Calculating Object's Height A boulder sitting on the edge of a cliff has 15,500 J of gravitational potential energy and a mass of 500 kg. Determine the height above Earth's surface that the boulder rests. P.E. = mass × 9.8 (gravity) × height​

Answer:

1)x=20

3)p=−12

5)n=−9

7)r=−18

9)x=−2

11)n=46

2)n = 3

4)v=9

6)n=−6

8)k=−17

10)x=12

12)x=−32

Step-by-step explanation:

Let's solve your equation step-by-step.

1) 2+x=22

Step 1: Simplify both sides of the equation.

x+2=22

Step 2: Subtract 2 from both sides.

x+2−2=22−2

x=20

3) −6+p=−18

Step 1: Simplify both sides of the equation.

p−6=−18

Step 2: Add 6 to both sides.

p−6+6=−18+6

p=−12

5) −29=−20+n

Step 1: Simplify both sides of the equation.

−29=n−20

Step 2: Flip the equation.

n−20=−29

Step 3: Add 20 to both sides.

n−20+20=−29+20

n=−9

7) −5+r=−23

Step 1: Simplify both sides of the equation.

r−5=−23

Step 2: Add 5 to both sides.

r−5+5=−23+5

r=−18

9) 11=x+13

Step 1: Flip the equation.

x+13=11

Step 2: Subtract 13 from both sides.

x+13−13=11−13

x=−2

11) 101=n+55

Step 1: Flip the equation.

n+55=101

Step 2: Subtract 55 from both sides.

n+55−55=101−55

n=46

2) −15=−18+n

Step 1: Simplify both sides of the equation.

−15=n−18

Step 2: Flip the equation.

n−18=−15

Step 3: Add 18 to both sides.

n−18+18=−15+18

n=3

4) −18+v=−9

Step 1: Simplify both sides of the equation.

v−18=−9

Step 2: Add 18 to both sides.

v−18+18=−9+18

v=9

6) −19=n−13

Step 1: Flip the equation.

n−13=−19

Step 2: Add 13 to both sides.

n−13+13=−19+13

n=−6

8) −12=k+5

Step 1: Flip the equation.

k+5=−12

Step 2: Subtract 5 from both sides.

k+5−5=−12−5

k=−17

10) 11=−1+x

Step 1: Simplify both sides of the equation.

11=x−1

Step 2: Flip the equation.

x−1=11

Step 3: Add 1 to both sides.

x−1+1=11+1

x=12

12) x−36=−68

Step 1: Add 36 to both sides.

x−36+36=−68+36

x=−32

Answer:

-34.5

Step-by-step explanation:

Put together like terms:

-7x-6.5

-28-6.5

-34.5

No. of children in lamb, chicken, duck, and turkey category is 66, 24, 18 and 12 respectively.

Percentage is the value per hundredth.

According to the given question a survey was carried out among 120 school children looked at which type of meat they preferred. 55% said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey and we have to calculate no. of children in each category.

55% said they preferred lamb, So the no. of students i this category is

= (55/100)×120

= 66 children.

20% said they preferred chicken, So the no. of children in this category is

= (20/100)×120

= 24 children.

15% said they preferred duck, So the no. of children in this category is

= (15/100)×120

= 18 children.

10% said they preferred turkey, So the no. of children in this category is

= (10/100)×120

= 12 children.

learn more about percentage here :

https://brainly.com/question/19670755

#SPJ4

The two column proof is completed by the substitution property of equality, which gives;

WX = XZ

XY = XZ

The completed two column table is presented as follows;

Statement. Reasons

1. X is the midpoint of [tex] \overline{WY}[/tex]. 1. Given

2. WX = XY 2. Definition of midpoint

3. [tex] \overline{WX} \cong \overline{XZ}[/tex]. 3. Given

4. WX = XZ 4. Definition of midpoint

5. XY = XZ 5. Substitution property of equality

6. [tex] \overline{XY} \cong \overline{XZ}[/tex] 6. Definition of congruency

Learn more about writing a two column proof here:

https://brainly.com/question/1788884

#SPJ1

The reciprocal of 150 will be 1/150.

We have a marine center has 150 parking spaces in front of its building.

We have to find the reciprocal of 150.

The reciprocal of a number is a number such that the product of both the numbers is equal to 1. Mathematically, if the original number is a, then its reciprocal will be 1/a , such that -

a x 1/a = 1

According to the question -

Let us assume that  A = 150

Now, from the definition of reciprocal, the reciprocal of A will be -

1/A. Therefore, the reciprocal of 150 will be = 1/150

Hence, the reciprocal of 150 will be 1/150.

