12. The energy E stored in an elastic band varies as the square of the
energy stored
extension x. When the elastic is extended by 3 cm, the
is 243 joules. What is the energy stored when the extension is 5 cm?
What is the extension when the stored energy is 36 joules?
carthworm is thought

Answer:

A

Step-by-step explanation:

The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)

The value of P(-3) is -12, Quotient is (-2x² + x - 3) and Remainder is 6.

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that a polynomial P(x) divided by a factor (x - a) is not really an element of the polynomial.

Given:

P(x) = -2x³-5x²-3.

Using the remainder theorem, the value of P(3) is given by:

P(-3)=  -2x³-5x²-3.

P(-3) =  -2(-3)³-5(-3)²-3

P(-3) = -2(-27) -5(-9) -3

P(-3) = -54 + 45 - 3

P(-3) = -12

As, the divisor of P(x) is (x+3).

so, the division is

                                  (x+3) | -2x³-5x²-3 | -2x² + x - 3

                                             -2x³-6x²

                                          __________

                                                        x² - 3

                                                        x² + 3x

                                                     ________

                                                               -3x - 3

                                                               -3x - 9

                                                              _______

                                                                      6

So, the Quotient is (-2x² + x - 3) and Remainder is 6.

Learn more about remainder theorem here:

https://brainly.com/question/29128071

#SPJ9

Answer: 55+p

Step-by-step explanation: Since p is in unlike terms as 55, you can just write that as is an the expression to represent the dog's weight.

Answer:

first remove the parentheses on both sides by distributing the multiplication. Then collect all the terms involving

y

on one side (say the left) and the terms without

y

on the right. Finally, divide both sides by the coefficient of

y

. (the number in front of

y

).

It looks like this:

4

(

2

y

−

1

)

=

4

(

y

+

3

)

8

y

−

4

=

4

y

+

12

8

y

−

4

y

=

12

+

4

(subtract

4

y

from both sides and add

4

to both sides)

4

y

=

16

4

y

4

=

16

4

y

=

4

Check your answer.

More thought, looking at the equation:

Instead of distributing the

4

's on both sides, you could start by dividing both sides by

4

(multiplying by

1

4

. This keeps the numbers smaller. It looks like this:

4

(

2

y

−

1

)

=

4

(

y

+

3

)

1

4

[

4

(

2

y

−

1

)

]

=

1

4

[

4

(

y

+

3

]

)

#1/4*4 = [1/4 *4] (y+3)

2

y

−

1

=

y

+

3

2

y

−

y

=

3

+

1

(subtract

y

and add

1

on both sides)

y

=

4

Check your answer.

Answer link

Gió

Mar 25, 2015

First multiply

4

to get rid of the brackets:

8

y

−

4

=

4

y

+

12

Now, isolate the

y

s on one side and numbers on the other of the

=

sign (remembering to change sign in crossing the

=

sign);

8

y

−

4

y

=

+

4

+

12

Notice the change of sign of

4

y

and

−

4

;

now we can add and subtract:

4

y

=

16

The

4

is multiplying the

x

and can go to the right dividing to get:

x

=

16

4

=

4

hope it helps!

The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].

Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.

The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:

[tex]0.25x + 0.10y[/tex]

Since Briana has $3 in her piggy bank, we can set up the following equation:

[tex]0.25x + 0.10y = 3.00[/tex]

To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:

[tex]25x + 10y = 300[/tex]

Therefore, the equation in standard form that represents this scenario is:

[tex]25x + 10y = 300[/tex]

Learn more about equation here:

https://brainly.com/question/29174899

#SPJ4

4 3/4 pounds amount of sugar were left after Garth used 9 1/2 pounds for the lemonade.

9 1/2 pounds of sugar were used from 14 1/4 minus 4 3/4.

Garth needed 14 1/4 pounds of sugar to make lemonade for the school carnival, so he purchased them. He had 4 3/4 pounds of sugar left over when he had done preparing the lemonade. This indicates that he made the lemonade using 9 1/2 pounds of sugar. He took the 14 1/4 pounds of sugar he purchased and subtracted the 4 3/4 pounds that were leftover to get at the amount of sugar he utilised, or 9 1/2 pounds. This indicates that the correct response is D: The lemonade required 9 1/2 pounds of sugar.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

The value of the expression when evaluated is -15

From the question, we have the following parameters that can be used in our computation:

The table of values for the function f(x)

The expression to evaluate is given as

f-1(3) - 4 * f(6)

Using the above as a guide, we have the following:

f-1(3) = 5

f(6) = 5

substitute the known values in the above equation, so, we have the following representation

f-1(3) - 4 * f(6) = 5 - 4 * 5

Evaluate

f-1(3) - 4 * f(6) = -15

Hence, the solution is -15

Read more about function at

https://brainly.com/question/28277110

#SPJ1

Answer:

Below

Step-by-step explanation:

Go to   x = 1 on the x axis number line.....go UP to where the graph crosses x = 1  to find   y = 1    <====this is your answer for f(1)

for f(-)   go to x = 3 then go UP to the graph crossing at y = 1   <--answer

Answer:

3w² = 243

Step-by-step explanation:

To draw a centroid for ΔABC, follow the steps below.

