A 1.5 kg pendulum swings from point A of height yA = 0.04m to point B of height yB = 0.12m. The heights are relative to the lowest height. What is the change in gravitational potential energy from A to B?

The rule for the graph changes form of the function is A)The graph is reflected across the x-axis.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Function is a relation that connects members of one set in a certain way to those of another set. Formally speaking, a function from to is an object such that each is specifically linked to an object. Therefore, a function is a many-to-one (or occasionally, one-to-one) relation.

Here Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let   h(x) = f(x)-c Shifting downward c units yields this graph of h from the graph of f.

We know that if the function reflected over x-axis then

g(x) = -f(x)

Here the given function f(x) = [tex]x^2-4[/tex] then reflection over x-axis then

=> g(x) = -f(x)

=> g(x) =-( [tex]x^2-4[/tex])

=> g(x) = [tex]-x^2+4[/tex]

Hence the correct option is A)The graph is reflected across the x-axis.

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The length of RZ is obtained as follows:

RZ = 11.5.

From the kite given by the image at the end of the answer, the segment lengths are given as follows:

Segments WX and WZ are congruent, hence segment WZ has the length given as follows:

WZ = 14.

Then the length of RZ is obtained considering a right triangle, for which:

The Pythagorean Theorem states that the length of the hypotenuse squared is equals to the sum of the lengths squared of the sides.

Considering the Pythagorean Theorem, the length RZ is obtained as follows:

x² + 8² = 14².

[tex]x = \sqrt{14^2 - 8^2}[/tex]

x = 11.5.

RZ = 11.5.

The problem is given by the image presented at the end of the answer.

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Answer:

a) Yes

The experienced person costs more per hour, but also increases sales per customer. To determine if it is more cost-effective to hire the experienced person, you would need to calculate the net gain or loss from hiring them.

You can do this by multiplying the increase in sales per customer by the number of customers per hour, and comparing that to the difference in hourly wages.

(12 customers/hour * $3/customer) - ($19/hour - $13/hour) = $36/hour - $6/hour = $30/hour

Since the net gain is positive, it is more cost-effective to hire the experienced person.

Answer:

a)

b)-4

Step-by-step explanation:

a) f(13) = 13-7=

b) f(3)= 3-7= -4

Answer:

a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.

Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.

Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.

It means that the store will sell a maximum number of batteries when the price is at $5.00

And the maximum daily revenue will be $5 * 700 = $3500.

So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.

The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

The zeroes of the equation are the points at which the function crosses the x and y-axis.

The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)

The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)

Step-by-step explanation:

Answer:

[tex]a=1, b=-3[/tex]

Step-by-step explanation:

[tex](3,1) \implies 3a-b=6 \\ \\ (0,2) \implies -2b=6 \implies b=-3 \\ \\ \therefore 3a-(-3)=6 \implies a=1[/tex]

Answer: To solve these simultaneous equations, we can substitute one equation into the other.

4x-3 = 3x + y.

3x+y =2y+5x-12

If we substitute the first equation into the second equation, we get:

3(4x-3) + y = 2y+5x-12

12x -9 + y = 2y+5x-12

Now we can solve the system of equations by isolating one of the variables and then substituting it back in one of the equations.

12x - 9 + y = 2y + 5x - 12

y = -9 + 2y + 5x -12

y = 2y + 5x -21

y - 2y = 5x -21 -9

-y = 5x -30

y = -5x + 30

Now we can substitute the value of y back into one of the original equations, we have:

4x-3 = 3x + (-5x + 30)

4x-3 = -2x + 30

4x-3+2x = 30

6x -3 = 30

6x = 33

x = 5.5

Now we can substitute the value of x back into one of the original equations to find the value of y:

4x -3 = 3x + y

4(5.5) -3 = 3(5.5) + y

22 - 3 = 16.5 + y

19 = 16.5 + y

y = 2.5

So the solution to the system of equations is x = 5.5 and y = 2.5.

Step-by-step explanation:

Answer:-7,-7

Step-by-step explanation:

Answer:

The inequality that describes the situation is 5x + 6y < 120

Step-by-step explanation:

This inequality states that the total cost of purchasing x hammers and y wrenches must be less than $120. Each hammer costs $5 and each wrench costs $6, so the total cost is represented by the expression 5x + 6y.

