The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh.

Answer:

(a - 5) (a + 2)

Step-by-step explanation:

Answer:

(a – 5)(a + 2).

Step-by-step explanation:

To factorize a²– 3a – 10​, we need to find two numbers whose product is -10 and whose sum is -3. These numbers are -5 and 2. So we can write:

a² – 3a – 10 = (a – 5)(a + 2)

Therefore, the factorization of a²– 3a – 10 is (a – 5)(a + 2).

Answer:

The answer is A.) 19 feet per minute

Step-by-step explanation:

hope this helped!

Answer:

its true or 0

Step-by-step explanation:

Answer:

18 r2

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

for the first answere

The number of homes in a community of 12, 000 which would be heated by electricity, given the rate of houses heated, is c. 3,360 homes

To find the number of homes in the community which would be heated by electricity, first find the percentage of homes that are heated according to the U.S. Census :

= Number of houses heated / Total number

= 7 / 25

= 28 %

When given a community of 12, 000 homes therefore, the number of homes which would be heated are:

= Percentage of houses heated x Community size

= 28 % x 12, 000

= 3,360 homes

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Answer:

c. 3,360 homes

Step-by-step explanation:

The coordinates of A are (3, 5).

According to the section formula-

If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-

x = (nx1 + mx2)/ (m + n)

and y = (ny1 + my2)/ (m + n)

Here, M (4,6) is the midpoint of AB and B is (5,7)

Let the coordinates of A be (x2, y2)

Therefore,

x1 = 5, y1 = 7

x = 4, y = 6

Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1

Now, substituting the values in the section formula we get-

4 = (5 + x2)/2

4 × 2 = 5 + x2

8 = 5 + x2

5 + x2 = 8

x2 = 8 - 5

x2 = 3

and 6 = (7 + y2)/2

6 × 2 = 7 + y2

12 = 7 + y2

7 + y2 = 12

y2 = 12 - 7

y2 = 5

Thus, the coordinates of A are (3, 5).

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There are 45 games played in a season of the youth soccer league with 10 teams.

In a youth soccer league with 10 teams, each team will play against every other team exactly once.

To determine the number of games played in a season, we can use the combination formula, which calculates the number of ways to choose 2 teams from a set of 10 teams. Each combination represents a unique game.

The formula for combinations, also known as the binomial coefficient, is:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of items and r is the number of items to be chosen.

In this case, we have 10 teams, and we need to choose 2 teams for each game.

Using the combination formula, we can calculate the number of games played as:

C(10, 2) = 10! / (2! * (10 - 2)!)

= 10! / (2! * 8!)

= (10 * 9) / (2 * 1)

= 45

Therefore, 45 games are played in a season.

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Answer:

4/3 or 1  1/3

Step-by-step explanation:

Answer:

4/3 or 1and1/3

Step-by-step explanation:

To find the slope, all we need to do is plug in both coordinates into the slope formula and the result will be the slope.

the slope formula is \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

to make it easier, we can label each x and y as x2, x1, y2, and y1 (it really doesn't matter which y or x value is the one as long as they are from the same pair like (4,3) can be x1 and y1 but can't be x2 and y1)

(4,3) (x1,y1)            (1,-1)  (x2,y2)

so just plug it into the formula and solve:

\(m=\frac{-1-3}{1-4} =\frac{-4}{-3} =\frac{4}{3} or 1\frac{1}{3}\)

Answer:

c = 64

Step-by-step explanation:

Given

x² - 16x + c

To complete the square

add ( half the coefficient of the x- term )² to x² - 16x

x² + 2(- 8)x + 64

= (x - 8)²

Thus

x² - 16x + 64 = (x - 8)² ← a perfect square

with c = 64

f(-2) = -3

F(-1) = 2

f(0) = -1

There ought to be infinitely many solutions.

How many solutions can a system of 3 linear equations with 5 variables have?

