In boot camp, a cadet must use a rope swing to cross an obstacle withoutfalling into the water hazard below. Unfortunately, they miss the platform onthe other side and swing back to where they started. If it takes the cadet 3.5seconds to swing from one side of the obstacle to the other and back, howlong is the rope swing? Use the formula:

The first one the 3 sides are equal to 1, this mean that it is a equilater triangle, so it is possible to made exactly one unique triangle.

now for the other triangles we will add the two shortest sides of the triangle, and if they are more than the greater side of the triangle, then it will be a unique triangle, if not there will be more than one triangle

for the second one:

so the second one have exactly one unique triangle.

for the number 3:

So in this case there is none unique triangles.

for the number 4:

So in this case there is none unique triangles.

and for the number 5:

So we hace exactly one unique triangle.

Let's set x as the variable that has a solution of 2/3.

A possible equation is:

Now, in order to know the y-value, replace the x-value=2/3 and solve for y:

Now, replace the y-value in the initial equation, and we obtain:

If you solve this equation, you will get x=2/3.

A statement which best describes how the reasonable domain compares to the mathematical domain is that: C. the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of any graph comprises all the input numerical values or numbers which are primarily shown on the x-axis.

Next, we would evaluate the function which represents the perimeter of this rectangle by substituting the value of 2 as follows:

f(w) = 6w – 8

f(2) = 6(2) – 8

f(2) = 12 – 8

f(2) = 4.

For the length of this rectangle, we have:

Length = 2w - 4

Length = 2(2) - 4

Length = 4 - 4

Length = 0

Therefore, the width of this rectangle must be real numbers that are greater than 2.

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Complete Question:

A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.

Which statement describes how the reasonable domain compares to the mathematical domain?

Both the mathematical and reasonable domains include only positive real numbers.

Both the mathematical and reasonable domains include only positive whole numbers.

The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.

The mathematical domain includes all real numbers, while the reasonable domain includes only whole numbers greater than 2.

Answer:

( -11/2, -2)

Step-by-step explanation:

Finding the midpoint

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and then divide by 2

(-10+-1)/2 = -11/2

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and then divide by 2

(11+-15)/2 = -4/2 = -2

The  mid point is ( -11/2, -2)

The intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method is (x + (√3 - 2)/2)² = 77/4.

In Mathematics, the standard form of a quadratic equation is given by:

ax² + bx + c = 0.

In this exercise, you're required to determine the intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method. Therefore, we would re-write the quadratic equation by subtracting 19 from both sides as follows:

x² + 6x + 19 = 4x

x² + 6x + 19 - 19 = 4x - 19

x² + 6x = 4x - 19

x² + 6x - 4x = 19

x² + 2x = 19

In order to complete the square, we would have to add (half the coefficient of the x- term)² to both sides of the quadratic equation as follows:

x² + 2x + (1/2)² = 19 + (1/2)²

x² + 2x + 1/4 = 19 + 1/4

(x + (√3 - 2)/2)² = 77/4

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Complete Question:

What is the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?

x² + 6x + 19 = 4x

Answer:

Step-by-step explanation:

7/5 = 1.4

15/10 = 1.5

so 7/5 is not equal to 15/10

The price of the two stocks will be same in 1 hours .

in the question ,

it is given that

the price of the stock A at 9 A.M is $15.21

price increases at the rate of 0.07 each hour .

so the price of the stock A at 12 P.M. is 15.21 + 0.21 = $15.42

and the price of the stock A after x hours from 12 P.M. is given by the equation

stock A = 15.42 + 0.07(x)

the price of stock B at 12 P.M. is $15.96

price decreases at the rate of 0.15 each hour .

the price of the stock B after x hours from 12  P.M. is given by the equation

stock B = 15.96 - 0.15(x)

since the price of the two stocks is same , we equate both the equations .

15.42 + 0.07(x) = 15.96 - 0.15(x)

15.42 + 0.07x = 15.96 - 0.15x

0.15x + 0.07x = 15.42 - 15.21

0.22x = 0.21

x = 0.9545

x ≈ 1

Therefore , The price of the two stocks will be same in 1 hours .

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Start making the percentage as a fraction

multiply the fraction by the total of the daily routine

You have to determine the cost for 4.5 inches of the construction using the graph.

The height is on the y-axis, and the cost is on the x-axis.

First, locate 4.5 in the y-axis, which is the value in the midpoint between 4 and 5.

Draw a horizontal line until you intersect with the line, then draw a vertical line from the function until the x-axis:

The line crosses the x-axis at the midpoint between values 102 and 127.5 to determine the value at this point you have to average both costs:

The cost of 4.5 inches of construction is $114.5

Answer:

Explanation:

For Blue Car:

Distance = 33 & 1/2 miles

Gasoline = 1 & 1/4 gallons

For Red Car:

Distance = 22 & 2/5 miles

Gasoline = 4/5 gallon

To determine the rate unit rate for miles per gallon for each car, we use the following formula:

First, we find the unit rate for blue car:

Convert mixed numbers to improper fractions: 33 & 1/2 = 67/2 and 1 & 1/4 = 5/4

Next, we find the unit rate for red car:

Therefore, the car that could travel the greater distance on 1 gallon of gasoline is the red car.

