The length is twice the sum of its width 3. What are the dimension of the rectangle if it’s area 216 square inches?

From the information given, the slope (m) of the equation is -1.5. This means that there is an inverse relationship between the Lenght of the Candle and the number of hours. Where, the longer the number of hours, the smaller the length of the candle. See further explanation below.

The slope of a line is its steepness as it goes from LEFT to RIGHT. The slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always fixed (it never changes) regardless of whatever two locations on the line are chosen.

When dealing with a linear relationship, the question is usually represented in this format:

y = mx + b; where
m = slope and

b= y-intercept (or constant)

From the case above, the equation shows the relationship between time   (t) the candle spends burning and the length of the candle (l).

Logically, we can infer that there will be a negative relationship between the two but first lets us determine the slope.

Restating the equation in intercept format, we have:

L = 15 - 1.5t................................1; in intercept format the slope we have

L = -1.5t + 15   ...........................2.

Where L [tex]\sim[/tex] y; m [tex]\sim[/tex] -1.5 and t [tex]\sim[/tex] x; and b [tex]\sim[/tex] 15

Hence we can state that the m (slope) = -1.5 and that if plotted on a graph, the line crosses the y-axis at y = 15 where x = 0.

Also, if L (that is y) is set to zero, then the total time taken for ALL the candles to burn is 10 hours.

See attached graph as proof.

The logical interpretation above is hence confirmed that there is an inverse relationship between x and y. This means that the longer the time, the shorter the length of the candle.

This also means that the length of the candle cannot be or is not longer than 15.

Learn more about slopes:

https://brainly.com/question/3493733

#SPJ1

The slope of the equation is -3/2 describing the rate at which the length of the candle is decreasing.

We know lines have various types of equations, the general type is

Ax + By + c = 0.

We know slope is the rate of change of the y-axis with respect to the x-axis

also, rise over run which is (y₂ - y₁)/(x₂ - x₁).

The burning equation of the candle is represented by  L = 15 - 1.5t.

Where L = length of the candle and any point of time and t = time in hours.

Now, we'll need two points from this equation to obtain the slope.

At, t = 2, L = 12. and at t = 4, L = 9.

So, the two points are (2, 12) and (4, 9).

∴ Slope(m) = (9 - 12)/(4 - 2).

Slope(m) = -3/2.

The slope of this equation describes the rate at which the height of the candle is changing.

learn more about slopes here :

https://brainly.com/question/16941905

#SPJ1

Answer:

  (c)  131°

Step-by-step explanation:

Given exterior angle z of a triangle with remote interior angles 97° and 34°, you want the measure of angle z.

An exterior angle is equal to the sum of the remote interior angles.

  z = 97° +34°

  z = 131°

1/3 and 3/9

Simplify 3/9 by 3

(3/3) / (9/3 ) = 1 /3

So, both fractions are equal

1/3 is not greater than 3/9

All of the possible answers for the vertices of triangle A'B'C' after using this translation rule (x, y) →  (2x, y - 3) include the following:

A. (14, 3)

D. (-8, 6)

In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.

Next, we would transform triangle ABC by using this translation rule (x, y) →  (2x, y - 3) to create the vertices of triangle A'B'C' as follows:

(x, y)                               →                 (2x, y - 3)

Coordinate A = (7, 6)    →    Coordinate A' (2(7), 6 - 3) = (14, 3)

Coordinate B = (-3, 5)   →    Coordinate B' = (2(-2), 5 - 3) = (-4, 2)

Coordinate C = (-4, 9)   →     Coordinate C' = (2(-4), 9 - 3) = (-8, 6)

Read more on translation here: brainly.com/question/16486008

#SPJ1

The meaning of estimate is approximately calculating an answer to check its accuracy.

Approximate calculation:

Approximate value means the value that is close to this number, less than it, as close as possible, and with a requested level of precision.

For example, the approximate value of π is 3.14

Given,

Here we have the word estimate.

Now, we have to find the meaning of it.

Estimate value means to find a value that is close enough to the right answer, usually with some thought or calculation involved.

For example, let us consider Alex estimated there were 10,000 sunflowers in the field by counting one row then multiplying by the number of rows. Here we doesn't have the exact value instead of that we take the approximate value to identify the number. This process is called estimation.

To know more about Approximate calculation here.

https://brainly.com/question/2140926

#SPJ1

ANSWER

854x

EXPLANATION

We have that:

850x + 40(x)

First, expand the bracket:

850x + 40x

Because the two terms are of the same kind (terms of x) we can add them up:

850x + 4x = 854x

That is the answer.

(A) The customer that owns a 3-kW system exports 120 kWh monthly to the grid will have the following bills for both companies:

For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be

For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be

(B) The customer that owns a 5-kW system exports 300 kWh monthly to the grid will have the following bills for both companies:

For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be

For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

12, 20, 18, 25 , 6

range = ?

We must order the data.

Step 02:

6 , 12 , 18 , 20 , 25

Range = 25 - 6 = 19

The answer is:

The range is 19

Pythagorean theorem

(Type an integer or decimal rounded to the nearest tenth as needed.)

Integer = 8'

decimal rounded to the nearest tenth as needed = 8.1'

Replacing with the values we already know, we have:

PV = 10,000

i = 5% or 0.05 but it is compounded monthly, then it is 0.05/12

n = 18 years or 216 months

10,000 = FV * 0.4073

FV = 10,000/0.4073

FV = $ 24,551.93

It is very close to option D, where the term "about" is included.

