If the measure of an interior angle of a regular polygon is 108, what type of polygon is it?
F octagon
G hexagon
H pentagon
J triangle

Answer:uh I think its a carrot

Step-by-step explanation:

By substitution, the solution of the system of equations, x + 12y = 68 and x = 8y - 12, is (20 , 4).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 12y = 68     (equation 1)

x = 8y - 12     (equation 2)

Since the second equation is already expressed in x in terms of y, substitute the value of x to the first equation.

x + 12y = 68     (equation 1)

(8y - 12) + 12y = 68

8y - 12 + 12y = 68

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

8y - 12 + 12y = 68

8y + 12y = 68 + 12

20y = 80

y = 4

Substitute the value of y in the second equation and solve for x.

x = 8y - 12     (equation 2)

x = 8(4) - 12

x = 32 - 12

x = 20

Hence, the solution of the given system of equations is (20 , 4).

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20x-14x=21-10

6x=11

x=11/6

☞ user58580~ ♥

Answer:

The Answer is x=11/6

Step-by-step explanation:

Hope this helps!!

The feasible solution is the best solution possible for a mathematical model , the statement is False.

Feasible Solution for a mathematical model is defined as the solution that satisfies all the constraints of the linear program.

Whereas an Optimal Solution is a feasible solution that minimizes or maximizes the function.

Optimal Solution is a part of feasible Solution .

So , an Optimal Solution can also satisfy all the constraints of the linear program.

Hence, The feasible solution is the best solution possible for a mathematical model statement is False .

Therefore , the correct option is (b) false.

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Mark has:  1 1/3 = 4/3  gallons of Yellow

                1 1/4 = 5/4  gallons of Green

                           7/8  gallons of Blue.

Total =  (4/3 + 5/4 + 7/8)    LCM = 24

       =  (32 + 30 + 21)/24 = 83/24  Gallons of Paint in total.

If he used 3/4 of each, he would have = 1/4 of each left.

Therefore gallons left =  1/4 * (83/24) = 83/96 gallons left.

=  0. 8646 gallons left in total.

We can say that ΔRUQ ≅ ΔTUS under RHS condition.

So,

Given: RQ ≅ ST and RQ || ST

To Prove: ΔRUQ ≅ ΔTUS

So, we can say that ΔRUQ ≅ ΔTUS under RHS.

Therefore, ΔRUQ ≅ ΔTUS.

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Answer:16 and 24

Step-by-step explanation:

The solution of the given linear equation 3(w -8) = 36 in one variable is at w = 20.

According to the given question.

We have a linear equation in one variable 3(w - 8) = 36.

Since, we have to solve the above equation for w.

As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Therefore, the solution of the linear equation in one varibale 3(w - 8) = 36 is given by

3(w - 8) = 36

⇒3w - 24 = 36      ( by distributive property)

⇒ 3w = 36 + 24     (adding 24 both the sides)

⇒ 3w = 60

⇒ w = 60/3   (dividing both the sides by 3)

⇒ w = 20

Hence, the solution of the given linear equation 3(w -8) = 36 in one variable is at w = 20.

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The vertex and range are (-2, -3) and y >= -3 respectively

The equation is given as:

y = |x +2| - 3

The above equation is an absolute value equation

An absolute value equation is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-2, -3)

Also, we have

a = 1

Since a is positive, then the vertex is a minimum

Hence, the vertex and range are (-2, -3) and y >= -3 respectively

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Answer:

30

Step-by-step explanation:

Substitute 24 for w

2(24) - 18

multiply 24 by 2

48 - 18

Subtract 18 from 48

Answer: 30

The number of chickens are J. 90.

Let the chickens be represented by x and the pigs be represented by y.

Forming the equation according to first information -

Equation 1 : x + y = 120

x = 120 - y

Both chicken and pig has one head. Chicken has 2 feet while pig has 4 feet. Forming the equation according to second information -

Equation 2 : 2x + 4y = 300

Simplifying the equation 2 by dividing by number 2

x + 2y = 150

Keep the value of x from equation 1 in equation 2

120 - y + 2y = 150

Performing subtraction

120 + y = 150

Further shifting the value and performing subtraction

y = 150 - 120

Performing subtraction

y = 30

Now, 30 is the number of pigs.

Number of chickens = 120 - y

Number of chickens =  120 - 30

Number of chickens = 90

Hence, the number of chickens the farmer has is J. 90.

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Answer:

[tex]4(5) {m}^{3} \times {m}^{2} \times {n}^{2} \times {n}^{1} [/tex]

since you know the rules of exponents we are multiplying powers of the same bases meaning we will add the exponents.

[tex] = 20 {m}^{3 + 2} {n}^{2 + 1} \\ = 20 {m}^{5} {n}^{3} [/tex]

Answer:

3x-26

Step-by-step explanation:

-4(x+7)+7x+2

Multiple -4 By 7

-4x -28 +7x +2

Group like terms

-4x +7x -28+2

-4+7= 3

3x -28 +2

-28+2=-26

3x-26

Hope this helps! ^^

Answer:

3.6cm

Step-by-step explanation:

the points lie in order like this

A.....B.....C

we know that A......B......C total spans 4cm (or 40mm)

we know that A......B spans 4mm

we need to know the length of B......C

B......C = A.......B.......C - A.....B = 40mm - 4mm = 36mm = 3.6cm

Measure of angle 5 i.e. m∠5 = 50°

The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.