There are infinitely many solutions. Assuming the 3 linear equations are linearly independent you have 2 free variables that can be chosen freely and depending on those two values you can find the 3 remaining variables as function of those two so for any choice of those two variables you can find a solution. If the equations are not linearly independent you have effectively only 1 or two equations so you can pick 4 or 3 variables freely and then the remaining variable or variables are function of these.

How do you solve a system of equations with 3 variables?
Simultaneous equations. Easy, if they are all linear. Possibly difficult otherwise. Basically pick 1 variable and 1 equation to rearrange so that variable is expressed in terms if the other 2. Then simplify. Now you have 2 equations in 2 variables. Repeat with the remaining 2 variables. When you have solved for the last variable, you can then substitute to solve for the second last. Then backtrack to the original substitution and solve that. General advice that works even for nonlinear equations.

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Answer:

Nice

Step-by-step explanation:

The original price of the laptop was $862.00

How to calculate the original price

The original price of the laptop, denoted by x, can be found by setting up an equation that relates it to the final price after markup.

We know that the final price of the laptop is $1,137.84, and that this price is 32% higher than the original price.

So, one way to set up an equation to solve for x is to use the formula:

final price = original price + markup

where the markup is defined as a percentage of the original price.

In this case, we can write:

$1,137.84 = x + 0.32x

Simplifying this equation, we get:

$1,137.84 = 1.32x

To solve for x, we can divide both sides by 1.32:

x = $1,137.84 ÷ 1.32

x = $862.00

So the original price of the laptop was $862.00.

Using this approach, we can see that option C (1.32p = 1,137.84) is the correct equation for finding the original price of the laptop.

Option A (p(1 − 0.32) = 1,137.84) is incorrect because it represents the final price, not the original price.

Option B (p + 0.32p = 1,137.84) is also incorrect because it represents the sum of the original price and the markup, which is not what we need to find.

Option D (0.68p = 1,137.84) is incorrect because it represents a calculation that is not relevant to finding the original price.

Option E (p(1 + 0.32) = 1,137.84) is incorrect because it represents a calculation that adds the markup to the original price, which is not what we need to find.

Option F (p − 0.32p = 1,137.84) is also incorrect because it represents the difference between the original price and the markup, which is not what we need to find.

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If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Answer: \(\frac{21}{2}+\frac{\sqrt{41}}{2}, \frac{21}{2}-\frac{\sqrt{41}}{2}\)

Step-by-step explanation:

Let the two numbers be x and y.

\(x+y=21 \implies y=21-x\\\\xy=100\\\\\therefore x(21-x)=100\\\\21x-x^2 =100\\\\x^2 -21x+100=0\\\\x=\frac{21 \pm \sqrt{21^2 -400}}{2}=\frac{21}{2} \pm \frac{\sqrt{41}}{2}\)

Using the sample space, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.

In the given question we have to find the probability of rolling an even number with a six-sided dice.

The sample space of dice through the experiment is

{1,2,3,4,5,6}

The even numbers is {2,4,6}.

The probability of rolling an even number with a six-sided dice is

P(E)=Total number of even outcome/Total number of outcome

P(E)=3/6

P(E)=1/2

Hence, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.

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Answer: 8/9

Step-by-step explanation: 0.888... can be simplified to 8/9.

Answer:

a = 2

Step-by-step explanation:

1/4 (20-4a)=6-a

5 - 1 = 6 - a

4 = 6 - a

a = 6 - 4

a = 2

:) Hope this helps, please mark as brainliest!

