The gravitational potential energy, ‘G’ of an object is directly proportional to its height, ‘h’ above
the surface of Earth. When the object is at a height of 40 meters above Earth, its gravitational
potential energy is 2200 joules. Find
I. An equation connecting G and h.
II. The gravitational potential energy of the object when it is at a height of 22 meters above the
surface of Earth.
III. The height of the object above the surface of Earth when it has a gravitational potential
energy of 3025 joules.

The length of the other leg is 13.1

Given.

The length of the hypotenuse of a right triangle is 30 inches.

The length of one leg is 27 inches.

To the nearest tenth, we need to find the length of the other leg.

It states that in a right-angled triangle the square of the hypotenuse is equal to the square of the other two sides.

We have,

Length of the hypotenuse = 30 inches.

Length of One leg = 27 inches.

Let the length of the other leg be x.

Now,

Applying the Pythagorean theorem.

30² = 27² + x²

900 = 729 + x²

Subtracting 729 on both sides

900 - 729 = 729 + x² - 729

171 = x²

x² = 171

x = 13.07669

Rounding to the nearest tenth

We get,

x = 13.1

Thus the length of the other leg is 13.1

Learn more about the finding length of a side of a right-angled triangle here:

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Step-by-step explanation:

Odd numbers from the list are 75, 189, and 315.

75, 189, and 315, are composite numbers.

Prime factorization of 75 = 3 × 5 × 5

Prime factorization of 189 = 3 × 3 × 3 × 7

Prime factorization of 315 = 3 × 3 × 5 × 7

315 is an odd number, and a composite number that is divisible by 3 different prime numbers.

The correct answer would be Option D 315

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into other numbers. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Numbers that have more than two factors are called composite numbers.

Given here: The number must be odd and has three prime factors

In option D 315 its prime factorization is 315=3²×5×7

It has 3 different prime factors 3,5,7 and thus option D is the correct answer.

Hence, The correct answer would be Option D 315

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Answer:

50°

Step-by-step explanation:

Transformation is the movement of one point from its initial location to a final location. If an object is transformed, all its points are transformed. Types of transformation is reflection, dilation, rotation and translation.

If an object is translated, it maintains its shape and size as well as the length of its sides and angles, only the location changes.

If polygon LMNP with ∠M of 50° is translated 5 units right and 4 units down to a new point, M' has the same angle measure. Hence ∠M' = 50°

Answer:

The answer was obtained by first taking the measurement for the temperature drop, the duration of the temperature drop, and the rate at which the temperature is dropping which are -28 F, 4 hours, and dropping at a steady rate.

The measured temperature drop of -28 F, is then divided by the duration of the drop which is 4 hours, to get the amount the temperature drop each our as -28F/4 = -7 F per hour

Step-by-step explanation:

The rate at which the local meteorologist claims that the temperature is going to drop = Steady rate

The duration over which the local meteorologist states that the temperature is going to drop = 4 hours

The amount by which the temperature is observed to drop = -28F

The rate at which the temperature is observed to drop = The same amount each hour

Therefore, the temperature drop per hour = -28F/4 = -7 F per hour

Answer:

plane WRT

Step-by-step explanation:

Answer:

1.  y = (-5x/2) + -3

2. y = (3x/2) + 7

Step-by-step explanation:

For both these problems, we simply need to apply point-slope form.

1.  The point (0, -3) and the slope that is perpendicular to the line is the reciprocal of the coefficient, slope = -5/2.

From here, we simply apply the formula:

y - y0 = m ( x - x0)

y - -3 = -5/2 ( x - 0 )

y + 3 = -5/2 x

y = (-5x / 2) + -3

2.  The point (0, 7) and the slope that is parallel to the line must maintain the same slope.  First, we need to rewrite the equation into slope-intercept:

-3x + 2y = 10

2y = 3x + 10

y = 3x/2 + 5

Now we want to apply the point-slope form

y - y0 = m ( x - x0 )

y - 7 = (3/2) (x - 0)

y - 7 = 3x / 2

y = 3x/2 + 7

Cheers.