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

https://brainly.com/question/24983465

#SPJ1

Required values:

The length of one side of the garage was originally 17.7 ft long

The length of one of the sides of the garage is now 21.7 ft long

The percentage increase in length is 22.5%.

Given parameters are;

The area of the square garage is 314 ft.²

The area of the new garage has 50% more space

Required;

Initial side length:

The initial side length, given to the nearest tenth, s, is the square root of the area, A, given as follows;

s = √(314 ft.²) ≈ 17.7 ft.

New Side length:

The side was increased by 50%, to give,

314 + 0.5×314 = 471

The new area of the garage = 471 ft.²

The side length of the new garage, s = √(471) ≈ 21.7 ft

The side of the garage now is 21.7 ft.

Percentage increase in length:

The percentage increase is given as follows;

% increase in length

= new side length - old side length / old side length * 100  

= 21.7 - 17.7 / 17.7 *100

= 22.5 %

To learn more about the percentage increase in length refer below

https://brainly.com/question/24832148                            

#SPJ9

Answer:

length x width x height (or depth) = volume

Step-by-step explanation:

761.25 or 761 1/4 is the answer

Answer:

-0.28

Step-by-step explanation:

4 ÷ 8/9 -1/2

BODMAS

8/9 ÷ 4

8/9 x 1/4

2/9 x 1

2/9 - 1/2

= -0.2777

= -0.28

Answer:

11

Step-by-step explanation:

80 /7=11.428

so each gets 11 so 77 so u do 80-77=3 so u would have 3 left over

Answer:800

Step-by-step explanation:

2×2×2×10×10=800

Answer:

2^3*3^2=72

Step-by-step explanation:

The given table of the values of f(x) is used to complete the table for the function [tex]y = f \left( \frac{1}{5} \cdot x \right) [/tex], to give;

The following values of x and y as follows;

x: -0.8, -0.2, 0, 0.6, 1.2

y: 7, -2, 3, -4, 5

Please also see the attached table

The question is with regards to scaling a graph horizontally.

Using the rule of scaling a graph, we have;

Given that a point on the graph of f(x) is (x, y), the corresponding point in the graph of f(C•x) is (C•x, y).

The given modification of the function is presented as follows;

[tex]y = f \left( \frac{1}{5} \cdot x \right) = f \left( 0.2 \cdot x \right)[/tex]

The points on the graph that completes the table are therefore;

The completed table is therefore;

x y

-0.8 7

-0.2. -2

0 3

0.6. -4

1.2. 5

Learn more about scaling of a function here:

https://brainly.com/question/3381225

#SPJ1

Answer: Unable to answer

Step-by-step explanation: If you do not show what the constant rate is, I am unable to solve it for you.

1. A(2,8)  A'(6,7)

2. B(5,2) B'(9,1)

3. C(2,2) C'(6,1)

4. P(x,y) P'(x ₊ 4 , y ₋ 1)

5. x units to x ₊ 4 units.

   y units to y ₋ 1 units.

6. triangle A'B'C' (6 , 4)

7. triangle A'B'C' (7 , 5)

8. triangle ABC ( 3,2)

9. triangle ABC (4 , 4)

Given,

A set of values called coordinates helps to display a point's precise location in the coordinate plane.

we can observe the points from the graph we get the values for B' and C'.

P(x,y) P'(x₊,y₋)

P(2,5) P'=(6,4) ⇒(2₊4,5₋1)

P(3,6) P' = (3₊x' , 6₋y')  ⇒ (3₊4 , 6₋1) = (7,5)

P'(7,1) P = (x'₋4 , y'₊1)  ⇒ (7₋4 , 1₊1) = (3,2)

P'(8,3) P =  (x'₋4 , y'₊1) ⇒ (8₋4 , 3₊1) = (4,4)

hence we acquired the desired values of the points from the graph given.

Learn more about Coordinate geometry here:

brainly.com/question/17206319

#SPJ9

i think its 8. is the x days and y money?

Answer:

The equation for this question should be n+7=25

where n=18

Step-by-step explanation:

Step-by-step explanation:

find the value of 8x³-y³if 2x-y and xy=-1

Answer: 35.

Step-by-step explanation: 33 + 34 + 35 is 102. Your 35 is the largest of the three.

