Which of the following lengths and widths represents a rectangle whose diagonal is rational? Question 3 options: length = 2, width = 1 length = 4, width = 4 length = 3, width = 2 length = 4, width = 3

Answers

Answer 1

Answer:

Correct option is length = 4, width = 3.

Step-by-step explanation:

Given:

Diagonal of a rectangle is rational.

To find:

Which of the following length and width options represent a rectangle ?

options:

length = 2, width = 1

length = 4, width = 4

length = 3, width = 2

length = 4, width = 3

Solution:

First of all, let us consider a rectangle as shown in the attached answer image.

Rectangle ABCD.

Width of rectangle is AB.

Width of rectangle is BC.

And the diagonal AC or BD can be found by using Pythagorean Theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = AB^{2} + BC^{2}\\\Rightarrow Diagonal^{2} = Length^{2} + Width^{2}[/tex]

Now, let us find diagonal for each option and check whether it is rational or not.

Option 1:

length = 2, width = 1

[tex]Diagonal^{2} = 2^{2} + 1^{2}\\\Rightarrow Diagonal^{2} = 5\\\Rightarrow Diagonal = \sqrt5[/tex]

Not rational

Option 2:

length = 4, width = 4

[tex]Diagonal^{2} = 4^{2} + 4^{2}\\\Rightarrow Diagonal^{2} = 32\\\Rightarrow Diagonal = 4\sqrt2[/tex]

Not rational.

Option 3:

length = 3, width = 2

[tex]Diagonal^{2} = 3^{2} + 2^{2}\\\Rightarrow Diagonal^{2} = 13\\\Rightarrow Diagonal = \sqrt{13}[/tex]

Not rational.

Option 4:

length = 4, width = 3

[tex]Diagonal^{2} = 4^{2} + 3^{2}\\\Rightarrow Diagonal^{2} = 25\\\Rightarrow Diagonal = \sqrt{25} = 5[/tex]

Diagonal is rational.

Correct option is length = 4, width = 3.

Which Of The Following Lengths And Widths Represents A Rectangle Whose Diagonal Is Rational? Question

Related Questions

An average person's hair grows at a rate of 19cm per year how fast in inches per month does the average person hair grow in conversion factor round you answer to the nearest tenths

Answers

Answer:

Around 1.6 cm per month

Step-by-step explanation:

We can set up a proportion to find how much the hair grows per month. It's important to note that there are 12 months in a year, so we can represent a year as 12 months.

[tex]\frac{19}{12} = \frac{x}{1}[/tex]

We can now cross multiply:

[tex]19\cdot1=19\\\\19\div12=1.58\overline{33}[/tex]

1.58333... rounds to 1.6.

Hope this helped!

Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.

Answers

Answer:

[tex]AC=20[/tex]

Step-by-step explanation:

The line segment AC is the entire length of the line. Within this segment, point  B is found.

Point B, in a way, splits the segment into two, creating the segments AB and BC.

To find the length of AC, add the lengths of the lines AB and BC together:

[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]

The length of AC is 20.

:Done

Answer:

20 units.

Step-by-step explanation:

Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.

If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.

Hope this helps!

Two rectangles are joined together to form a single large area. The rectangles do not overlap. The first rectangle has side lengths of 333 meters and 555 meters. The second rectangle has side lengths of 777 meters and 444 meters. What is the combined area?

Answers

Answer:

Step-by-step explanation:

333 times 555=184815

777 times 444=344988

now add 184815+344988=529803

Allie, Ben, and Cliff plant ceilings in the neighborhood park. Ali plans 40% of the total number of ceiling, then place 45% of the total number of seed wings, and Cliff plans the rest of the siblings. If Cliff +84 siblings how many seedling do the three boys play together

Answers

Answer:

The number of seedlings the three boys planted together is 560 seedlings

Step-by-step explanation:

The possible information in the question are;

Percentage of the seedlings planted by Ali = 40%

Percentage of the seedling planted by Ben = 45%

The percentage of the seedling planted by Cliff = The rest of the seedling

The number of seedling planted by Cliff = 84 siblings

Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%

Given that Cliff planted 15% of the seedlings, we have;

15% of seedlings Cliff planted = 84

Let X = the total number of seedlings

15/100 × X = 0.15×X = 84

X = 84/0.15 = 560

The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.