Answer:

The energy, 'E', increases by a factor of 1000,000,000

Step-by-step explanation:

The given equation relating moment magnitude of an earthquake and the energy (in ergs) released by it obtained from a similar question online is presented as follows; \(M_W = \dfrac{2}{3} \times log_{10} (E) - 10.7\)

Where;

\(M_W\) = The moment magnitude

E = The energy

If \(M_W\) is increased by 6, we have;

Δ\(M_W\) = 6

\(\Delta M_W = M_{W2} - M_{W1} = 6\)

From which we get;

\(\Delta M_W = M_{W2} - M_{W1} = 6 = \dfrac{2}{3} \times log_{10} (E_2) - 10.7 - \left(\dfrac{2}{3} \times log_{10} (E_1) - 10.7 \right)\)

\(6 = \dfrac{2}{3} \times log_{10} (E_1) - 10.7 - \left(\dfrac{2}{3} \times log_{10} (E_2) - 10.7 \right) = \left(\dfrac{2}{3} \right ) \times \left ( log_{10} (E_2) - log_{10} (E_1) \right)\)

\(6 = \left(\dfrac{2}{3} \right ) \times \left ( log_{10} (E_2) - log_{10} (E_1) \right) = \left(\dfrac{2}{3} \right ) \times log_{10} \left( \dfrac{E_2}{E_1} \right)\)

\(6 = \left(\dfrac{2}{3} \right ) \times log_{10} \left( \dfrac{E_2}{E_1} \right)\)

\(log_{10} \left( \dfrac{E_2}{E_1} \right) = 6 \times \left(\dfrac{3}{2} \right ) = 9\)

Therefore;

\(\dfrac{E_2}{E_1} = 10^9\)

E₂ = E₁ × 10⁹ = 1000,000,000 × E₁

Therefore, when the moment magnitude, \(M_W\), increases by 6, the energy increases by a factor of 1000,000,000

Answer:

i don get it

Step-by-step explanation:

i stil don get it

Answer: 92

Step-by-step explanation:

Observe that the probability is symmetric around \(45^{\circ}\).

If \(0^{\circ} < x < 45^{\circ}\), then \(\cos^2 x > \cos x > \sin x\). By the triangle inequality, it follows that \(\cos^2 x > \sin^2 x+\sin x \cos x\).

We can now rearrange as follows:

\(\cos^2 x > \sin^2 x+\sin x \cos x\\\\\cos^2 x -\sin^2 x > \sin x \cos x\\\\\cos 2x > \frac{1}{2}\sin 2x\)

Since \(\cos 2x\) and \(\sin 2x\) are both positive for the chosen interval,

\(2 > \tan x \implies x < \frac{1}{2}\arctan 2\).

Therefore, the probability is \(\frac{\frac{1}{2} \arctan 2}{45}=\frac{\arctan 2}{90}\).

This means, \(m=2, n=90 \implies m+n=92\).

The sum is 56

Here, we want to find the sum of the given expression

To do this, we need to evaluate what we have in each of the brackets and add up

Thus, we have that;

Answer:

Step-by-step explanation:

x=-15

Answer:

- 15

Step-by-step explanation:

Step 1:

3x + 8 = 2x - 7

Step 2:

x + 8 = - 7

Answer:

x = - 15

Hope This Helps :)

Answer:

The factor is 4.

Step-by-step explanation:

You can divide both 24 and 20 by 4, leaving you with 6x-5.

Highest common factor should be 4.

Given that,

Based on the above information, the calculation is as follows:

Here 24 and 20 should be divisible by 4

So,

= 4(6x - 5)

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Answer:

equation is 29x+32=90

answer x=2

Step-by-step explanation:

29x+32=90

29x=90-32

29x=58

x=58/29

x=2

Answer:

Step-by-step explanation:

\(\pmb {sin(22)^o=\cfrac{x}{35} }\)

\(\pmb {35sin(22)=w}\)

\(\pmb {w=13.11}\)

_________________

Hope this helps!

Have a great day! :)

Answer:

x=20

Step-by-step explanation:

Since all the angles in any give triangle adds up to 180, we can make an equation from this geometry question. x+5+7x-5+x=180 (Adding all the angles). If you simplify this, it becomes 9x=180, or x=20.

Answer:

9. 16.34

10. 51.84

11. 20.11

12. 76.03

13. 64.09

just look up circumference of a circle and you should be able to put the radius in the first thing that pops up :)