In the question,

Let given angle is ∠8.

Given, ∠8 = 50°

Now, according to vertical angle property

∠5 = ∠8

therefore, ∠5 = 50°

Thus, m∠5 = 50°

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The complete question is :

Find measure m∠5

Answer:

D. x = 3

Step-by-step explanation:

[tex] {x}^{3} = 27[/tex]

[tex]x = \sqrt[3]{27} = 3[/tex]

Answer:

$30.87

Step-by-step explanation:

Saturday

- gross: $90

- net: $77.75

Sunday

- gross: $120

- net: $101.38

Total gross: 90 + 120 = $210

Total net: 179.13

Total tax: 210 - 179.13 = 30.87

The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.

It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.

Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.

The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.

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Answer:

Step-by-step explanation:

The answer is R

Josh collected 60 stickers, Ann collected 67 stickers and Claire collected 30 stickers.

Ann, Claire and Josh collect stickers. One week, Ann collects 7 more stickers than Josh.

let use variables to represent the amount of stickers they collected.

Therefore, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers as Claire

Josh stickers = x

Ann stickers = 7 + x

Claire stickers = 1 / 2 x

Total stickers collected = 157

Therefore,

x + 7 + x + 1 / 2 x  = 157

x + x + 1 / 2 x = 157 - 7

2.5x = 150

divide both sides by 2.5

x = 150 / 2.5

x = 60

Therefore, Josh collected 60 stickers, Ann collected 67 stickers and Claire collected 30 stickers.

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Answer: 103/13

Step-by-step explanation:

7 * 13 = 91

91 + 12 = 103

The person that is most likely considered the authority on the subject is A. a zoologist.

It should be noted that a zoologist simply means the individual that study animals and how they interact with their ecosystem.

In this case, Myra is reading an article about the success of introduced species of animals into the United States.

Therefore, the person that is most likely considered the authority on the subject is a zoologist.

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The length of slant height l is √98 ft. when diameter of cone and  height of cone is 7 ft.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

Here, the diameter of cone is given as : 14ft.

also, the height of cone is : 7 ft.

the radius r of base will be half of diameter :

r = b/2  

r = 14/2 = b

Now to find the slant height of the cone we use Pythagoras theorem between the base of cone b, height of cone h and slant height l that is :

h² + r² = l²

7² + 7 ² = l²

l² = (2x7²)

l = 7 √2 ft. or √98 ft.

Therefore, the length of slant height l is √98 ft.

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We can use the pythagorean theorem to answer this question.

We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.

So, we can build the equation:

[tex]7^2+7^2 = l^2[/tex]

[tex]98 = l^2[/tex]

[tex]\sqrt{98} = l[/tex]

.

Answer:

repeated

Step-by-step explanation:

The tire travels 7536 inches.

We are given the diameter of tire of bicycle. Now, to find the distance traveled, we will use the following formula -

Distance = number of rotations × circumference of tire.

Now, further calculating the circumference of tire using the formula -

Circumference = π×diameter.

Firstly keep the values in the formula of circumference to calculate it.

Circumference = 3.14×24

Performing multiplication

Circumference = 75.36 inch

Now, keep the values in formula to find the distance traveled by the tire of bicycle.

Distance = 100×75.36

Again performing multiplication

Distance = 7536 inches

Hence, the distance traveled by the tires 7536 inches.

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The find two consecutive odd integers is 7 and 9

These are functions that has a linear degree of 1. Let the two consecutive odd numbers be 2x + 1 and 2x + 3

If their product is the same as fifteen more than three times their sum, then;

(2x+1)(2x+3) = 3(2x+1+2x+3) +15

4x²+6x+2x+3 = 3(4x+4)  +15

4x²+8x+3 = 12x+12 + 15

4x² - 4x + 3 = 27

4x² - 4x - 24 = 0
x² - x - 6 = 0

On factorizing, the value of x is 3 and -2

First number = 2(3) + 1 = 7

Second number = 2(3) + 2 = 9

Hence the find two consecutive odd integers is 7 and 9

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The algebraic expression for total hours that represents the number of hours per week the theater is open is 4 x + 3 y

Number of hours the theatre is opened on Monday to Thursday = x hours.

Number of hours the theatre is opened on Friday to Sunday = y hours.

Number of hours from Monday to Thursday = 4 x hours.

Number of hours from Friday to Sunday = 3 y hours.

Total hours will be represented by the algebraic expression:

Total hours = 4 x + 3 y.

Therefore, the algebraic expression for total hours that represents the number of hours per week the theater is open is 4 x + 3 y

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Answer: [tex]x=\frac{7-2y}{4}\\[/tex]

Step-by-step explanation:

4x+2y-2y=7-2y

4x= 7-2y

[tex]\frac{4x}{4}=\frac{7}{4}-\frac{2y}{4}[/tex]

Simplify: [tex]\mathrm{Divide\:the\:numbers:}\:\frac{4}{4}=1[/tex] = x / [tex]\frac{7}{4}-\frac{2y}{4}[/tex] x = [tex]\frac{7-2y}{4}[/tex]