Bob says that he can find the area of the triangle below using the formula: A = [tex]\frac{1}{2}[/tex] * 8 *18 * sin (120°). Is he correct? Explain why or why not.

Answers

Answer:

No.

Step-by-step explanation:

No, Bob is not correct.

The formula he's using is the following:

[tex]A=\frac{1}{2} ab\sin(C)[/tex]

The important thing here is that the angle is between the two sides.

In the given triangle, 120 is not between 8 and 18. Therefore, using this formula will not be valid.

Either Bob needs to find the other side first or find the angle between 8 and 18.

Figure A is a scale image of Figure B. What is the value of x?
please answer asap!

Answers

Answer:

[tex]\huge \boxed{x=30}[/tex]

Step-by-step explanation:

[tex]\sf We \ can \ use \ ratios \ to \ solve.[/tex]

[tex]\displaystyle \frac{45}{27} =\frac{x}{18}[/tex]

[tex]\sf Multiply \ both \ sides \ by \ 18.[/tex]

[tex]\displaystyle \frac{45}{27}(18) =\frac{x}{18}(18)[/tex]

[tex]\sf Simplify \ the \ equation.[/tex]

[tex]\displaystyle \frac{810}{27} =x[/tex]

[tex]30=x[/tex]

James conducted an experiment with 4 possible outcomes. He determined that the experimental probability of event A happening is 10 out of 50. The theoretical probability of event A happening is 1 out of 4. Which action is most likely to cause the experimental probability and theoretical probabilities for each event in the experiment to become closer? removing the last 10 trials from the experimental data completing the experiment many more times and combining the results to the trials already done including a fifth possible outcome performing the experiment again, stopping immediately after each event occurs once

Answers

Answer:

Completing the experiment a few more times and combining the results to the trails already done.

Answer:

Completing the experiment a few more times and combining the results to the trails already done.

Step-by-step explanation:

20 squared (+5) divided by 100

Answers

The answer is 4.05

Step-by-step explanation:

20^2 is 20•20 which is 400 || +5=405 || /100=4.05

Consider the plot created from the residuals of a line of best fit for a set of data.


Does the residual plot show that the line of best fit is appropriate for the data?

Yes, the points have no pattern.
No, the points are evenly distributed about the x-axis.
No, the points are in a linear pattern.
Yes, the points are in a curved pattern.

Answers

Answer:

No, the points are in a linear pattern.

Step-by-step explanation:

Residual plot is a graph that shows the residuals on the vertices. The y-axis has residual values and x-axis has independent variables. The horizontal axis shows the independent variables to determine the best fit for a set. The graph given is in a linear pattern. The random pattern shows that linear model is good fit.

Answer:

C: No, the points are in a linear pattern

Step-by-step explanation:

edg2021

I have been seeing this question with multiple different answers, and no one is sure about anything! All I can say for sure is that IT IS NOT A! So C makes the most sense. B is simply not true, and neither is D, its not curved or evenly distribute.

A personal trainer keep track of the number of minutes each of his 20 clients exercise on the treadmill and the number of calories each client burned during that time removing. which TWO of these data points will cause the correlation coefficient to decrease the most?


A). Data point A

B). Data point B

C). Data point C

D). Data point D

Answers

Answer:

Data Point B and Data point E

Step-by-step explanation:

Data point B and data point E are the farthest and are more distant away from the best line of fit compared to other data points. The more clustered data points are, the more the correlation that exists between the variables in question.

Therefore, data point B and data point E, will cause the correlation coefficient to decrease the most.

How many equilateral triangles in the plane have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)}?

Answers

Answer:

12

Step-by-step explanation:

There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of  

points and since two equilateral triangles can be drawn having

that pair of points as vertices, there are 12 equilateral  

triangles that can be drawn having two vertices in the set  

{(0,0), (0,1), (1,0), (1,1)}.

