Kim is drawing a map of the different schools in her school district.she knows that her middle school is 10.6 miles away from the middle school that her best friend attends.if every 2 inches on the map represents 5 miles, how far apart will the two schools be on the map,to the nearest tenth of an inch

The slope of the line that goes through the point  (-15,70) and (5,10) is - 3.

The slope is the measure of the angle a line has with respect to the positive x-axis.

We know when two points of a line is given slope can be obtained by rise over run where the rise is the difference between the points of the y-axis and run is the difference of the points of the x-axis.

Given points are (-15,70) and (5,10) through which a line passes.

∴ Slope(m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Slope(m) = (10 - 70)/(5 + 15).

Slope(m) = -60/20.

Slope(m) = -3.

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The coordinates of the midpoint of the segment HK are (7, 6).

The midpoint coordinates of a line segment can be found using the midpoint formula:

Midpoint =[tex]\((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\)[/tex]

Given the endpoints of the segment as H(8,2) and K(6,10), let's plug these values into the formula:

Midpoint =[tex]\((\frac{8 + 6}{2}, \frac{2 + 10}{2})\)[/tex]

Midpoint =[tex]\((\frac{14}{2}, \frac{12}{2})\)[/tex]

Midpoint =[tex]\((7, 6)\)[/tex]

The coordinates of the midpoint of the segment HK are (7, 6).

To calculate the midpoint of a line segment, you can follow these steps:

1. Identify the coordinates of the endpoints of the segment. Let's call them[tex]\( (x_1, y_1) \) and \( (x_2, y_2) \).[/tex]

2. Use the midpoint formula:[tex]\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).[/tex]

3. Substitute the coordinates into the formula and calculate.

In this case, the endpoints are H(8,2) and K(6,10). Plug these values into the midpoint formula:

Midpoint = [tex]\( \left( \frac{8 + 6}{2}, \frac{2 + 10}{2} \right) \).[/tex]

Simplify the equation:

Midpoint =[tex]\( \left( \frac{14}{2}, \frac{12}{2} \right) \).[/tex]

Finally, calculate the values:

Midpoint =[tex]\( (7, 6) \).[/tex]

So, the coordinates of the midpoint of the segment HK are (7, 6).

complete question

Find the coordinates of the midpoint of the segment whose endpoints are H(8,2) and K(6,10).

Answer: Option A inverse variation

Explanation:

when we  compare the values from the given  table  x is increasing and y is decreasing hence we can see it is  an inverse variation.

In option B difference among  all consecutive  values of x is 2 but in y it is not same among  all consecutive  terms. In linear function change in y over change in x must be same.

In option C  x is increasing but y is decreasing which is violating the property of logarithmic function. In logarithmic function  if  x  increases then y should increase.

In option D first value of x is 2 following quadratic property meaning giving square of itself in y which is 4. But not all values of y are square of x except first value. In quadratic function value of y should be square of x.

The type of function that best models the table given is: A. inverse variation.

Inverse variation can be described as a relationship between two variables, whereby, the product of the two variables will give a constant. It is expressed as, k = xy.

In an inverse variation, if one variable increases, the other variable decreases.

The table shows an inverse variation because as x increases, y decreases, and can be expressed as k = xy.

Therefore, the type of function that best models the table given is: A. inverse variation.

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Final answer:

To factor a number, variable, or expression out of the polynomial 15x³ + 20xa, you can factor out 5x to get 15x(x²+5x).

Explanation:

To factor a number, variable, or expression out of the polynomial 15x³ + 20xa, you need to identify a common factor.

In this case, the common factor is 5x. So, you can factor out 5x from each term to get: 15x(x²+5x)

Therefore, the correct answer is option a. 15x(x²+5x).

Answer:

Step-by-step explanation:

(-5, 0) and (6, 0) is the correct answer.

To find the x-intercepts, use the Zero Product Property and solve for x:

x - 6 = 0  

x = 6

x + 5 = 0

x = -5

Therefore, the x-intercepts are (6,0) & (-5,0).

The given argument is valid by the law of syllogism which is the correct answer would be option (C).

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.

Premise: If two angles form a linear pair, they are supplementary.

If two angles are supplementary, the total of their measurements equals 180.

Conclusion: If two angles form a linear pair, the total of their measurements equals 180.

If two angles form a linear pair, they are always supplementary.

Thus, if two angles form a linear pair, the total of their measures is 180°; however, if two angles are supplementary, it does not ensure that they will form a linear pair.

