Mathematics Middle School

Hugo just joined the cross-country team and can run at a rate of 1/7 mile each minute. How long will it take him to run a 5-mile race?

Answers

Answer 1

1/7 miles in 1 minute
5 mile in ? Minutes

5 divide by 1/7
= 5 x 7
= 35 minutes

Answer 2

Answer:

It will 35 minutes to run a 5-mile race by Hugo

Step-by-step explanation:

Distance ran by Hugo each minute is given by

[tex] \frac{1}{7} miles \\ [/tex]

Time required for Hugo to run 1 mile = 7 minutes.

Time required for Hugo to run 5 miles = 7 x 5 = 35 minutes.

It will 35 minutes to run a 5-mile race by Hugo

Related Questions

PTINO Can you unscramble this... It's the answer to this riddle; Decimals always win in arguments with fractions. What do decimals have that fractions don't?

Answers

Could it be a point?

Decimal Point 1.25 fraction 1 1/4

:) help me please & tyyyy

Answers

So all you do is plug in the variables to make sure the equation is a solution.

x = 12 and y = 46

y = 3x + 10
46 = 3(12) + 10
46 = 36 + 10
46 = 46
The answer is true. I hope this helps love! :)

Melissa is 24 years younger than Joyce. In 2 years Joyce will be 3 times as old as Melissa will be then. How old are they right now?

Answers

Mellissa is 10 years and Joyce is 34 years right now. They will be 12 and 36 in two years.

Joyce will be 34 because Melissa is 10 so 10+24 will be 34 and if she will be three times as much so still in two years she will still be 2 years older so Joyce will be 36 and Melissa will be 12 so.....

Melissa 12 and Joyce 36

Please help me with this. What is the slope of a line parallel to the line with equation 5x-2y=11?

Answers

use the slope-intercept form y = mx + b to find the slope, m.

5x - 2y = 11 this equation is given in standard form

-2y = 11 + 5x add both sides by 5x and then divide all by -2

y = 5/2x - 11/2

so the slope is 5/2.

hope this helped, God bless!

The slope of a line parallel to another line must have the same slope as the other line. So therefore, we just want to first find the slope of this line.

To do this, we can switch it to slope intercept form, which is y = mx + b.

-2y = -5x + 11

Notice that the y doesn't have a variable next to it in slope intercept form. This means you have to divide all the sides to -2 to cancel out that -2.

-2y = -5x + 11
/-2 /-2 /-2

y = 5/2x + 11/-2

Since in the equation, y = mx + b, the number in the position of m = the slope, we know that 5/2 is the slope.

So therefore, the slope of a line parallel to the line with equation 5x - 2y = 11 must be 5/2.

explain how it to use linear factors to determine the equation of a polynomial function

Answers

Since linear factors can be written as (x-a)*(x-b) with a and b as the solutions, we can do it in two ways. First, we can use the quadratic equation. In an equation ax²+bx+c=0, the solutions are
[tex]x= \frac{-b+- \sqrt{ b^{2}-4*a*c} }{2*a} [/tex] with the +- meaning that you can have one solution (a) by adding and (b) by subtracting.

Next, in ax²+bx+c=0, we want to add b up to have dx+zx=bx as well as (d*z)=(c*a). For example, in 6x²+2x-4, we have 6*-4=-24. We have to find 2 numbers that add up to 2 but multiply to 24 - -4 and 6 work. Therefore, we have 6x²+6x-4x-4. Factoring it out, we have 6x(x+1)-4(x+1). Since x+1 is the same in both, we have the equation being (6x-4)(x+1) as the factorization

For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Answers

Given that [tex]r=\theta[/tex], then [tex]r'=1[/tex]

The slope of a tangent line in the polar coordinate is given by:

[tex]m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta} [/tex]

Thus, we have:

[tex]m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta} [/tex]

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

[tex]\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta[/tex]

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

θ = 0

θ = 2.02875783811043

θ = 4.91318043943488

Part B:

For vertical tangent lines, [tex] \frac{1}{m} =0[/tex]

Thus, we have:

[tex]\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta[/tex]

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

θ = 4.91718592528713

Final answer:

For the polar curve r = θ, the tangent lines are horizontal when θ = 0 and θ = π, and the tangent lines are vertical when θ = π/2 and θ = 3π/2.