The number of the equilateral triangles in the plane have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.

What is an equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of points and since two equilateral triangles can be drawn having that pair of points as vertices, there are 12 equilateral triangles that can be drawn having two vertices in the set {(0,0), (0,1), (1,0), (1,1)}.

Therefore, the number of the equilateral triangles in the plane that have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.

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What is the perimeter of the figure shown?

Answers

Answer:

[tex]\boxed{16 units}[/tex]

Step-by-step explanation:

Hey there!

Well since all the sides are congruent and there are 8 sides we can make the following expression,

P = 2*8

P = 16

Hope this helps :)

Answer:

16

Step-by-step explanation:

The sides of this figure are equal to each other .

the permiter is the sum of the sides

The figure has 8 sides.

● P = 8 × 2

● P = 16

4x
5.
If 7:5 = (x + 2y): (x - y), find the value of
5y

Answers

Answer:

5/2 OR 2.5

Step-by-step explanation:

( x + 2y ) = 7 , ( x - 2y ) = 5

x = 7 - 2y , x = 5 + 2y

substitute the two eqns together:

7 - 2y = 5 + 2y

7 - 5 = 2y + 2y

2 = 4y

y = 1/2

when y = 1/2 ,

5y = 5(1/2)

= 5/2 OR 2.5

The table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day. What is P(took a vitamin | got the flu)? (Note: If your fraction will reduce, you need to reduce it.)

Answers

Answer:

1/4

Step-by-step explanation:

25 people took a vitamin and still got the flu and the total number is 100 so the fraction is 25/100 which can be reduce to 1/4

The P(took a vitamin | got the flu) will be 1/4.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Here, the table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day.

We need to find the P(took a vitamin | got the flu).

Now, 25 people took a vitamin and still got the flu.

The total number is 100.

So, the fraction is 25/100 which can be reduce to 1/4.

P(took a vitamin | got the flu) = 25/100

P(took a vitamin | got the flu) = 1/4

Therefore, the P(took a vitamin | got the flu) will be 1/4.

Learn more about the unitary method;

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The pepper plant has 2/3 as many fruits on it as the tomato plant has. The tomato plant has 9 fruits on it. How many fruits does the pepper plant have on it?

Answers

Answer:

The pepper plant has 15 fruits on it.

Step-by-step explanation:

Let the tomato plant have x plants. Let the pepper plant have y plants. Since the pepper plant has 2/3 more fruits on it than the tomato plant, we have that y - x = 2x/3

collecting like terms,

y = 2x/3 + x

The above is the number of plants the pepper plant has.

y = 2x/3 + x

y = (2x + 3x)/3

y = 5x/3

Since x = number of fruits on tomato plant = 9, then

y = 5x/3

y = 5(9)/3

y = 5 × 3

y = 15

Since y = number of fruits on pepper plant = 15

So, the pepper plant has 15 fruits on it.

i will mark brainlist!!​

Answers

3/5 + 2 3/4
= 3/5 + 11/4
= 12/20 + 55/20
= 67/20
= 3 7/20

Answer:

3/5 + 2 3/4 = 3 7/20

Step-by-step explanation:

2 = 8/4

2 3/4 = 2 + 3/4

then:

3/5 + 2 3/4 = 3/5 + 8/4 + 3/4

= 3/5 + (8+3)/4

= 3/5 + 11/4

3/5 = 12/20

11/4 = 55/20

then:

3/5 + 11/4 = 12/20 + 55/20 = 67/20

67/20 = 60/20 + 7/20 = 3 + 7/20

= 3 7/20

I answered all my work correctly but I don’t understand this one.

Answers

Take your x values in each coordinate and subtract 2, and take your y values and subtract 1.

Q (0-2), (-1-1)
= (-2,-2)

D (-2-2), (2-1)
= (-4, 1)

V (2-2), (4-1)
= (0,3)

J (3-2), (0-1)
= (1,-1)

You can also draw it on a graph and then translate all coordinates 2 units left and 1 down to see the end results.