So the given argument is valid by the law of syllogism.

Hence, the correct answer would be option (C).

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To determine what percent of 10 is 6, you multiply 6/10 by 100, which equals 60%, thus 6 is 60% of 10.

To find what percent of 10 is 6, we can use the formula for percentage which is (Part / Whole) * 100.

In this case, the 'part' is 6 and the 'whole' is 10.

So the equation to find the percentage is (6 / 10) * 100.

Calculating that out, we get 0.6 * 100, which equals to 60%.

Therefore, 6 is 60% of 10.

This is a basic concept in mathematics where you are trying to find out how one number compares to another in terms of percentage.

Answer:

yes 4

Step-by-step explanation:

The relationship that is continuous is the distance a runner ran during training.

The relationship that is continuous is D. the distance a runner ran during training.

A continuous relationship is one in which the values of one variable change smoothly and consistently over a given interval. In the case of the distance a runner ran during training, the distance can be any real number and can be measured with great precision, allowing for smooth changes in the values.

The continuous relationship is the distance a runner ran during training.

A continuous relationship is one where the variable changes smoothly and can take any value within a given range. Let's analyze the options:

A. The number of cows a farmer has owned over the years:

This relationship is likely continuous, as the number of cows can change smoothly over time, and there are no discrete jumps in ownership.
B. The number of cookies Stan baked for the party:

This relationship is likely discrete, as the number of cookies is typically counted in whole numbers without smooth transitions. Stan would bake a specific, countable quantity of cookies.
C. The number of people attending the assembly:

This relationship is likely discrete, as the number of people is counted in whole numbers and does not change smoothly. Attendees come in whole individuals, not fractions.
D. The distance a runner ran during training:

This relationship is continuous, as distance can vary smoothly and take any real value within a given range. Runners can cover fractional distances, making it a continuous variable.
Therefore, the continuous relationship is D, the distance a runner ran during training.

Answer:

They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position

Step-by-step explanation:

To gain a new set of downs, a football team has four downs(tries) to gain 10 net yards, in total.

Gained 6 yards on first down

Net of 6 yards gained

Needs 10-6 = 4 yards

Lost 15 yards on second down

6 - 15 = -9

In all, they have lost 9 yards, so they need

4 + 15 = 19 yards

Gained 12 yards on third down

-9 + 12 = 3 net yards(need 10)

19 - 12 = 7

They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2 

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  2 
                     x2 - 1x + 2x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x-1)
Step-5 : Add up the four terms of step 4 :
                    (x+2)  •  (x-1)
             Which is the desired factorization

Answer:

A. 4

Step-by-step explanation:

Answer: the question

Step-by-step explanation:Select the correct answer from the drop-down menu.

John has 54 white marbles and 9 yellow marbles. Ben has 16 white marbles and 96 yellow marbles. Noel has 12 white marbles and 72 yellow marbles.

The boys who have the same ratio of white marbles to yellow marbles are .

The square root of the given number 121 is 11.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

The given number is √121.

We need to find the square root of given numbers.

Here, 121=11×11

= 11²

So, √121 = √11²

= 11

Therefore, the square root is 11.

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The expression 85 + C; 85 + (-9) = 76; 76 degrees F option is (C) 85 + C; 85 + (-9) = 76; 76 degrees F is correct.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

The temperature on a summer afternoon is 85 degrees Fahrenheit.

Let C be the temperature in degrees

F = (9/5)C + 32

Or

C = [5/9](F - 32)

From the data given in the question:

Any temperature change is the sum of the initial temperature and the new value.

Temperature plus changes The figure will be positive if there has been an increase. The number will be negative if there is a reduction.

Thus, the expression 85 + C; 85 + (-9) = 76; 76 degrees F option is (C) 85 + C; 85 + (-9) = 76; 76 degrees F is correct.

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Answer: C

Step-by-step explanation:

To determine the size of an angle and its supplement when the angle is four times the size of its supplement, we use the equation x = 4(180 - x) and solve for x to find that the angle measures 144 degrees and its supplement measures 36 degrees.

To find the measures of an angle and its supplement when the angle is four times its supplement, we use the expressions x and 180 - x. We can set up the equation x = 4(180 - x). Then we can solve for x to find the measures of the angle and its supplement.

By expanding and rearranging the equation, we get:

Thus, the angle measures 144 degrees and its supplement measures 36 degrees (since 180 - 144 = 36).