Answer

(x - 2)² + (y - 2)² = 8

Step-by-step explanation

The equation of the circle centered at (h, k) with radius r is:

In this case, the center of the circle is the point (2, 2), then h = 2 and k = 2, that is,

Given that the circle passes through the center, then the point (0, 0) satisfies the above equation. Substituting x = 0 and y = 0 into the equation and solving for r²:

Substituting r² = 8 into the equations, we get:

Given: The points a line intersects as shown below

To Determine: The slope of the line in its simplest form

Solution

The formula for finding the slope of two points is as shown below

Let us apply the formula to the given points

Hence, the slope of the line in simplest form is -6

The initial point is (5,5)

the final point is (9, 3)

The formula for determining slope is expressed as

slope = (y2 - y1)/(x2 - x1)

y2 and y1 are the final and initial y values

x2 and x1 are the final and initial x values

From the information given,

x1 = 5, y1 = 5

x2 = 9, y2 = 3

Slope = (3 - 5)/(9 - 5) = - 2/4

Slope = - 1/2

Answer:

Explanation:

Part 1:4(5c + 3) and 9c + 7

The answer is NO.

Part 2: 10f – 10 and 2(8f - 5)

The answer is NO.

Part 3: 12g + 21 and 3(4g + 7)

Part 4: 6(4) – 6) and 24 - 36

The Solution:

The correct answer is 13.26 centimeters.

Explanation:

Given that Jason has 29 yards of ribbon, and he plans to make 200 bookmarks.

We are asked to find the approximate length (in centimeters) of each bookmark.

Step 1:

Convert 29 yards to centimeters.

So,

Step 2:

To get the length of each bookmark, we shall divide 2651.76 by 200.

Therefore, the correct answer is 13.26 centimeters.

Answer:

√52

Step-by-step explanation:

[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]

[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]

Given: A small toy rocket is launched from a 32-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formula

Required: To find out how long will it take the rocket to hit the ground.

Explanation: When the rocket touches the ground its height will be zero i.e.,

Which gives

Neglecting the negative value of t since time cannot be negative. We have

Final Answer: Time, t=4 seconds.

Answer:

slope = 5/3

y-intercept = -4

Step-by-step explanation:

First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4

Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.

Hope this helps!

Answer:

[tex]y = \frac{5}{3}x - 4[/tex]

Step-by-step explanation:

move the 5x to a -5x

-3y= -5x+12

-3/-3= -5x÷ -3 12÷ -3

The fabric  has a cost per yard of $6 per yard

From the question, the given parameters are:

Yards of fabric = 2 1/2 yards

Cost of the fabric = $15

The cost per yard of the fabric is then calculated as

Cost per yard = Cost of the fabric/Yards of fabric

Substitute the known values in the above equation

So, we have

Cost per yard = 15/(2 1/2)

Evaluate the quotient

So, we have

Cost per yard = 6

Hence, the cost per yard is $6 per yard

Read more about rates at

https://brainly.com/question/12652779

#SPJ1

The number of pieces of sod to lay around the church is 1450 and 25 men volunteered to lay it.

If sod is equally distributed among the men, then each man get sod is equal to number of sod divided by number of men. So,

So each man get 58 number of sod.

Answer: 58

Substitute second expression (x=y) in the first expression.

Substitute the above value of y in the expression number 2.

Thus, the value of x=3 and the value of y=3.

The problem is asking as to perform an addition of signed numbers.

The firs one to add is 3 and the other one is -7.

We can understand the meaning of this type of addition by using the number line forst, and then have a very simple "short cut" every time we fce problems like this.

The number line approach:

locate yourself at the mark "3" on the number line, and then add the number "-7" whichmeans go to the left (as the negative indicates) 7 units. You will see that you move through zero, and then land on the number "-4".

f(2) means that we must substitute the value 2 in the place of x, that is

which gives f(2)=5.

To calculate the hypotenuse of a right angled triangle as shown in the diagram, we can apply the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (the longest side) 28 units, AB is one of the other two sides, 23 units and BC is the third side.

We can now re-write the formula as follows;

28^2 = 23^2 + BC^2

784 = 529 = BC^2

Subtract 529 from both sides of the equation

255 = BC^2

Add the square root sign to both sides of the equation and you have

BC = 15.9687

BC is approximately 16 units

The difference in math means the result of subtracting one number from another.

m = Mai’s height

Therefore, the equation is:

Here, we are given a 45°-45°-90° triangle.

Let's find the length of the legs.

A 45°-45°-90° triangle is an isosceles triangle, and the two legs of an isosceles triangle are of equal lengths.

To find the length of each leg apply the formula:

Where;

c = 12

Thus, we have:

Solve for a:

Divide both sides by √2

Therefore, the length of each leg in radical form is 6√2

ANSWER:

ANSWER

Monomial

EXPLANATION

A polynomial is a expression that contains variables, coefficients and sometimes constants.

These terms relate with one another by the use of mathematical signs like addition, subtraction, multiplication, etc

A polynomial with just one term is called monomial.

An example of a polynomial is:

An example of a monomial is:

Answer:

monomial

Step-by-step explanation:

Explanation

Step 1

Let's remember one propertie of the roots

hence

replacing in the expression

therefore, the answer is

I hope this helps you

The equation for the total amount after compounded interest is as follows:

Where A is the final amount, P is the initial amount, r is the annual interest, n is how many times per year the interest is compounded and t is the time in years.

Since the interest is compounded annually, it is compounded only once per year, so

The other values are:

So, substituteing these into the equation, we have:

So, she will have approximately $6421.

The given transformation is 8 units left.

The pre-image vertices are A(1,-4), B(1,-6), C(5,-6), and D(5,-4).

Using the transformation, we have:

The image below shows the graph of the image