Part I: Making the Race


Henri is Emile's younger brother and they are having a walking race. Emile can walk 2.5 meters per second whereas Henri walks 1 meter per second. Because Emile is faster, they give Henri a 45 meter head start. Emile knows Henri would enjoy winning the race, but they do not want to make the race so short that it is obvious Emile let Henri win.


1. How long should the race be so that Henri will win in a close race?

2. Describe or show your strategy on how you came up with your answer for #1.

Answers

Answer 1

74 meters

Step-by-step explanation:

The difference in Emile and Henry's speed is 1.5, and the lead for Henry is 45 meters, so 45÷1.5= 30 seconds which means Henry will go another 30 meters at 1 meter per second.

2. To make it a close race we want Henry to go a longer distance than Emile, so make it 74 meters, which means Emile will go only have 45+29 = 74 seconds to get to 74 meters, but Henry only have 29 seconds in total = 29*2.5 = 72.5 meters.  


Related Questions

Find the slope and the y-intercept of the graph of the linear equation. y= -2x - 1

Answers

Answer:

slope = -2

y-intercept = -1

Step-by-step explanation:

for y = -2x - 1

Using the slope intercept formula y = mx + b, then slope m = -2 and y-intercept is (0,b) or (0,-1)


Y=mx+ c
M=Slope or Gradient
C=Y-intercept

(M) Slope= -2
(C) Y- intercept= -1

HELP ASAP
What is the value of x?

Enter your answer in the box.
Two intersecting lines. The angle formed at the top is labeled 3 x plus 50 degrees. The angle formed at the bottom directly opposite it is labeled 6 x minus 10 degrees.

Answers

We know that the two angles are opposite and therefore are equal, so we can set them equal to each other and solve for x:

3x + 50 = 6x - 10

Adding 10 to both sides, we get:

3x + 60 = 6x

Subtracting 3x from both sides, we get:

60 = 3x

Dividing both sides by 3, we get:

x = 20

Therefore, the value of x is 20.

A bowl contains red and brown marbles. A scoop of marbles that is a representative sample contains 18 red marbles and 27 brown marbles.

a. Can you predict if there are more red marbles or more brown marbles in the​ bowl? Explain.
b. There are 850 marbles in a bowl. If you pick one marble from the​ bowl, are you more likely to pick a red marble or a brown ​marble?

Answers

a. Based on the information provided, it is not possible to predict if there are more red marbles or more brown marbles in the bowl, because the sample size is not given. It is possible that the sample is not representative of the overall population of marbles in the bowl, and thus the sample proportions may not accurately reflect the actual proportions of red and brown marbles in the bowl.

b. To determine the probability of picking a red or brown marble from the bowl, we need to know the overall proportion of red and brown marbles in the bowl. From the given sample, we know that the proportion of red marbles is 18/45 or 0.4, and the proportion of brown marbles is 27/45 or 0.6. Assuming that these proportions are representative of the overall population of marbles in the bowl, we can predict that we are more likely to pick a brown marble (with a probability of 0.6) than a red marble (with a probability of 0.4) if we pick one marble from the bowl.

What is 2. 8×4. 6 find the missing partial products

Answers

—> 12.88 <—

A N S W E R

the answer would be 12.88
hope this helps

What is the equation in slope-intercept form that represents the information? y=mx+b.
(2 points)





D. How much money will you save after 20 weeks? (2 points)

Answers

Answer:not y=1/2x+2

not so sure about answer i am new to this

Please help solve this two step problem.Put an answer for A and B please enplane steps how to solve

Answers

Answer:

The correct answer is Letter D).

Step-by-step explanation:

Answer:

B

Explanation: I got it right

helpp mee please asap please

Answers

A and B is the answer everything less than 20

Answer:

A and B.

Step-by-step explanation:

Since 18 is less than 20, A is correct.

Since 12 is less than 20, B is correct.

C and D are not correct because they are larger than 21.

Hope it helped!

WHATS THE ANSWERRRRRRD

Answers

Answer: V = 6250m^3.

