the rectangle repersents the base of a right rectangular prism. The height of the prism is 6 inches. What is the volume of this prism

The ordered pair representing the point where both companies would charge the same amount is (25, 136.25).

From the given table, we can form the following equation for monthly cost of each company.

Company 1, the function for the monthly cost is;

(5, $55.25 ) and (10, $75.5). Let the monthly cost = y₁

(y₁ - 55.25 )/(x - 5) = ( 75.5 - 55.25 )/ (10 - 5)

y₁ = 4.05x + 35

Company 2, the function for the monthly cost is;

(5, $31.25 ) and (10, $57.5). Let the monthly cost = y₂

(y₂- 31.25 )/(x - 5) = ( 57.5 - 31.25 )/ (10 - 5)

y₂ = 5.25x + 5

To find the point where both companies charge the same amount, we need to set their costs equal to each other and solve for the number of garments, x:

y₁ = y₂

4.05x + 35 = 5.25x + 5

Subtracting 4.05x and 5 from both sides:

30 = 1.2x

Dividing both sides by 1.2:

x = 25

So both companies would charge the same amount when 25 garments are laundered. T

To find the cost, we can plug x = 25 into either equation:

y₁ = 4.05(25) + 35 = 136.25

y₂ = 5.25(25) + 5 = 136.25

Ordered pair = (25, 136.25)

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The complete question is below:

Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.

Number of Garments      Company 1       Company 2

5                                         $55.25              $31.25

10                                        $75.50             $57.50

15                                        $95.75              $83.75

Determine when both companies would charge the same amount and what that cost would be. Write your answer as an ordered with x representing the number of garments and y representing the cost.

1) The volume of the first rectangular prism is 175 ft³

2) The volume of the second rectangular prism is 60ft³

3) The volume of the third rectangular prism 140ft³

4) The volume of the Fourth rectangular prism 216ft³

Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.

Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:

a)

Length = 7ft

Height = 2ft

widht = 2ft

Volume = Volume = 7ft x 2ft x 2ft
Volume = 28  ft³

b)

Length = 7ft

Height = 3ft

width = 7ft
Volume = 147 ft³

Total Volume = 28  ft³ + 147 ft³

Volume for Shape 1 = 175 ft³

Shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 3ft

Height = 2ft

width = 1ft

Volume = 6 ft³

b) Length = 6ft

Height = 3ft

width = 3ft

Volume = 54 ft³

Thus, total volume for shape 2 is:

Volume = 6 + 54

Volume = 40 ft³

Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 7ft

Height = 1ft

width = 2ft
Volume = 14ft³

b)
Length = 7ft

Height = 3ft

width = 6ft
Volume = 126ft³

Thus, the total volume fior shape 3, =

Volume = 14ft³ + 126ft³

Volume = 140ft³


Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 4ft

Height = 3ft

width = 2ft
Volume = 24 ft³


b) Length = 4ft

Height = 12ft

width = 4ft
Volume = 192 ft³

Thus, the total volume for Shape 4:

Volume =  24 ft³+ 192 ft³
Volume = 216ft³

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Answer: a) The equation to represent the cost of the car suggested by the son is:

C1 = 250 + 0.22k

where C1 represents the total cost of renting the car, and k represents the number of kilometers driven.

b) The equation to represent the cost of the car suggested by the daughter is:

C2 = 96 + 0.5k

where C2 represents the total cost of renting the car, and k represents the number of kilometers driven.

c) To find when the two cars cost the same, we need to solve the equation:

C1 = C2

Substituting the expressions for C1 and C2 from parts a and b, we get:

250 + 0.22k = 96 + 0.5k

Simplifying this equation, we get:

0.28k = 154

Dividing both sides by 0.28, we get:

k = 550

Therefore, the two cars cost the same when the number of kilometers driven is 550.

d) If the Clarke's plan to drive 500km, we can calculate the total cost for each car by substituting k=500 into the equations from parts a and b:

C1 = 250 + 0.22(500) = 360

C2 = 96 + 0.5(500) = 346

Therefore, the car suggested by the daughter is less expensive for a 500km trip, as it would cost $346 compared to $360 for the car suggested by the son.

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Hello!

The topic we should review for this problem is Order of Operations.

Order of Operations is a rule that identifies which part of an equation should be simplified first.

You might've heard of PEMDAS, where;

P for Parentheses, always first unless there's an exponent inside.

E for Exponent, simplified after the Parentheses.

M or D - Multiplication or Division after the Exponent(s).

A or S - Addition or Subtraction after Multiplication or Division.

[tex](5+3^2)+18[/tex]

First we know that there's an Exponent inside the Parentheses, so we must evaluate that number first.

[tex](5+9)+18[/tex]

Next, evaluate what's in the Parentheses.

[tex]14+18\\32[/tex]

Our correct answer is 32.

We are asked what mistake did Raquel make, and what's the correct simplified version of the expression.

1a.) Raquel's mistake is combining unlike terms. It's impossible to combine together a natural number (5) and an exponential number. (3²)

1b.) The correct simplified version of the expression is represented here;

[tex](5+9)+18\\(First \ Step)[/tex]

Answer:

500 words per minute.

Step-by-step explanation:

The set using Roster method is, D = {76, 90, 92, 94, 96}

The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.

A roster method example is to write the set of numbers from 1 to 10 as

{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.

Given:

Set D is the set of positive two-digit even numbers greater than 74

that do not contain the digit 8

First, Even numbers greater than 74 are

76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.

Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.

Using Roster method the set is

D= {76, 90, 92, 94, 96}

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As a result, there are 1140 different methods to select a committee of three from a group of 20 people.

The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is a way to gauge how likely something is to happen. Probability is expressed as a number between 0 and 1, with 0 denoting that the occurrence won't happen and 1 denoting that it will definitely happen. By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an occurrence. Numerous disciplines, including statistics, finance, engineering, and science, use probability extensively to forecast the chance of an event happening and base decisions on that forecast.

given

The following combination formula determines how many options there are to select a committee of three from a class of 20 members:

C(20, 3) = 20! / (3! * (20-3)!) = 20 * 19 * 18 / (3 * 2 * 1) = 1140

As a result, there are 1140 different methods to select a committee of three from a group of 20 people.

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Answer:

16yd

Step-by-step explanation:

I am from Michigan thank me this is really easy you nerd

This is funny helping you big people as a kid.

Answer:

0

Step-by-step explanation:

I remember learning this in math class. The smallest possible probability is zero meaning that event can't happen to be true.

The order of operations (also known as BODMAS) should be used to evaluate this expression:

6 + 2*6 + 20/4 = 6 + 12 + 5 = 23

So the answer is 23.

Answer:

25

Step-by-step explanation:

let the no of days food avl for eat be X .

according to question...

100/80=X/20

=X × 80 = 100×20

=80x =2000

= x =2000/80

x=25 days

In slope-intercept form, the line's equation is y = (3/5)x + 3.

The definition of the an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A formula that describes how two expressions on either side of a sign are connected. It typically has an equal sign and one variable. similar to this: 2x − 4 Equals 2.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Where (x1, y1) = (0, 3) and (x2, y2) = (-5, 0)

m = (0 - 3) / (-5 - 0) = 3/5

To estimate the y-intercept, we just found the intersection of two endpoints just on line (0, 3):

[tex]y=mx+b[/tex]

[tex]3=(\frac{3}{5} )(0)+b[/tex]

[tex]b=3[/tex]

So the equation of the line in slope-intercept form is: [tex]y=(\frac{3}{5}x )+3[/tex]

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Answer:

When two proper fractions are multiplied together, the product will be smaller than both factors.

Step-by-step explanation:

To understand why this is true, we can consider the concept of fractions as parts of a whole. When we multiply two proper fractions, we are essentially taking a part of a part, which results in a smaller portion overall.For example, if we multiply 1/2 by 2/3, we are taking half of something and then taking two-thirds of that half. The result is 1/3, which is smaller than both 1/2 and 2/3.Therefore, the correct answer is: The product will be smaller than both factors.

Answer:The product will be smaller than both factors.

When two proper fractions are multiplied together The product will be smaller than both factors.Take a look at the equation below.

¾ * ⅔=  3 times 2 is 6 and 4 times 3 is 12. So the equation is 6/12 .

6/12 is simplified to 1/2. 1/2 is less than both 2/3 and 3/4. Which means the product is smaller. Hence, the correct answer is the product will be smaller than both factors.

I hope this helped & Good Luck <3!!!!

The length of the side of the square would be 12 inches.

A square is a two-dimensional plane object in geometry that has four equal sides and four equal but 90° angles. The characteristics of a rectangle and a square are somewhat similar, although a rectangle only has its opposite sides equal. As a result, a rectangle is only referred to as a square if its four sides are of the same length.

Given : side of the triangle = 16 inches

So, the perimeter of the triangle = 16+16+16

                                                      = 48 inches

Now, the wire is unbent and shaped into a square.

So, the length of the wire would be same.

Hence, we can say that:

Perimeter of triangle = perimeter of square

                             48 =  4 × side

                 So, side = 12 inches.

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Answer:

x = 9/4 y = 15/4

Step-by-step explanation:

$68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.

The appraisal of a single item or part within one group is known as unit value.

So,

$68/10 tickets = 68/10

$68/10 tickets = $6.8 for each ticket.

Now,

$15/2 tickets = 15/2

$15/2 tickets = $7.5 for each ticket.

Thus, $68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.

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Answer:

Its a parallelogram because it has two sets of equal sides.

(let me know if I have to explain it more)

RS is Parallel to PQ and ∠ P has the same size as ∠ QRS. We find the answer by knowing the definition of Rhombus.

Rhombus is a special case of a parallelogram having four equal sides and opposite equal acute and obtuse angles . The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths i.e. Rhombus.

In mathematics, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides.

a. RS is Parallel to PQ

b. ∠ P has the same size as ∠ QRS

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The composite function when evaluated is -61

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

f(a) = 3a +5

g(a)=a²-4

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

f(-7) = 3(-7) +5 = -16

g(-7) = (-7)²- 4 = 45

So, we have

f(-7) - g(-7) = -16 - 45

Evaluate

f(-7) - g(-7) = - 61

Hence, the solution is -61

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The value of x and y in the triangle are 0 and 4 respectively.

The mid segment of a triangle is a line connecting the midpoints between two sides of a triangle. The mid segment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side .

Therefore,

x + 2 = 3 / 2 x + 2

x - 3 / 2 x = 2 - 2

-0.5x = 0

x = 0

Let's find y

2y - 1 = 3y - 5

2y - 3y = -5 + 1

-y = -4

y = 4

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Answer:

15 ft

Step-by-step explanation:

Use the Pythagorean theorem.

9² + 12² = c²

c² = 225

c = √225 = 15

Answer: 15 ft

Answer:

15 feet

Step-by-step explanation:
So, to start we have to find the area of the wall.
9(12)=108
Now, we need to find half of the walls area
108/2=54

We have our length and height, but we need to find the hypotenuse using Pythagoreans theorem.
9 is our A and 12 is our B
a^2+b^2=c^2
81+144=c^2
c^2=225
The square root of 225 is 15.
C=15

Therefore, the stripe will be 15 feet.

Answer:

20cm³

Step-by-step explanation:

Volume = Base x Height

1/2 x 5 x 2 x 4

=20cm³

The value of y, given that Triangle FEG is similar to Triangle IHJ is 10.

Seeing as Triangle FEG is similar to Triangle IHJ, we can assume that angle EGF is the same as angle HJ1.

This means that 5 y + 8 is equal to 58 degrees.

The value of y is therefore :

5 y + 8 = 58

5 y = 50 - 8

y = ( 50 - 8 ) / 5

y = 50 / 5

y = 10

In conclusion, given the two similar triangles and the angles EGF and HJI, the value of y can be found to be 10.

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By answering the above question, we may state that The range of -3 x 2 inequality is the answer to the compound inequality.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

We must first remove 6 from each of the three elements of the compound inequality -6 4x + 6 14 in order to arrive at the following result:

-6 - 6 ≤ 4x < 14 - 6

If we simplify, we get:

-12 ≤ 4x < 8

Then, we divide each of the three inequality components by 4, keeping in mind that we don't need to reverse the inequality's signs because 4 is positive, to arrive at:

-3 ≤ x < 2

The range of -3 x 2 is the answer to the compound inequality.

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Answer:

x = -4/3

Step-by-step explanation:

hope this helps^^

It should be noted that AP'Q'R' a 180° rotation about the origin of APQR.

It should be noted that to perform a 180° rotation about the origin, one has to draw the original figure and label its coordinates and draw the origin and label it O.

One can also use the following formula to find the coordinates of the image of a point (x,y) after a 180° rotation about the origin:

(x', y') = (-x, -y)

Here, P'Q'R' represents the coordinates of the image of the point PQR. We simply take the negative of the original x and y coordinates to find the new coordinates after the rotation.

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Answer:

Step-by-step explanation:

The value of cos^-1(-sqrt(3)/2) is -π/6 or -30 degrees.

We know that cos^-1(x) gives the angle whose cosine is x, in the range [0, π]. In this case, we are looking for the angle whose cosine is -sqrt(3)/2.

Recall that the cosine function is negative in the second and third quadrants of the unit circle. In the second quadrant, the reference angle whose cosine is sqrt(3)/2 is π/6 or 30 degrees, but the cosine function is negative in this quadrant. Therefore, the angle whose cosine is -sqrt(3)/2 is -π/6 or -30 degrees, which is in the fourth quadrant.

So, cos^-1(-sqrt(3)/2) = -π/6 or -30 degrees.

Answer:

f (3) = 142

Step-by-step explanation:

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