We first need to calculate the slope of the line.

m=(0-0)/(5-0)=0 since the slope is equal to zero we have that the line is horizontal.Then the equation is

the equation is y=0

EXPLANATION

Let's see the facts:

Appetizers = 30%

The discount price is given by the following equation:

Discount percentage=

Could you send me a screenshot of the question for better understanding, please?

Answer:

Step-by-step explanation:

List the conditions as per question:

Inequality to represent the total number of pieces of sushi is:

The next step is to subtract -21x from 9x, which obtains 30x.

Then bring down -2 and form the new dividend 30x - 2

Given:

To determine the next step in the division, we need to solve the long division:

From our calculation, we subtract -21x from +9x and this gives 30x. We bring down -2 to combine with 30x. The result is 30x - 2

The next step is to subtract -21x from 9x, which obtains 30x.

Then bring down -2 and form the new dividend 30x - 2

we have that

x1 ----> number of cars with a 7,000 gal capacity

x2 ---> number of cats with a 14,000 gal capacity

x3 ---> number of cars with a 28,000 gal capacity

so

7000x1+14000x2+28000x3=462000

using a 3x3 system of equations solver

the solution is

x1=-2s-4t+66

x2=s

x3=t

The answer is option B

Part A

we have that

A(4) ----> looking at the graph

A(4) means----> population in the year 1994

so

A(4)----> less than 2 million

and

B(4) -----> greater than 2 million

therefore

the answer Part a is option B

Part B

there is only one value of t where A(t)=B(t)

the value of t is 6 (the year 1996)

According to the given data we have the following:

Total copies she buys= 25 copies

book cost=$7.19

Therefore, in order to calculate the amount of money that Mrs. Reeder spend we would have to make the following calculation:

Amount of money that Mrs. Reeder spend= quantity of copies * book cost

Amount of money that Mrs. Reeder spend=25 copies*$7.19

Amount of money that Mrs. Reeder spend=$180

The amount of money that Mrs. Reeder spend was $180

We will find the measure of angle V as follows:

*From theorem we have that angles that are opposite to congruent sides are congruent. So, Angle W will also have a measure o 74°. Now, we also have that the sum of all internal angles of a triangle add 180°, so the following is true:

Now, we solve for V:

So, the measure of angle V is 32°.

The solution set does have only one element: {7000}

Given:

f(x) = 8x + 11

g(x) = 4x² + 7x - 2

We are asked to evaluate using the following:

(a) f(8)

f(8) = 8(8) + 11

f(8) = 64 + 11

f(8) = 75

(b) f(-8)

f(-8) = 8(-8) + 11

f(-8) = -64 + 11

f(-8) = -53

(c) g(6)

g(6) = 4(6)² + 7(6) - 2

g(6) = 4(36) + 42 - 2

g(6) = 144 + 42 - 2

g(6) = 184

(d) g(-7)

g(-7) = 4(-7)² + 7(-7) - 2

g(-7) = 4(49) - 49 - 2

g(-7) = 196 - 49 - 2

g(-7) = 145

(e) g(a)

g(a) = 4(a)² + 7(a) - 2

g(a) = 4a² + 7a - 2

As observed, all the questions in the list can be answered on the basis of some data collection and analysis.

So they all can be considered as statistical questions.

Thus, all the questions in the given list are statistical questions.

1.

If you have to answer the question for most popular lunch choice, you have to collect data of the lunch choices by a large portion of the called population. Then the lunch choice corresponding to highest frequency will be considered as the most popular lunch choice. Since the conclusion is data driven, this is a statistical question.

2.

In order to answer the question, you need to collect the information about the name of school each of the called population is admitted to. If all the students are found to be admitted to the same school, then the name of that school would be the answer.

Here also, the conclusion is data driven, so this is also a statistical question.

3.

To answer this question, you have to gather all the teaching staff of the school, and take individual answers to which subject they teach. The number of teachers who answered math will be the answer for this question.

Here also, the conclusion is data driven, so this is also a statistical question.

4.

To answer this question, you have to gather the individual age of each teacher in the school. The age corresponding to the maximum frequency would be the answer to this question.

Here also, the conclusion is data driven, so this is also a statistical question.

5.

To answer this question, you have to collect data about how much sleep each student gets in the school. Then only you can answer this question.

Since the conclusion is data driven, this is a statistical question.

6.

To answer this question, you have to collect data that how many students travel by which mode of transport to travel from home to school. The mode corresponding to highest frequency is the answer to this question.

Here also, the conclusion is data driven, so this is also a statistical question.

Thus, it is seen that all the six questions are statistical questions.

Line equation: y = 5

Slope: 0

Intercept: 5

Formule:

. Equation : y = mx + b

. Slope: m = () / ()

The equations are

The smallest negative number is the pivot column

so the smallest negative number is -3 and hence the pivot column is

3

5

-3

The row pivot hence = 5

so pivot will be (x= -3 and S = 5)

From the given figure, we can see that the angle (12x+4) and the angle (17x+2) lie on the same straight line.

Theerfore, they are supplimentary to each other.

Let x be the measure of JK so we get that

We have to write a word problem using,

• 72 tokens/12 games

• tokens/10 games

We can first give an information related to 72 tokens PER 12 games.

Then we can ask "how many tokens" per 10 games.

Let us devise a word problem.

The local game center sells tokens to play online games. Jeremy used 72 token to play 12 online games. At this rate, how many token would Jeremy use to play 10 online games?

The above problem uses both the information provided.

Given

Using the scale of 1/2

This means we divide each coordinate by 2