The inequality states that 5x + 6y < 120 which means for any number of hammers and wrenches she buys it should be less than 120.

The other options:

6x + 5y < 120: the coefficient of x is 6 instead of 5 and that of y is 5 instead of 6.

5x + 6y > 120: the inequality is greater than instead of less than, which means that the total cost should be greater than $120 which is not the case.

6x + 5y ≥ 120 : the inequality is greater than or equal to instead of less than, which means that the total cost should be greater than or equal to $120 which is not the case.

Answer: Nicole Kicked the ball Father by  22 feet than Tyrell.

The force of gravity caused the soccer ball to return to the girl.

By means of gravity, a planet or other body pulls items toward its center.

It is, in ideal circumstances, abiding by Newton's third law of gravitation and force.

Each action has a corresponding and opposing reaction.

So, when a boy kicks a ball and it comes back, that signifies he is abiding by the law.

Nicole kicked the ball 57 feet

Tyrel kicked the ball 35 feet

Nicole  Kicked the ball Father by = 22feet

This is gotten by subtracting the distance Nicole kicked from that of Tyrel

=57 feet - 35feet = 22feet

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Answer:

7 and 4/9

Step-by-step explanation:

Answer: The area of the circle with a radius of 9 is approximately 253.94 square units.

Step-by-step explanation:

The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately 3.14.

Given that the radius of the circle is 9, we can substitute this value into the formula to find the area:

A = πr^2 = π(9)^2 = 3.14 * 81 = 253.94

So the area of the circle with a radius of 9 is approximately 253.94 square units.

Note that the diameter of the circle is 18, which is twice the radius. If you knew the diameter you could also use the formula A = (π/4)*D^2 to calculate the area, where D is the diameter.

Step-by-step explanation:

(R○R)(x) = (5 - 2((5 - 2x)/x))/((5 - 2x)/x)

we simply put the original R function into the places of x.

so,

(R○R)(-6) = (5 - 2((5 - 2×-6)/-6))/((5 - 2×-6)/-6) =

= (5 - 2((5 + 12)/-6))/((5 + 12)/-6) =

= (5 - 2×17/-6)/(17/-6) =

= (5 + 17/3)/(17/-6) = (15/3 + 17/3)/(17/-6) =

= 32/3 / 17/-6 = -6×32 / (3×17) =

= -2×32 / 17 = -64/17

Answer:

-64/17

Step-by-step explanation:

Same person here who answered previous question.

(R · R)(-6)

This basically means R(R(-6))

Now, R(-6) = (5 + 12)/-6 = -17/6

Put that value again, in (5 - 2x)/x = (5 + 34/6)/(-17/6)

= (64/6)/(-17/6) = -64/17

So, the answer is correct.

If you have any questions, please leave a comment.

Otherwise, cheers

Answer: Lauren's unit rate is 2.95 Miles per hour (MPH)

Step-by-step explanation:

divide the distance Lauren traveled by the time it took to travel said distance

112/38 hours=2.95 mph

Answer:

2.95 miles/hour or 2.95mph

Step-by-step explanation:

112/38 = 2.94736842 ⇒ 2.95 miles/hour

Answer:

(a) 1/6. One out of six sides will give you the desired result.

(b) 3/6. 3 out of 6 sides will give you the desired result.

(c) 2/3. 4 out of 6 sides will give you the desired result.

Answer: 6

Step-by-step explanation:

Let's start by rewriting the expression. Essentially, this is asking us for 3 * (times) √4 (square root of four).

Now, we can solve √4. Since we know that 2*2 = 4. That means that 2² = 4, so essentially, if we take the square root of 4, we will get back to two.

Now, we can solve the rest: 3 * 2 = 6

In the end, 3√4 = 6. Hope this helps!