Explanation:

The question is asking us to find the values of θ for which the tangent lines to the polar curve r = θ are horizontal and vertical. To do this, we need to first derive the slope of the tangent line in polar coordinates.

The derivative dr/dθ represents the slope of the radius with respect to θ, or in other words, the slope of the curve. When r = θ, the derivative dr/dθ = 1. This slope is equal to the tangent of the angle that the tangent line makes with the positive x-axis.

Therefore, for the tangent lines to be horizontal, the angle needs to be 0 or π rad (0 or 180 degrees). For the tangent lines to be vertical, the angle needs to be π/2 or 3π/2 rad (90 or 270 degrees). Using the equation r = θ in rad, we find the horizontal tangents are when θ = 0 and θ = π, while the vertical tangents are when θ = π/2 and θ = 3π/2.

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Hector planted 185 flowers in 2 days.there were 5 volunteers,including Hector, who each planted about the same number of flowers. About how many flowers did they plant?

Answers

925 in 2 day that right

Answer: They planted 925 flowers.

Step-by-step explanation:

Given : Hector planted 185 flowers in 2 days.

There were 5 volunteers,including Hector, who each planted about the same number of flowers.

Then, the number of flowers they planted is given by :-

Number of volunteers x Flower planted by each volunteer

=[tex]5\times185=925[/tex]

Hence, They planted 925 flowers.

Prime factorization of 84

Answers

Check my attached photo for the answer

Hello There!

Find factors of 84:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Out of those, find the prime factors:
Prime factorization: 84 = 2 x 2 x 3 x 7
Simplify:
It can also be written 2² x 3 x 7.

Hope This Helps You!
Good Luck :)

- Hannah ❤

The base of a triangle is 3cm greater than the height. The area is 14cm. Find the height and base of the triangle.

Answers

the base....b
the height....h
b*h/2=14
b=h+3
h*(h+3)=28
h*(h+3)=4*7
h=4 cm , b=7 cm

Hello There!

base x height/2 = 14
base x height = 28
Base - height = 3
Base = 7
Height = 4.

Hope This Helps You!
Good Luck :)

- Hannah ❤

Mrs Kipling ordered flowers for centerpieces.She ordered 168 flowers.She needs to put 15 flowers in a vase for 14 tables.Does Mrs.Kipling have enough flowers for 14 tables? Explain why or why not.

Answers

Hello! Mrs. Kipling order 168 flowers, and she needs to put 15 flowers in each vase for 14 tables. To find out if she has enough for 14 tables, let's multiply 15 (the amount needed for each vase) by 14. 15 * 14 is 210. 210 > 168. No. Mrs. Kipling does not have enough flowers for 14 vases.

Lafayette county has a population of 7,022 people .Columbia county population is 8 times as great as Lafayette County's population.WHAT IS THE POPULATION OF COLUMBIA COUNTY

Answers

7,022 times 8 is 56,176.

The term "8 times as great" basically translates into "multiply by 8".
So, you would get this equation:

7,022(8) = population
Your answer is: 56,176 people.

how do i solve? i don’t understand how you have to get the denominator

Answers

4⁻³ · 12⁰

Remember, if a power is ever negative, then you have to turn it into a fraction, and if a power is zero, then the whole number turns into 1 :)

4⁻³ turns into 1/4³ due to the fact that the power is negative.

So, our question now looks like this :

1/4³ · 1

Simplify.

1/64 · 1

Simplify.

Our answer is : 1/64

~Hope I helped!~

During the weekend at the movie palace theaters, 24,875 tickets were sold. Add the following to the number of tickets sold. 100 tickets _____ and 1,000 tickets ____

Answers

24,875 + 100 = 24,975 and 24,875 + 1,000 =25,875

Answer: 24,975 tickets and 25,875 tickets

Step-by-step explanation:

Given : The number of tickets sold at the movie palace theaters during the weekend = 24,875

If we add the the number of tickets sold to 100 tickets, we get

[tex]24,875+100=24,975[/tex]

If we add the the number of tickets sold to 1000 tickets, we get

[tex]24,875+1000=25,875[/tex]

Hence, when we add 100 tickets and 1000 tickets to the number of tickets sold we get 24,975 tickets and 25,875 tickets

can someone please help md

Answers

The first 3 boxes and the last one

A trapezoid has one pair of sides parallel.
If you look at the slopes of sides WZ and XY, they are equal.
Those two sides are parallel.
Also, keep in mind that a line that goes up to the right has a positive slope, and a line that goes down to the right has a negative slope.

