Zoe and Mackenzie are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Zoe is 249 miles away from the stadium and Mackenzie is 237 miles away from the stadium. Zoe is driving along the highway at a speed of 58 miles per hour and Mackenzie is driving at speed of 55 miles per hour. Let ZZ represent Zoe's distance, in miles, away from the stadium tt hours after noon. Let MM represent Mackenzie's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine whether Zoe or Mackenzie is closer to the stadium 2 hours after noon.

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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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:

$30.87

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

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

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:

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! ^^

The coordinates of the point on the directed line segment is (-5,5)

In the given sum we are using the internal division formula which goes like:  (x,y) = (nx₁ + mx₂)/(m+n), (ny₁ + my₂)/(m+n)

with the available data we can interpret that where m = 1 , n = 4 , (x₁,y₁) = (-8,8) , (x₂,y₂) = (7,-7)

substituting the given values in the above formulae

The coordinates of the point is :

(x,y) = (4(-8) + 1(7))/(1 + 4) , (4(8) + 1(-7))/(1 + 4)

= ( -32 + 7)/5, (32 - 7)/5

= (-25/5) , (25/5)

= (-5,5)

∴ (x , y) = (-5 , 5)

So here the coordinates are (-5 , 5) which directed line segment from (-8,8) to (7,-7) that partions the segment into a ratio of 1 to 4

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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

Characteristics exhibited by continuously varying traits are called quantitative traits. These continuously varying traits always measure phenotypes which usually depend on the cumulative behavior of many genes.

What are continuously varying traits?

Continuous varying traits exhibit the characteristics whose traits do not fall in the discrete categories like height and weight. Different traits which come under continuous varying traits are anatomical traits, physiological traits, behavior traits as well as diseases. It shows the continuous phenotypic variation within the group of individuals.

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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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Answer:16 and 24

Step-by-step explanation:

The last one.

It states that "The video games cost $43 each." and the total price was $72 in movies meaning that the x would go with the 43 and 1,128 would have to be greater than the amount she's buying or she won't be able to buy it.

20x-14x=21-10

6x=11

x=11/6

☞ user58580~ ♥

Answer:

The Answer is x=11/6

Step-by-step explanation:

Hope this helps!!

Answer:

x = -2

Step-by-step explanation:

First, distribute:

-12x + 28 = 52

Then, subtract 28 on both sides:

-12x = 24

Finally, divide -12 on both sides:

x = -2

Step-by-step explanation:

hope it helps

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]

Based on the linear pair theorem, the value of x is: 42°.

A linear pair is a pair of two angles that are formed adjacent to each other on a straight line. These two angles, according to the linear pair theorem, have a sum of 180d degrees when their measures are added together.

From the image, we see that x° and 138° are a linear pair as they lie on a straight line.

Therefore:

x + 138 = 180 [linear pair theorem]

Subtract 138 from both sides of the equation

x + 138 - 138 = 180 - 138

x = 42°

Therefore, based on the linear pair theorem, the value of x is: 42°.

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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:

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

Answer:

6.1 * 10^-3

Step-by-step explanation:

This is because 10^-3 = 0.001 so 0.0061=6.1 * 10^-3

Answer:

6,100,000,000

Step-by-step explanation:

0.0061 x 10^12 =6,100,000,000

Answer: 103/13

Step-by-step explanation:

7 * 13 = 91

91 + 12 = 103

Answer: different and subtract go in the empty spaces

Answer:

D. x = 3

Step-by-step explanation:

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

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

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]

The arithmetic mean of the monthly salaries of two employees is $ 3210 . One employee earns $ 3470 per month. What is the monthly salary of the other employee.

Then $2950 is the salary of the other employee.

$2950 is the monthly salary of the other employee.

a. the given information = mean of two salaries =  3210

                                       = salary of 1st employee =3470

the unknown information = salary of 2nd employee = 2950

The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.

The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).

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Answer:

repeated

Step-by-step explanation:

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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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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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.