Answer:

7y2 + 8xy - 3

Step-by-step explanation:

7y2 + 6xy + 2xy -3  You distribute the - sign through the second binomial.  You are distributing or multiplying (-2xy -3) by -1  Combine like terms

7y2 + 8xy -3

Answer:

What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3

7y2 + 8xy – 3 Correct

7y2 + 4xy + 3

7y2 + 8xy + 3

Step-by-step explanation:

Answer:

9 u^2

Step-by-step explanation:

there's 2 ways to solve this problem

easy way

plot every coordinate and youll see it's a square

square area = side^2

3^2 = 9 answer

and this method

working with 3 points (triangle)

W - X - Y

0       0                

0       3

-3       3

0       0

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

    2

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

0      0

0      -9

0      0

-----------

l-9/2l

4.5

since a square is made of 2 triangles

4.5 * 2 = 9 u^2

Answer:

-1 31/65

Step-by-step explanation:

I did this before trust me

Answer:

[tex] \sf \large - 1 \frac{31}{65} [/tex]

Step-by-step explanation:

6 2/5/-4 1/3

6 2/5/−4 1/3

=32/5/−4 1/3

= 32/5 −13/3

=32/5/−13/3

=−96/65

= −1 /31/65

Answer: x = 10

Step-by-step explanation:

3(10) = 30 +2 + 32

Answer:c=16

Step-by-step explanation:5c+35=-45=5c=-45-35=5c=-80. C=16

Answer:
14

Explanation:

14 - 10 = 4

the product is 4 and its a number thats subtracting 10

[tex] \: \: \: \: \: \: \: \bf\implies \: x > \frac{7}{2} [/tex]

[tex] \tt \mapsto2x > 7 \\ \tt \mapsto 2x = 7 \\ \ \ \tt \mapsto x = \frac{7}{2} \\ \tt \mapsto x > \frac{7}{2} [/tex]

The value of the square root of 64 is -8

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

The square root of a number is the values that will can multiply twice to give the resulting value in the root.

Given the expression below:

- √64

Since the square root of 64 is 8, hence;

-√64 = -1 * √64

-√64 = -8

Hence the value of the square root of 64 is -8

Learn more on square root of integer here: https://brainly.com/question/237728

#SPJ1

use this formula and solve the question

AREA OF BASE = 1 by 2 ×base × Height

Answer:

y = -4/3x + 2

Step-by-step explanation:

Point slope form is this:

y - y1 = m (x - x1)

Where m is the slope. y1 and x1 are where you put your coordinates.

so now we just plug it in.

y - (-2) = -4/3 (x - 3)

We should clean it up in order to make it look like this equation:  y = mx + b

y + 2 = -4/3x -4/3(-3)

y + 2 = -4/3x + 4

y = -4/3x + 2

Answer:

[tex]\frac{211}{500}[/tex]

Step-by-step explanation:

[tex].4\bar{2}[/tex]  means the 2 repeats till infinity
[tex].4\bar{2}[/tex]  = .4222222222.....

To convert to fraction just take the first three decimal place digits 422 and divide by 1000 to convert to fraction

[tex].4\bar{2} = \frac{422}{1000}[/tex]

Dividing numerator and denominator of this fraction by 2 gives
[tex]\frac{422/2}{1000/2} =\frac{211}{500}[/tex]

This cannot be simplified further and therefore
[tex].4\bar{2} = \frac{211}{500}[/tex]

If we had chosen first 4 decimal digits then it would be[tex].4\bar{2} = \frac{4222}{10000} = \frac{2111}{5000}[/tex]
i.e. we divide by 10,000

Answer:

-53

Step-by-step explanation:

if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2

-| 10 - 7r + 8m + 2p |

Substitute the given values into the equation.

-| 10 - 7(5) + 8(-4) + 2(2) |

Simplify

-| 10 - 35 + -32 + 4) |

-| -53 |

= -53

Absolute value of -53 is 53 however there is a negative sign outside of it, so the answer is -53

There are 5 people in the family.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that each member of angela's family drank an 8-ounce mixture of coffee with milk.  

Let the number of people would be n.

And a represents the coffee, and  b represents the milk,

One-quarter of the milk and one-sixth of the coffee was consumed by Angela.

⇒ Angela drank b/4 of milk and a/6 of coffee.

Since everyone drank the same amount of coffee,

We have been to create an equation as

⇒ (a/6 + b/4)p = a + b

⇒ 2a(6 - n) = 3b(n - 4)

Given that both a and b are positive, we must fulfill the condition.

⇒(6 - n) > 0 and (n - 4) > 0

⇒ 6 > n and n > 4

So, the correct number of people = 5.

Hence, there are 5 people in the family.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ4