Create an expression for the perimeter of the triangle.
Side 1: x
Side 2: x
Side 3: y

Subtract 7 from both sides. Subtract 7 from 23 to get 16. Divide both sides by 4. Divide 16 by 4 to get 4.

According to the symmetric property, if one geometric form is congruent to another, the second shape is likewise congruent to the first. The symmetric property of congruence states that for all angles A and B, if AB A B then BA B A.Transitive Property of Congruence. “If two shapes are congruent to the third shape, then all the shapes are congruent to each other,” asserts the transitive property of congruence.

We can solve an equation by applying the four equality properties: addition, subtraction, multiplication, and division. To get the value of an unknown variable, we simply add, subtract, multiply, or divide both sides of an equation.

To learn more about Symmetric to refer:

https://brainly.com/question/14466363

#SPJ1

The surface area of the right rectangular prism is given as follows:

358 m².

The surface area of a prism is obtained with the sum of the areas of each part of the prism.

The parts that compose the prism are given as follows:

The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.

Hence the surface area of the prism is calculated as follows:

S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².

(multiplication by two due to the two rectangles with each of the dimensions).

The prism is given by the image shown at the end of the answer.

More can be learned about surface areas at https://brainly.com/question/16519513

#SPJ1

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

The solution of the LP model using the graphical method and MS Excel are;

The acronym LP stands for Linear Programming, which is a mathematical (modeling) method of optimizing a linear objective function based on a set constraints which are linear.

Graphical method:

The constraints on the graph are;

x₁ + 2·x₂ ≤ 8

4·x₁ ≤ 16

4·x₂ ≤ 12

The third constraint indicates; x₂ ≤ 3, which is the horizontal line, y = 3

The second constraint indicates; x₁ ≤ 4, which is the vertical line, x = 4

The first constraint indicates; x₂ ≤ 4 - (1/2)·x₁, which is a line with slope (-1/2), passing through the points (0, 4) and (8, 0)

The feasible region that satisfies all the constraints is shaded in the attached graph of the inequality, created with MS Excel

The maximising function indicates;

Point A (0, 0); z = 2 × 0 + 3 × 0 = 0

Point B (0, 3); z = 2 × 0 + 3 × 3 = 9

Point C (2, 3); z = 2 × 2 + 3 × 3 = 13

Point $ (4, 2); z = 2 × 4 + 3 × 2 = 14

Point E (4, 0); z = 2 × 4 + 3 × 0 = 8

The maximum value of z is 14, which is obtained at the point D(4, 2)

Excel Method;

The MS Excel Solver add-in can be used to solve the LP problem using the following steps;

The optimal solution is obtained when x₁ = 4, x₂ = 2, and the maximum value of the objective function is 14, z = 2·x₁ + 3·x₂ = 14

Learn more in linear programming here: https://brainly.com/question/29750786

#SPJ1

In linear equation, 33  is the cost of supply when q=20 .

What is the most effective way to explain linear equations?

An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). A linear equation is an algebraic equation of the form y=mx+b.

                          In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.

demand function D(q) = 100 - 5q

 supply function s(q) = 0.75q

 for equilibrium point

              D(q) = S(q)

  100 - 5q = 0.75q

 0.75q + 5q = 100

   2.25q = 100

    q = 100/2.25

     q = 400/ 9

so, supply functions's value at q = 400/9

        s(400/9) = 0.75 * 400/9

                    = 100/3

                    = 33.33

                  ≈ 33

  the value of the supply functions at q = 400/9  = 33

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

For similar question on total amount:

https://brainly.com/question/11807738

#SPJ11

The maximum area is 12.25 square feet

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

Perimeter = 14 feet

This means that

P = 2(l + w)

So, we have

2(l + w) = 14

Divide by 2

l + w = 7

Make l the subject

l = 7 - w

The area is calculated as

A = lw

So, we have

A = (7 - w)w

Expand

A = 7w - w²

Differentiate and set to 0

7 - 2w = 0

So, we have

w = 3.5

Substitute w = 3.5 in A = (7 - w)w

A = (7 - 3.5) * 3.5

Evaluate

A = 12.25

Hence, the area is 12.25 square feet

Read more about area at

https://brainly.com/question/25292087

#SPJ1

Complete question

There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

GIVEN :

TO FIND :

USING FORMULA :

\( \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}\)

SOLUTION :