The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.

See the sample attached. Note that this is not constructed to scale.

The centroid is the point where the three medians of a triangle intersect.

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.

Learn more about Centroid:
https://brainly.com/question/10708357
#SPJ1

Answer: C= 24-4t

Step-by-step explanation: Since four were eaten each dat the blue is getting lower, use -4t to represent it. 24 is the total amount gotten by substitution.

Answer: x = 22

Step-by-step explanation:

Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22

Answer:

x = 20

Step-by-step explanation:

since the 3 sides of the triangle are congruent then it is equilateral with 3 congruent angles, each of 60° , then

3x = 60 ( divide both sides by 3 )

x = 20

Answer:

20

Step-by-step explanation:

We know that sum of corner of a triangle is 180° and if the triangle is equilateral, the corners are same

180:3=3x

60=3x

x=20

The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:

$1,830.

The total cost is obtained applying the proportions in the context of the problem.

The number of kilowatt hours is given as follows:

Hence:

200 x 61 x 3 = 36,600 kwh.

The cost is of $0.05 per kwh, hence the total cost is given as follows:

0.05 x 36600 = $1,830.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

-2a-2

Step-by-step explanation:

We can start solving this expression by combining like terms: Constants, or the number values, and Variables(the letters)

We can combine -6, 4, and 0 to get -2.

We can combine 3a and -5a to get -2a.

-2a + (-2) is the expression we are left with.

We can simplify this to

-2a - 2.

It can't be simplified further, so our answer is

-2a-2.

The two major properties of similar shapes include the following:

In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.

Read more on scale factor here: brainly.com/question/18067651

#SPJ1

The value of m <2 is C. 120°

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Therefore,

m<2 = m<6

This is because they are corresponding angles

With this in mind, m<6 = 120°

Therefore, m<2 = 120°

Read more about geometry here:

https://brainly.com/question/24375372

#SPJ1

The correct option is E, another rule that takes a line to a perpendicular line (x,y)→(4y,-4x) A B C D OE.

(x,y)→(y,-x)

E:(x,y)→(4y,-4x)→4(y,-x)

So E = (x,y)→(4y,-4x) A B C D OE.

Perpendicular lines play an important role in geometry and trigonometry. They are used to construct right angles, which are essential in measuring angles and finding distances between points. In construction, perpendicular lines are often used to ensure accuracy when building structures, such as walls or flooring.

Perpendicular lines also have real-world applications in navigation, surveying, and astronomy. For instance, in navigation, perpendicular lines are used to calculate a ship's course and location. In surveying, perpendicular lines are used to create precise measurements of land plots, while in astronomy, they are used to calculate distances between celestial objects.The slope of a perpendicular line is the negative reciprocal of the slope of the other line.

To learn more about Perpendicular line visit here:

brainly.com/question/2096532

#SPJ4

Complete Question: -

The rule (x,y)→(y,-x) takes a line to a perpendicular line. Select all the rules that take a line to a perpendicular line.

A. (x,y)→(2y,-x)

B. (x,y)→(-y,-x)

C. (x,y)→(-y,-x)

D. (x,y)→(0.5y,-2x)

E.  (x,y)→(4y,-4x) A B C D OE

Answer:

(a) P(A ∩ E) = 0.03

(b) P(A) = 0.39

(c) P(A | E) = 0.1

Step-by-step explanation:

The first level of the tree gives the following probabilities

P(E) = 0.1

P(E') = 1 - P(E) = 0.9

The second level gives conditional probabilities

P(A|E) = 0.3  this is the top most branch from the root

P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03      Answer(a)

To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities

For event E happening, P(A ∩ E) = 0.03 which is computed in A

However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36

Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)

P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch

This is 0.1   answer (c)

There are 11/3 pounds of cherries at Johnson's Farm in order to pay the same amount as picking 6 pounds of cherries at Mood's Farm.

In general, the unitary method is a useful tool for solving problems like this where we need to compare the cost of two different scenarios. We can set up equations based on the rates or costs involved, and then use algebra to solve for the unknown variables.

To begin, let's use a unitary method to find the total cost of picking cherries at Johnson's Farm. We know the entry fee is $26, so we can start with that. Then, for each pound of cherries picked, the cost is $6. So, if we let x be the number of pounds of cherries picked, the total cost at Johnson's Farm would be:

Total Cost = $26 + $6x

Now, let's use a unitary method to find the total cost of picking cherries at Mood's Farm. We know that there is no entry fee, so we can start with just the per-pound cost of $8. If we let y be the number of pounds of cherries picked, the total cost at Mood's Farm would be:

Total Cost = $8y

To find how many pounds of cherries you would need to pick at each farm in order to pay the same amount, we need to set these two total costs equal to each other and solve for x:

$26 + $6x = $8y

$6x = $8y - $26

x = (8/6)y - 13/3

x = (4/3)y - 13/3

So, if you picked 6 pounds of cherries at Mood's Farm (y = 6), the equivalent cost at Johnson's Farm would be:

x = (4/3)(6) - 13/3

x = 8 - 13/3

x = 11/3

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

Multiplying the total number of children by the fraction that like chocolate yields [tex]32(3/8)=12[/tex]

The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number which is divisible by 15, 20, or 30 will be given as,

LCM of the numbers 15, 20, and 30 will be given as,

2  |    15,       20,       30

2  |    15,        10,       15

3  |    15,         5,       15

5  |     5,          1,        5

          1,          1,         1

LCM = 2 x 2 x 3 x 5

LCM = 60

The number whose remainder is always 8 is given as,

⇒ 60 + 8

⇒ 68

The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ9

The shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The mean of the sampling distribution of the sample mean height for samples of size 10 will also be 40 inches.

The standard deviation of the sampling distribution of the sample mean height can be calculated as:

σ/sqrt(n) = 5.2/sqrt(10) = 1.645

So, the shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The variability of the sampling distribution is smaller than the variability of the population distribution, because the standard error is smaller than the population standard deviation. This means that the sample means are more likely to be closer to the population mean than the individual heights in the population.

Learn more about standard deviation here:https://brainly.com/question/475676

#SPJ1

Answer:

61.25

Step-by-step explanation:

brainlest pls and I hope this helped u :)

The mass of the roller coaster is 800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

PE = 235,200

Height = h = 30 m

Now,

PE = mhg

We use g = 9.8

So,

Substituting the values.

235,200 = m x 30 x 9.8

m = 235200 / (9.8 x 30)

m = 235200 / 294

m = 800

Thus,

The mass of the roller coaster is 800.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ9

Kathy should take 4 trips if the price of a round-trip ticket is 230.

Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:

Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.

It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.

Learn more about graph here:

https://brainly.com/question/17267403

#SPJ4

The following are the area of the sectors:

6a). π square inches

6b). 24π square centimeters

7a). 9 square centimeters

7b). 16.7 square inches

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For question 6:

a). (40/360) × π × 3 in × 3 in = π in²

b). (135/360) × π × 8 cm × 8 cm = 24π cm²

For question 7:

a). (90/360) × π × 6 cm × 6 cm = 9 cm²

b). (60/360) × π × 10 in × 10 in = 16.7π in²

Therefore, the following are the area of the sectors:

6a). π square inches

6b). 24π square centimeters

7a). 9 square centimeters

7b). 16.7 square inches

Know more about area of sector here: https://brainly.com/question/22972014

#SPJ1

The numbers 2 2 2 2 can be arranged to make the equation true as follows

The numbers arranged by applying the rule which had acronym of PEMDAS

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= (2 + 2/2)²

solving the parenthesis first we solve the problem inside the parenthesis. Inside the parenthesis we start with division

= (2 + 2/2)²

= (2 + 1)²

Then addition

= (3)²

having completed the parenthesis, we solve for the exponents

= 9

Learn more about PEMDAS here:

https://brainly.com/question/29393553

#SPJ1

The statement that " t-value changes depending on the number of data points collected" is (b) False because t-value is a statistic that is used in hypothesis testing to determine the difference between 2 sample means is significant or not.

The t-value does depend on the sample size (number of data points) as well as the sample mean and standard deviation, but it does not change "depending on" the number of data points in the sense that the same data set will always produce the same t-value for a given statistical test.  

So , it is important to note that the t-value is a fixed value for a given set of data, regardless of the number of data points collected.

Therefore, if the same data set is used to perform a t-test multiple times, the resulting t-value will always be the same.

Learn more about t-Value here

https://brainly.com/question/29844684

#SPJ4