Which system of linear inequalities is represented by
the graph?
Oy> x-2 and y < x + 1
O y< x-2 and y > x + 1
Oy x + 1
O y > x-2 and y < x + 1

Answers

Answer:

The correct option is;

y < x - 2, and y > x + 1

Step-by-step explanation:

The given graph of inequalities is made up of parallel lines. Therefore, the slope of the inequalities are equal

By examination of the graph, the common slope = (Increase in y-value)/(Corresponding increase in x-value) = (0 - 1)/(-1 - 0) = 1

Therefore, the slope = 1

We note that the there are three different colored regions, therefore, the different colored regions opposite to each inequalities should be the areas of interest

The y-intercept for the upper bounding linear inequality, (y >) is 1

The y-intercept for the lower bounding linear inequality, (y <) is -2

The two inequalities are y > x + 1 and y < x - 2

The correct option is y < x - 2, and y > x + 1.

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Inequalities is an expression that shows the non equal comparison of two or more variables and numbers.

Given that:

y and x are variables, plotting the inequalities using geogebra online graphing tool.

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Find out more on linear inequalities at: https://brainly.com/question/21103162

x^{2m+n} * x^{n-m} / x^{m+2n}

Answers

Answer:

=x

Step-by-step explanation:

Answer:

[tex]\boxed{1}[/tex]

Step-by-step explanation:

[tex]x^{2m+n} * x^{n-m} / x^{m+2n}[/tex]

When bases are same for exponents in division, subtract exponents.

[tex]x^{2m+n} * x^{n-m-(m+2n)}[/tex]

[tex]x^{2m+n} * x^{n-m-m-2n}[/tex]

[tex]x^{2m+n} * x^{-n-2m}[/tex]

When bases are same for exponents in multiplication, add exponents.

[tex]x^{2m+n+-n-2m}[/tex]

[tex]x^{2m+0-2m}[/tex]

[tex]x^0[/tex]

Any base with power or exponent of 0 is 1.

[tex]x^{0}=1[/tex]

Please solve (will make brainiest)

Answers

Answer:

1a) 1/64

1b) 1/169

1c) 1/9

Step-by-step explanation:

You have to apply Indices Law :

[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]

Question A,

[tex] {4}^{ - 3} = \frac{1}{ {4}^{3} } = \frac{1}{64} [/tex]

Question B,

[tex] {13}^{ - 2} = \frac{1}{ {13}^{2} } = \frac{1}{169} [/tex]

Question C,

[tex] {( - 3)}^{ - 2} = {( - \frac{1}{3}) }^{2} = \frac{1}{9} [/tex]

Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(250)?

Answers

Answer:

Hey There!! The Correct answer C: ) is the average number of days a house stays on the market before being sold for price p in $1,000s

A little more clearer explanation:

p is the price in $1000s, and

f(p) is the number of days before its sold for p

Hence, f(250) would be the number of days before its sold for 250,000 (since p is in $1000s)

Answer choice C is the correct one.

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer: C

Step-by-step explanation:  This is the average number of days the house stayed on the market before being sold for $250,000

Remember, a percent is a fractional part
of 100. In a bag of candy, 15 of the 50
pieces are red. What percentage of the
candy is red?
mex
B 50%.
C 3006
D 659​

Answers

Answer:

Step-by-step explanation:

B

Answer:

The answer would be 30% (although I don't see that as an answer).

Step-by-step explanation:

This is because when you multiply the denominator times a number that makes the denominator 100 and multiply that same number by the numerator you get the percentage of the sample you are looking at on the numerator.

15/50 = (15*2)/(50*2) = 30/100 = 30%

Pattern A starts at 20 and has the rule 'subtract 2 Pattern B starts at 20 and has
the rule 'subtract I". Which shows the first several terms of Patterns A and B?
Pattern A: 20, 17, 15, 13, 11,
Pattern B: 20, 19, 18, 17, 16, 15
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 21, 22, 23, 24, 25
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 19, 18, 17, 16, 15
Pattern A: 20, 22, 24, 26, 28, 30
Pattern B: 20, 21, 22, 23, 24, 25

Answers

Answer:

The correct option is C.