Substituting the given values in the formula to find the length of the missing diagonal :

\( \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}\)

\( \longrightarrow{\sf{20 = \dfrac{10 \times d_2}{2}}}\)

\( \longrightarrow{\sf{20 \times 2= 10 \times d_2}}\)

\( \longrightarrow{\sf{40= 10 \times d_2}}\)

\( \longrightarrow{\sf{d_2 = \dfrac{40}{10}}}\)

\( \longrightarrow{\sf{d_2 = \cancel{\dfrac{40}{10}}}}\)

\(\longrightarrow{\sf{\underline{\underline{d_2 = 4 \: miles}}}}\)

Hence, the length of the missing diagonal is 4 miles.

Answer:

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

To find the length of the missing diagonal, we can use the formula for the area of a rhombus, which is:

\(\sf\qquad\dashrightarrow Area_{(Rhombus)} = \dfrac{(Diagonal_1 \times Diagonal_2)}{2}\)

We know that the area is 20 square miles and one of the diagonals is 10 miles, so we can substitute these values into the formula as follows:

\(\sf\qquad\dashrightarrow20 = \dfrac{(10 \times Diagonal_2)}{2}\)

Simplifying the equation, we get:

\(\sf\qquad\dashrightarrow 40 = 10 \times Diagonal_2\)

Dividing both sides by 10, we get:

\(\sf\qquad\dashrightarrow \boxed{\bold{\:\:Diagonal_2 = 4\:\:}}\:\:\:\bigstar\)

Therefore, the length of the missing diagonal is 4 miles.

Answer:

the monthly rents of the apartments

Step-by-step explanation:

In the field of statistics, the population of interest may be defined as the group or the population from which the experimenter or the researcher tries to make conclusions or draw their results.

In the context, I am interested to study the cost of the rented house that is more than others in the West Campus area.

So I recorded the monthly rents of the apartments from a sample of 30 one bedroom apartments.

Therefore, the population of interest for my study here is the monthly rents recorded from the sample of one bedroom apartments.

Answer:

x = 2

Step-by-step explanation:

hope that helps....

If triangle ABC is rotated 180 degrees, reflected over the y-axis, and reflected over the x-axis, point A' would lie at: D. (−5, 4).

In Mathematics and Geometry, the rotation of a point 180 degrees about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180 degrees about the origin is given by this mathematical expression:

(x, y)                       →            (-x, -y)

Point A (-5, 4)        →     Point A = (5, -4)

Next, we would apply a reflection over the y-axis to the new coordinate A as follows:

(x, y)                       →            (-x, y)

Point A (5, -4)        →     Point A = (-5, -4)

Lastly, we would apply a reflection over the x-axis to the new coordinate A as follows:

(x, y)                       →            (x, -y)

Point A (-5, -4)        →     Point A' = (-5, 4)

Read more on rotation here: brainly.com/question/28515054

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

------------------------

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

Answer:

69 miles

Step-by-step explanation:

53 + 16 = L

69 = L

It's 8x + 16y/2 + 4x - 4y :))

Answer:

8x+4y

Step-by-step explanation:

Distribute:

=4x+8y+(4)(x)+(4)(−y)

=4x+8y+4x+−4y

Combine Like Terms:

=4x+8y+4x+−4y

=(4x+4x)+(8y+−4y)

=8x+4y

Answer:

=8x+4y

I hope I helped!!

Answer:

108

Step-by-step explanation:

2x+12 and 3x-18 are vertical angles which mean they are congruent. We can write the equation 2x+12=2x-18 from this. When we solve for x, the answer is x=30. Now we can plug 30 into the equation 2x+12 to get 72. Notice that angle 2x+12 added to angle EFG is 180 degrees because they are supplementary. We subtract 72 from 180 to get the resulting answer of 108.

The measure of <EFG is 102.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

line m is parallel to line n.

As, 3x- 18 = 2x + 12 (Alternate Exterior Angle)

3x -2x = 12+ 18

x = 30

and, <EFG = 180 - (2x+ 12)  (Linear Pair)

<EFG = 180 - (60+12)

<EFG = 180 - 72

<EFG = 108

Learn more about Parallel line here:

https://brainly.com/question/16701300

#SPJ2

Parents of children under the age of 18.

