you run one lap around a mile track every 8 minutes. Your friend runs around the same track every 10 minutes. You both start at the starting line at the same time

Answer:

[tex]\sqrt{\frac{7}{11} }[/tex]

Step-by-step explanation:

The right expression of the question is

[tex]\frac{\sqrt{7} }{\sqrt{11} }[/tex]

The simplest radical form of this expression is obtained by applying the right property, which is about the quotient between radicals. According to this property, the quotient of radical is equal to the radical of the quotient, that is

[tex]\frac{\sqrt{7} }{\sqrt{11} }=\sqrt{\frac{7}{11} }[/tex]

Answer:

85.75 cubic units

Step-by-step explanation:

You got the formula [tex]V=2s^3[/tex] and you know that s = 3.5 units

The only thing you need to do is to substitute the value of s in your formula. This is

[tex]V= 2(3.5)^3[/tex]

And you need to do all the operations

[tex]V= 2(3.5)^3 = 2(42.875) = 85.75[/tex]

And your answer is D

The value of V for s = 3.5 units is,

⇒ V = 85.75 cubic units

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The equation below shows the total volume (V),in cubic units, of 2 identical boxes with each side equal to s units as,

⇒ V = 2s³

Here, We have;

s = 3.5 units

Hence, We get;

⇒ V = 2s³

⇒ V = 2 × 3.5³

⇒ V = 85.75 cubic units

Thus, The value of V for s = 3.5 units is,

⇒ V = 85.75 cubic units

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The value of A that will satisfy the equation (-3/4 + 4/3) + A = 0 is -7/12 after finding a common denominator and simplifying the fractions.

To find the value of a that will make the equation (-3/4 + 4/3) + a = 0 a true statement, we need to first simplify the fraction part of the equation.

Let's find a common denominator for the fractions, which is 12. Converting both fractions, we get:

Now, adding these two fractions we have:

-9/12 + 16/12 = 7/12

So, the equation now is:

7/12 + a = 0

To solve for a, we need to isolate a on one side of the equation:

a = -7/12

Therefore, the value of a that makes the equation true is -7/12.

-5(-2f-6)

 distribute by multiplying -5 by everything inside the parenthesis

-5 * -2f = 10f

-5 *-6 = 30

so you get 10f+30

It would be 7 units because when you put down the points and you draw a diaganal line between the two points and it crosses 7 intersections.

Hope you stay safe and this answer helps you.

The value of b in the equation of the trend line is 21

The equation of the trend line of the scatter plot is given as:

y = 15x + b

The points are given as: (6.4, 117) and (6.6, 120).

Using (6.4, 117), we have:

117 = 15 * 6.4 + b

Evaluate the products

117 = 96 + b

Subtract 96 from both sides

21 = b

Rewrite as:

b =21

Hence, the value of b in the equation of the trend line is 21

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The coordinates for the points of intersection of the line y=-1.5x + 3 with the coordinate axes are (0,3) for y-axis and (2,0) for the x-axis.

To find the points of intersection of the line with the coordinate axes, we will set the values of y and x to zero separately. So, let's start from the intersection of the line with the y-axis. For this, we set x=0 in the equation y = -1.5x + 3. Thus, y = 0*(-1.5) + 3 which gives us y = 3. So one point of intersection is (0,3). Next, finding the x-intercept requires setting y=0, which gives 0 = -1.5x + 3. Solving this equation, we get x = 3 / 1.5 or x=2. Hence, the other point of intersection is (2,0). Therefore, the coordinates for the points of intersections are (0,3) and (2,0).

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Answer:

A. [tex]f(x)=-4|x+2|+3[/tex]

Step-by-step explanation:

We have been given an image of an absolute function. We are asked to find the formula for our given absolute function.

The formula of parent absolute function is [tex]f(x)=|x|[/tex] with vertex at (0,0)

We can see that the vertex of our given function is at [tex](-2,3)[/tex]. This means that our function is shifted to left by 2 units. We can represent this information as: [tex]f(x)=|x--2|=|x+2|[/tex]

We can also see that our graph is reflected across x-axis, so after reflection our function would be [tex]f(x)=-|x+2|[/tex]

We can see that our graph is shifted upwards by 3 units, so graph after shifting would be [tex]f(x)=-|x+2|+3[/tex].

Our graph is stretched vertically by a scale factor of 4, so after stretching our function would be [tex]f(x)=-4|x+2|+3[/tex].

Therefore, option A is the correct choice.

Answer:

Step-by-step explanation:

The slope of the line in simplified form is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The slope of a line which contains points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex]

is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The given is:

1. Point (-12 , -60) lies on the line

2. Point (60 , -42) lies on the line

We need to find the slope of the line

∵ [tex](x_{1},y_{1})[/tex] = (-12 , -60)

∵ [tex](x_{2},y_{2})[/tex] = (60 , -42)

- Substitute these values in the rule

∴ [tex]m=\frac{-42-(-60)}{60-(-12)}[/tex]

∴ [tex]m=\frac{-42+60}{60+12}[/tex]

∴ [tex]m=\frac{18}{72}[/tex]

∴ [tex]m=\frac{1}{4}[/tex]

The slope of the line in simplified form is [tex]\frac{1}{4}[/tex]

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Final answer:

By adding the distance from A to M to A's coordinate, we find that M's coordinate is 1.

Explanation:

The question asks to find the coordinate of point M on a number line where point A has a coordinate of −1.5, point B has a coordinate of 6, and the ratio of the distances AM to MB is 1:2. To solve this, we first identify that AM and MB are segments on the number line with point M somewhere between A and B. Since AM:MB = 1:2, we know that for every unit distance from A to M, there are 2 unit distances from M to B.

The total distance between A and B is 6 - (−1.5) = 7.5 units. Dividing this distance in the ratio 1:2, implies that AM takes up one-third of the total distance and MB takes up two-thirds of the total distance. Therefore, AM = ¼ * 7.5 = 2.5 units. Adding this distance to the coordinate of A gives us the coordinate for M: −1.5 + 2.5 = 1. So, the coordinate of point M is 1.

Answer:

5n = 30 + 3(n - 4)

Step-by-step explanation:

To find the missing rate and new balance, we used the simple interest formula. The rate was calculated to be 5% and the new balance after 3 years, including interest earned, was determined to be $517.50.

The subject in question here is simple interest calculation, which is a fundamental concept in finance and mathematic subjects. To solve for the missing rate and new balance, we can use the formula Interest = Principal x rate x time.

First, we rearrange the interest formula to solve for the rate:

Rate = Interest / (Principal x Time)

Plugging in the provided numbers:

Rate = $67.50 / ($450 x 3)

Rate = $67.50 / $1350

Rate = 0.05 or 5%

Now, we find the new balance using the formula:

New Balance = Principal + Interest

New Balance = $450 + $67.50

New Balance = $517.50

Therefore, the interest rate is 5% and the new balance after 3 years is $517.50.