Answer:

The Domain should be (10,+infinity) as x>10

Step-by-step explanation:

Answer:

4n+13

Step-by-step explanation:

Answer:

4n+13

Step-by-step explanation:

group all the like terms together to get 5n-4n+3n= n+3n= 4n, and group 3+10 together to get 13. the finished answer should be 4n+13

Answer:

Absolute value equation: |x - 13| = 5

Step-by-step explanation:

The midpoint between 8 and 18 is;

(8 + 18)/2 = 26/2 = 13

This means that the distance between 13 and either 8 or 18 will be 5.

Now, the absolute value equation will have to say that the distance between x and 13 is 5.

Thus, plugging those numbers into the pattern of |x - m| = b. Where m is the midpoint and b is the distance from midpoint to either values of x.

This gives us the absolute value equation: |x - 13| = 5

Answers:

Step-by-step explanation:

A linear function must be straight. It can have a slope, but it must not curve.

___________________________________________________________

Hello! :)

Answer:

[tex]\huge\boxed{NP = 7}[/tex]

Given:

MP = 24

MN = 17

Write an expression to represent NP:

MP = MN + NP

24 = 17 + NP

Isolate NP:

24 - 17 = NP

NP = 7.

Answer:

7cm is the correct answer

Step-by-step explanation:

Hope this is helpful for you

Answer:

−0.989010989010

Step-by-step explanation:

what is the 45th term of a sequence generated by the formula tn=(-1)^n * (2n/2n+1)?

When n= 45

tn=(-1)^n*(2n/2n+1)

tn = (-1)^45 * ( 2(45) / 2(45) + 1

= -1 * 90 / (90+1)

= -90 / 91

= −0.989010989010

The 45th term of the sequence generated by the formula tn=(-1)^n*(2n/2n+1) is −0.989010989010

Answer:

The sum of all internal angles of this polygon is: [tex]900^o[/tex]

Step-by-step explanation:

Recall that the formula for the number of diagonals of a polygon with n-sides is given by the formula:

[tex]diagonals=\frac{n\,(n-3)}{2}[/tex]

and since Lucero noticed that the number of digonals was 7 more that the number of sides, then, these two quantities (n + 7) and the number of diagonals must be equal. we can set an equation stating such, and solve for "n" (number of sides of the polygon):

[tex]n+7=\frac{n\,(n-3)}{2} \\2(n+7)=n(n-3)\\2\,n+14=n^2-3\,n\\n^2-3\,n-2\,n-14=0\\n^2-5\,n-14=0\\(n-7)\,(n+2)=0\\[/tex]

therefore n = 7 or n = -2

The only answer with meaning is the first one (7 sides), since a polygon must have a positive number of sides.

Now that we know the number of sides of the polygon, we can find what the sum of its internal angles should give, based on the equation;

Addition of internal angles of a polygon is = [tex](n-2)\,180^o[/tex]

Which in our case renders:

[tex](n-2)\,180^o=(7-2)\,180^o= 5\,(180^o) = 900^o[/tex]

Answer: Around 28 planes take off every hour

Step-by-step explanation: 336 / 12 = 28

Answer:

30 planes per hour

Step-by-step explanation:

Divide the number of plane takeoffs by the number of hours.

Answer:

The best option is the first one. It provides a higher present value.

Step-by-step explanation:

Giving the following information:

Option 1:

Receive $15,000,000 today.

Option 2:

Receive $1,000,000 for 30 years.

Discount rate= 7% compounded annually

To compare both options, we need to calculate the present value of Option 2. The option with the higher present value is the most convenient.

Option 2:

First, we need to determine future value:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

FV= {1,000,000*[(1.07^30) - 1]} / 0.07

FV= $94,460,786.32

Now, the present value:

PV= FV/(1+i)^n

PV= 94,460,786.32 / (1.07^30)

PV= $12,409,041.18

The best option is the first one. It provides a higher present value.

