease on the price = (250-200)/250×100

= 20%

Put these numbers in order from least to greatest.

0.92,0.43, and 9/10

Answers

Answer:

0.43,9/10,0.92

Step-by-step explanation:

Answer:

0.43, 9/10, 0.92

Step-by-step explanation:

9/10=0.9=0.90


Please help!

You want to buy a carpet for a room that is 15 feet wide and 18 feet long. Find the amount of carpet that you need.

Answers

15*18= 270 so 270 feet of carpet
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