It is seldom feasible to get data from every member of a group of individuals when conducting research on them. In its place, you pick a sample. The population that will actually take part in the study is the sample. It is referred to as a sampling method. You can use one of the following two main sampling techniques in your study:

Random selection is a key component of probability sampling, which enables you to draw robust statistical conclusions about the entire group.

Non-probability sampling entails non-random selection based on practicality or other factors, making it simple to gather data.

To know more about sampling visit: brainly.com/question/13287171

#SPJ4

Answer:

88

Step-by-step explanation:

M : R

3 : 7

R : E

1 : 2

So make Ryan equal

1×7=7

2×7=14

tfo R : E

7 : 14

then add all 3forM+7forR+14forE = 24

192/24=8

so for Ethan, 8×14=112and for Marc, 8×3=24

therefore Ethan has 112-24=88 more stickers than Marc

From the graph, f(x) decreases from (1, 3) , (3,∞)

Therefore, the correct answer is

Step-by-step explanation:

OK so

Tomatoes = 2 3/8 = 19/8 (turned into improper fraction)

Asparagus = 1 1/4 =5/4

Potatoes = 2 7/8 = 23/8

Total vegetables used =

19/8 + 5/4 + 23/8 = 42/8 + 5/4 = 42+10/8 =52/8

Answer is 52/8 = 6.5

Answer : 52/8 pounds were used altogether

See picture for solution.

Answer: \(\dfrac15\)

Step-by-step explanation:

Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.

Favorable outcome: sum of the numbers on the two drawn cards is 7

Since 1+6 = 7 , 2+5=7, 4+3 = 7

So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)

Probability of getting (first 1, second 6) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 2, second 5) = (\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 3, second 4) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 4, second 3) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 5, second 2) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 6, second 1) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Required probability =\(6\times\dfrac{1}{30}=\dfrac15\)

Hence, the required probability = \(\dfrac15\)

Lavage Rapide's total cost per car washed is $19.05.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Fixed costs are expenses that do not change based on the number of units produced or sold. Variable costs, on the other hand, change with the level of production or sales. Here, the fixed costs are cleaning supplies, electricity, maintenance, wages and salaries, depreciation, rent, and administrative expenses.

The variable cost is the cost per car washed, which includes wages and salaries and administrative expenses.

To calculate the total cost per car washed, we need to add fixed costs to the variable cost per car. So, the total cost per car washed for Lavage Rapide would be:

Total Cost per Car Washed = Fixed Costs + Variable Cost per Car Washed

Total Cost per Car Washed =\(($0.80 + $1,400 + $0.20 + $4,700 + $8,000 + $2,100 + $1,400) + ($0.40 + $0.05)\)

Total Cost per Car Washed = $18,620 + $0.45

Total Cost per Car Washed = $19.05

Therefore, Lavage Rapide's total cost per car washed is $19.05.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

complete question:

Fixed Cost per Month Cost per Car Washed

Cleaning supplies $ 0.80

Electricity $ 1,400 $ 0.08

Maintenance $ 0.20

Wages and salaries $ 4,700 $ 0.40

Depreciation $ 8,000

Rent $ 2,100

Administrative expenses $ 1,400 $ 0.05

Answer:

true

Step-by-step explanation:

The area of the rectangle is  (14 + 1/3)  square yards.

We know that for a rectangle of length L and width W, the area is:

A = L*W

Here we know that:

L = (4 + 2/3) yards.

W = (3 + 1/4) yards.

We just need to take the product between these two numbers, we will get:

area =  (4 + 2/3)* (3 + 1/4) yd²

Expanding the product:

(4 + 2/3)* (3 + 1/4) yd² = [ 4*3 + 4*(1/4) + (2/3)*3 + (2/3)*(1/4)] yd²

                                    = [ 12 + 1 + 2 + 2/6] yd²

                                     = (14 + 1/3)  yd²

That is the area of the rectangle.

Learn more about rectangles at:

https://brainly.com/question/17297081

#SPJ1

Answer:

In geometry symmetry has to measure to the same but in real life if they are close enough it is good enough

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

Answer:

y -12 21 -1.5 -11 11 -2 -10 14 -2.5 -9 17 ?

Step-by-step explanation:

Answer:

44 degrees

Step-by-step explanation:

The triangle sum theorem states that the three interior angles of a triangle equal 180 degrees.

so:

180 - 54 - 82 =44 degrees

Answer:

44

since a triangle has 180°

180°-(82+54)= 44°