[tex]-10w=-9[/tex]

Divide both sides by -10(to isolate the variable):

[tex]\dfrac{-10w}{-10} =\dfrac{-9}{-10}[/tex]

[tex]=0.9[/tex]

Answer: y = 15

Step-by-step explanation:

Subtract both sides by 3

3 + y = 18

y = 15

Answer:

Step-by-step explanation:

The area of the triangle KLM is found using Heron's formula as:

A = 60 in².

     S = (a+b+c)/2

     where a, b, and c are the triangle's three sides.

The sides of the triangle KLM are:

Then,

Semi perimeter s = a + b + c / 2

s = (13 + 13 + 10)/ 2

s = 18 in

Thus,

s - a : 18 - 13 = 5

s -b : 18 - 13 = 5

s - c : 18 - 10 = 8

By Heron's formula;

area of triangle KLM = √(s - a)(s -b)(s - c)

A = √18*5*5*8

A = 60

Thus, the area of triangle KLM is found using Heron's formula as:

A = 60 in².

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Answer:

c.

Step-by-step explanation:

this graph is exponential equation

The linear inequality represented by the graph is defined as follows:

y ≥ -2x + 1.

The ordered pairs that are solutions to the inequality x < -3 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the coefficients are given as follows:

The function in this problem crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by one, y decays by two, hence the slope m is given as follows:

m = -2.

The shaded region, considering the solid line, is given by the values to the right of the line, hence the inequality is defined as follows:

y ≥ -2x + 1.

The inequality for this problem is defined as follows:

x < -3.

The ordered pairs have the following format:

(x,y).

Hence all the ordered pairs that have x < -3, no matter the coordinate of y, are solutions to the inequality.

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The change between outputs found by dividing one output by its previous output is called output elasticity.

What is output elasticity?

Output elasticity is defined as the division of change in output by change in input which is the previous output.

General, elasticity is a concept that is used to measure the change in the aggregate quantity demanded of a good or service in relation to price movements of that good or service.

A product is considered to be elastic if the quantity demand of the product changes more than proportionally when its price increases or decreases.

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f(x) and g(x) are inverses using composition

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

To confirm the inverse relationship using composition.

For valid inverse f(g(x)) must be equal to g(f(x))

f(x) = ∛(x) + 13; g(x) = (x - 13)³:

f(g(x)) = f((x - 13)³)

f(g(x)) = ∛((x - 13)³) + 13

f(g(x)) = x - 13 + 13

f(g(x)) = x

g(f(x)) = g(∛(x) + 13)

g(f(x)) =  (∛(x) + 13 - 13)³

g(f(x)) =  (∛(x))³
g(f(x)) =  x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

f(x) = x³ + 1; g(x) = ∛(x - 1):

f(x) = x³ + 1; g(x) = ∛(x - 1)

f(g(x)) = f(∛(x - 1))

f(g(x)) =  (∛(x - 1))³ + 1

f(g(x)) =  x - 1 + 1

f(g(x)) =  x

g(f(x)) = g(x³ + 1)

g(f(x)) = ∛((x³ + 1) - 1)

g(f(x)) = ∛(x³)

g(f(x)) = x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

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Answer:

[tex]\huge\boxed{\sf b = 6.9}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{15}{b} =\frac{24}{11} \\\\Cross \ Multiply\\\\15 \times 11 = b \times 24\\\\165 = 24b\\\\Divide \ both\ sides\ by\ 24\\\\165/24=b\\\\6.9=b\\\\b = 6.9\\\\\rule[225]{225}{2}[/tex]

Answer:

a = √63

Step-by-step explanation:

We are given a right triangle (notice the right angle).

We know that the hypotenuse (the side opposite of the right angle) is 12.

We also know that one leg (a side that makes up the right angle) is 9, and that the other one is a.

We want to find what a is.

We can use the Pythagorean Theorem to help us find a.

The Pythagorean Theorem says a² + b² = c², where a and b are the legs and c is the hypotenuse.

Since we already know the values of the legs and hypotenuse, we can substitute these values in the theorem, but let's first label the values of everything to avoid confusion / mistakes.

a = a

b = 9

c = 12

Now, plug into the formula.

a² + 9² = 12²

Simplify:

a² + 81 = 144

Subtract 81 from both sides

a² = 63

Square root both sides to get the value of a.

a = √63