Answer:

x  = 3[tex]\sqrt{2}[/tex]

step-by step:

x -√2=√8

x = [tex]\sqrt{12}[/tex]

x = [tex]\sqrt{6 * 2}[/tex]

x = [tex]\sqrt{2 * 2 * 3}[/tex]

x  = 3[tex]\sqrt{2}[/tex]

Answer:

x = 3 sqrt(2)

Step-by-step explanation:

x -√2=√8

Add sqrt(2) to each side

x - sqrt(2) + sqrt(2) = sqrt(8)+ sqrt(2)

x = sqrt(8)+ sqrt(2)

Rewriting sqrt(8)  as sqrt(4) sqrt(2) = 2 sqrt(2)

x = 2 sqrt(2)+ sqrt(2)

x = 3 sqrt(2)

Answer:

answer is 25

Step-by-step explanation:

x+2+153=180

x+155=180

x=180-155

x=25

hope this helps :)

Answer:

46.15%

Step-by-step explanation:

(6 ÷ 13) × 100 = 46.15384615

= 46.15%

Answer:

Step-by-step explanation:

Given the average low temperature by month in Nashville is represented by the function  f(x)=-1.4x² + 19x +1.7, where x is the month, the average rate of change is expressed as d[f(x)]/dx = 2(1.4x) + 19

d[f(x)]/dx  = 2.8x + 19

Since the number of months between March and August is 5 months and x is in months, hence we will substitute x = 5 into the resulting function to get  the average rate of change from March to  August as shown;

d[f(x)]/dx  at x = 5

= 2.8(5)+ 19

= 14 + 19

= 33

Hence the average rate of change from March to August is 33

Answer:

[tex]\frac{1}{3} x-2[/tex]

Step-by-step explanation:

Answer:

y=1/3x-2

Step-by-step explanation:

HOPE THIS HELPS!!!! :)

<3333333333

Answer:

1

Step-by-step explanation:

2-6/6

You divide before subtraction

2-1

1

with this information provided all we have to do now is substitute

[tex]f(1):\\h=1 \\f(h) = 10h\\f(1) = 10*1 = 10[/tex]

so, first row:

[tex]f(h)=10 \\ h=1[/tex]

we repeat the same process with the rest of the values

[tex]f(4.5)\\h=4.5\\f(h)=10h\\f(4.5)=10*4.5 = 45[/tex]

second row:

[tex]f(h)=45\\h=4.5[/tex]

repeat that once more

[tex]f(10)\\h=10\\f(h)=10h\\f(10)=10*10= 100[/tex]

third and final row:

[tex]f(h)=100\\h=10[/tex]

and we're done, hope this helps. <3

Answer:

[tex](-1,2,-1)[/tex]

Step-by-step explanation:

we already know that c= -1

we can substitute in 4b + c =7

[tex]4b+(-1)=7\\\\4b-1=7\\\\4b=7+1\\\\4b=8\\\\b=2[/tex]

we can substitute in a + b -5c = 6

[tex]a+(2)-5(-1)=6\\\\a+2+5=6\\\\a+7=6\\\\a=6-7\\\\a=-1[/tex]

so it is

[tex](-1,2,-1)[/tex]

Answer:

x=-13

Step-by-step explanation:

divide each term by -7 and simplify I think I hope that works let me know if it's not right

Answer:

5a  

2

+4ab+5b  

2

Step-by-step explanation:

step  1. (((0-(4•(a2)))+3ab)+(12•(b2)))+(((9•(a2))+ab)-7b2)

 step 2. (((0-(4•(a2)))+3ab)+(12•(b2)))+((32a2+ab)-7b2)

step 3.(((0-(4•(a2)))+3ab)+(22•3b2))+(9a2+ab-7b2)

step 4. (((0-(4•(a2)))+3ab)+(22•3b2))+(9a2+ab-7b2)

step 5. 5.1    Factoring    5a2 + 4ab + 5b2

Answer:

1,3

2,4

5,5

Step-by-step explanation:

x,y

0,2

Answer:

(1,3),(2,4),(3,5)

Step-by-step explanation:

Remember that when plotting points, the x value comes first and then the y value.

Look at the graph, x value then y value, to find the point locations.

Cheers.

Answer:

-13

Step-by-step explanation:

Answer:

-13 is your answer

when a negative and a positive are next to each other they equal and negative l. So your final equation would be -8-5