Which problem can be solved with this model? A. 4 divided by 1/3 B. 1/3 divided by 4 C. 12 divided by 1/3 or D. 4 divided by 12

Answers

sorry man nobody can help you unless you give us the model

7/10 × 4/7 × 30/20 × 20/14=
I'm unsure how to multiply more than two fractions at a time

Answers

You answer is 6/7 do you need to know how or just the answer

6/7 hope this helps ;)

Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music.

Answers

180 greater than or equal to 450 - m

Helpppppp fast am being timed

Answers

The first one (up and lef) does represent a linear function because y increments a constant amount (5) as x increments a constant amount (1).

The second one (up and right) does represent a linear function because y decreases a constant amount (3) when x increases a constant amount (1).

Th third one (bottom and left) does represent a linear function because y increases a constant amount (1) when x increases a constant amount (1).

The fourth (bottom and right) does not represent a linear function because the change is y is not constant when x increases a constant amount.

Don't understand need help

Answers

Hello!
So, your questions are basically having to do with rotations. This means to rotate certain points in a grid.
The following are formulas for solving rotations-
90 Degrees Clockwise About The Origin = (X,Y) -> (Y,-X)
180 Degrees About The Origin = (X,Y) -> (-X,-Y)
270 Degrees Clockwise About The Origin = (X,Y) -> (-Y,X)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
90 Degrees Counterclockwise = 270 Clockwise
270 Degrees Counterclockwise = 90 Clockwise
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
*Note, in the formulas, the negative sign only stands for the opposite. So if your original point is a negative, it will become positive,
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now that we have our formulas, let's put them into affect with your points.

13) 90 Degrees CC = 270 Degrees Clockwise. Formula- (X,Y) -> (-Y,X)
A (2,-2) -> A' (2,2)
B (4,-1) -> B' (1,4)
C (4,-3) -> C' (3,4)
D (2,-4) -> D' (4,2)

*Note, the symbol _'_ Stands for prime. All this means, is the new point.

15) Now, I apologize, but I'm a bit confused on this one :( When it says about point L, I can't tell if it just wants that one point, or the whole figure translated. Again, I am so sorry :(

17) This one I do know. 270 degrees CC = 90 degrees Clockwise. Formula- (X,Y) = (Y,-X).
W (-6,-2) -> W' (-2,6)
X (-2,-2) -> X' (-2,2)
Y (-2,-6) -> Y' (-6,2)
Z (-5,-6) -> Z' (-6,5)

Hope this helped! Again, sorry about number 15. Have a great day!
Regards,
~KayEmQue

Theresa walked around the track 22 times. How far did she walk? Write as an improper fraction or mixed number.

Answers

Given that the track is 1/6 of a mile and she walks it 22 times
so 1/6 times 22 is 3.666666666666
that is (11/3)
or
(3 and 2/3)
Hope this helps :)

What is the product of 8.2 × 10/\9 and 4.5 × 10/\-5 in scientific notation?
36.9 × 10/\-45
12.7 × 10/\4
3.69 × 10/\5
3.69 × 10/\14

Answers

3.69 x 10^5, because the original answer is 369000, but scientific notation requires that you have your answer between 1-10. Just move 5 places to the left, which means your power of 10 will be positive.

To make things easier for you, the correct answer is C: 3.69 × 10^5

Using the diagram, which two planes would hg intersect in ?

Answers

we need to see the diagram..

Answer:

we need to see the diagram..

Step-by-step explanation:

Simplify
| -3.9 | + | 3.9 |
A. -7.8
B. 0
C. 7.8
D. 8

Answers

It would be C) 7.8

When a negative number is inside the absolute value, it turns out to be positive number anyways so the equation is basically 3.9 + 3.9 = 7.8

Jill decides to move her fish from a 20 gallon aquarium to a 50 gallon aquarium. She added 3 tablespoons of salt to her old aquarium. If she wishes to maintain to same salinity level, how many tablespoons should she add to her new aquarium?

Answers

she would have to add 7.5 tablespoons of salt to keep a 15% salinity level

one maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?