Step-by-step explanation:

The two patterns are defined as follows:

Pattern A starts at 20 and has the rule 'subtract 2'.Pattern B starts at 20 and has  the rule 'subtract 1'.

Form the two patterns as follows:

Pattern A : 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0

Pattern B : 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

The first several terms of Patterns A and B are shown by:

Pattern A: 20, 18, 16, 14, 12, 10

Pattern B: 20, 19, 18, 17, 16, 15

Thus, the correct option is C.

1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...

Answers

Answer:

The equation

[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]

can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.

Step-by-step explanation:

When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:

[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]

We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.

. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.

Answers

Answer:

The two polynomials are:

(x + 1) and (x² + x)

Step-by-step explanation:

A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.

Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.

So,

Let's multiply both numerator and denominator by (x + 1) to get;

(x + 1)/(x(x + 1))

This gives; (x + 1)/(x² + x)

Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.

Please help! Urgent! Will mark Brainliest!

Answers

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.

The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:

[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]

Combine like terms so we can get a simpler equation:

[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]

Now let's solve for x!

[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]

So [tex]x = 15[/tex].

Hope this helped!

Answer:

15

Step-by-step explanation:

3x + 6x + 45 = 180

9x = 135

x = 15

What is the rate of change and initial value for the linear relation that includes the points shown in the table?
ху
1 | 20
3 | 10
5 | 0
7 | -10
A. Initial value: 20, rate of change: 10
B. Initial value: 30, rate of change: 10
C. Initial value: 25, rate of change: -5
D. Initial value: 20, rate of change: -10

Answers

Answer:

C, at 0/25, 1/20, 2/15, 3/10,...

Answer:

C

Step-by-step explanation:

There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?

Answers

5 buses is the answer pls mark me brainliest

Least number of bus require for trip = 5 buses

What is Unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Total number of classes = 9

Number of student in each class = 25

Number of teacher = 4

Number of chaperones = Double of teacher

Bus hold = 45 people

Now,

Total number of student = 9 × 25

                                         = 225

Number of chaperones = 4 × 2

                                         = 8

Total people = 225 + 8 + 4

                     = 237

Least number of bus require for trip = Total people / Bus hold

= 237 / 45

= 5.266

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Write the equation for the line that passes through the points (4, 5) and
(6,9). *

Answers

Answer:

y = 2x + 1

Step-by-step explanation:

first find slops

(9-5)/(6-4) = 4/2 = 2 = m

y = mx + b

5 = 2(2) + b

1 = b

y = 2x + 1

Answer:

y = 2x - 3

Step-by-step explanation:

gradient of the line is

[tex] \frac{9 - 5}{6 - 4 } = 2[/tex]

equation will be:

[tex] \frac{y - 5}{ x - 4} = 2[/tex]

y - 5 = 2x - 8

y = 2x - 3

Sam ran 63,756 feet in 70 minutes. What is Sam's rate in
miles per hour? (There are 5,280 feet in one mile.)
Step 1: What is Sam's rate as stated?
63,756 feet
63, 756 ft
70 min
70 minutes
Step 2: What factor is used to convert feet per minute into
miles per minute?
Step 3: what factor is used to convert miles per minute to miles per hour

Answers

Answer:

10.35 miles per hour

Sam's rate as stated is 63,756 feet per 70 minutes

Divide by 5,280 feet

Divide by 60 minutes

Step-by-step explanation:

1. Find how many feet Sam ran in one minute

63,756 ÷ 70 = 910.8 ft.

2. Find how many feet he ran in one hour

910.8 · 60 = 54,648 ft.

3. Convert the feet to miles

54,648 ÷ 5280 = 10.35

Step 2: There are 5280 feet in one mile. Therefore, you would divide by 5280 feet to convert feet per minute into miles per minute.

Step 3: There are 60 minutes in one hour. Therefore, you would divide by 60 minutes to convert miles per minute to miles per hour.

Answer:

1: 63,756 and 70 mins

2: 1 mile and 5,280 feet

3: 60 mins and 1 hour

4: 10.35

Other Questions
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