Answers

Faster maid DATA:
time = x hr/job ; rate = 1/x job/jhr
Slower maid DATA:
time = 3x hr/job ; rate = 1/3x job/hr
Together DATA:
time = 3 hr/job ; rate = 1/3 job/hr
Equation:
rate + rate = together rate
1/x + 1/3x = 1/3
Multiply thru by 3x to get:
3 + 1 = x
x = 4 hrs (time for the faster maid to do the job)

Final answer:

By setting up and solving the equation based on the work rates of the maids, we find that the faster maid would need 4.5 hours to clean the complete house alone.

Explanation:

Let's denote the time it takes for the faster maid to clean the house alone as x hours and for the slower maid as 3x hours (since she is three times slower). When they clean the house together, their combined work rate is 1 house per 3 hours.

We can set up an equation based on the work done: The faster maid's work + the slower maid's work = the total work done. Here, the 'work' is a fraction of the house cleaned per hour, so the equation can be written as: 1/x + 1/(3x) = 1/3.

By solving this equation, we find that x = 4.5. Hence, the faster maid would need 4.5 hours to clean the house alone.

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A linear function F models a relationship in which the dependent variable decreases 6 units for every 3 units the independent variable decreases. The value of the function at 0 is 4. Graph the function. Identify the slope, y-intercept, and x-intercept of the graph.

Answers

A. Finding the slope

The slope of the function is simply the ratio of the value of the dependent variable over the independent variable, so in this case it is:

slope = 6/ 3 = 2

B. Finding the y – intercept

The y – intercept is simply the value of the dependent variable when the independent variable is equal to zero, therefore:

y – intercept (b) = 4

C. Finding the function of the graph

The general equation of a line is given as:

y = m x + b

where m is the slope and b is the y intercept therefore:

y = 2 x + 4

D. Finding the x – intercept

The x – intercept is simply the value of the independent variable (x) when the dependent variable (y) is equal to zero, therefore:

0 = 2 x + 4

x = - 2

E. Graph the function

Check out the image attached

Final answer:

The linear function described is y = -2x + 4, with a slope of -2 and a y-intercept at (0,4). The line for this function will pass through the points (0,4) and (2,0), the latter being the x-intercept.

Explanation:

The question asks to graph a linear function in which the dependent variable decreases 6 units for every 3 units the independent variable decreases, and the function's value at 0 is 4. The nature of this relationship implies that the slope of this function is -2 (calculated as -6 divided by 3). Therefore, the equation for this linear function, using the slope-intercept form y = mx + b, will be y = -2x + 4. In this equation, -2 is the slope (m) and 4 is the y-intercept (b, the function's value when x is 0).

To graph this function, you start by marking the point (0,4) on your graph. From this point, you then go down 2 units (as the slope is -2) and 1 unit to the right (as the decrease in y for a 1 unit increase in x). You will continue this pattern to graph the line. The x-intercept—the point at which the line crosses the x-axis (i.e., where y = 0)—occurs at x = 2, because plugging in 0 for y in the equation gives us -2x + 4 = 0, which simplifies to x = 2. So the final line should pass through the points (0,4) and (2,0).

Learn more about Linear Functions here:

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If Harry's new balance was $123.40, what would be his total available credit?

A. $500.00

B. $367.60

C. $376.60

D. $123.40

I'm not sure how to find total credit available but I tried it two different ways and got two answers so I'm between B and C. If you just subtract the new balance from the total credit you get C but if you subtract both the new balance and payments you get B. Please help

Answers

I think it would be D. $123.40 because I think credit is the amount that you are allowed to spend but can pay off later, like a credit card, basically barrowing money. If harry's balance is $123.40 that is the amount left he can use out of the original amount which was $500. Im not totally sure but if thats wrong, im sorry. I hope this helps some way :^)

You need to subtract the new balance from the credit line, which is option C

Jaces dad drives 605 miles in 11 hours

Answers

I'm not sure what the question is but, I'm guessing you are trying to find out how many miles are driven per hour.

To determine how many miles are driven per hour, you would divide the total number of miles driven by the total number of hours it took to drive it.
605 ÷ 11 = 55mph

Jace's dad drove 55 miles per hour.

I hope this helps!

I need help. If you can explain it, show me!!

Answers

In every case the larger number is rounded up to 2E13.
Divide this by 3E8:

2E13 = 200000E8
-------- --------------- is approx equal to 70000 (dollars).
3E8 3E8

What is the value of the function y = 2x + 3 ⁢when x=−1 ?

A. 5

B. 2

C. 1

D. −5

Answers

It would be C. Hope this helps

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