6250m cube would be ur answer

Please help, this is due tomorrow, HELP

Answers

Answer:u thoght

Step-by-step explanation:

2 and 5/8 your welcomeee

Infinitely many quadratic equations of the form ax^2 + bx + c = 0 can have the same two solutions. Sketch the graphs of two quadratic functions on the same grid to show how this could be true.
(picture)

Answers

Infinitely many quadratic equations of the form ax² + bx + c = 0 can have the same two solutions. Sketch the graphs of two quadratic functions on the same grid to show how this could be true.

A local animal rescue has 20 people that help foster pets while they are
waiting on finding their homes. They expect to gain two additional people
willing to foster animals each month. The amount of animals in need of
homes in the community is currently 10 and growing at a rate of 15% per
month. When will the amount of homeless pets surpass the amount of foster
homes available?

A) Write the two functions that represent this situation.

B) Create a table of values for x=0 to x=13.

C) Approximate the solution(s). Why is this the approximate solution?

D) Using graph paper (and the table of values), sketch the situation to
show the exact solution.

Answers

Answer:

A) Let f(x) represent the number of foster homes available after x months, and let g(x) represent the number of homeless pets after x months.

f(x) = 20 + 2x (since 2 additional people are expected to foster each month)

g(x) = 10(1.15)^x (since the number of homeless pets is growing at a rate of 15% per month)

70 points please help
(Also tell me if it says less points on the answer, just write yes or no)
ANSWER ALL QUESTIONS

Answers

1. 19+95= 114
2. 22+11= 33
3. 70+95= 165
No it shows likes 35 points but 70 and 95 greatest common of factor is 5 and 19 and 95 is 19 and 22 and 12 is 11

what are the oz and which one is better?

Answers

Answer:

Step-by-step explanation:

13oz bottle of dish soap sells for 2.34

Answer: hope this helps ♡

The unit price of the 13 oz bottle is $0.18 per oz

The unit price of the 30 oz bottle is $0.53 per oz

The 13 oz bottle for $2.34 is a better deal.

Step-by-step explanation:

Unitary method: diving the number that you want to find out over the already known number. (just try to understand this lol)  :)

13 oz = $2.34

13 oz bottle is  $?  per oz

[tex]\frac{2.34}{13}[/tex] = 0.18

1 oz = $0.18

(double check: 0.18×13=2.34)

30 oz = $15.90

30 oz bottle is $?  per oz

[tex]\frac{15.9}{30}[/tex] = 0.53

1 oz = $0.53

(double check: 0.53×30=15.9)

The 13 oz bottle for $2.34 is a better deal.

which ordered pair is the solution to this system of equations

Answers

Answer: (-1, 3)

Step-by-step explanation:

x = -1

y = 3

3 = -1 + 4

-1 + 3 = 2

Answer:

(-1, 3)

Step-by-step explanation:

One way to solve this is to simply plug the points into the equations, and see if both equations hold true.

(1, 5)

5 = 1 + 4 is true

However

1 + 5 = 2 is not true, therefore this isn't the answer.

(0, 2)

2 = 0 + 4 isn't true so we can move on to the next point.

(-1, 3)

3 = -1 + 4 is true

and

-1 + 3 = 2 is also true

Therefore, (-1, 3) is the answer.

Please help me Solve −17=5w+3 .Also show steps how you solved it

Answers

Answer:

w = -4

Step-by-step explanation:

-17 = 5w + 3

Subtract 3 from both sides:

-20 = 5w

Divide 5 from both sides:

[w = -4]

Answer:

w= -4

Step-by-step explanation:

Evaluate (whith steps) -3 - 5 (8 + 4) + 16 - 32

Answers

Answer:

Using the order of operations (PEMDAS), we evaluate the expression as follows:

First, we perform the operations inside the parentheses: 8 + 4 = 12.

Next, we multiply 5 by 12: 5(12) = 60.

Then, we combine the like terms: -3 - 60 + 16 - 32 = -79.

Therefore, -3 - 5 (8 + 4) + 16 - 32 = -79.

The answer is -79 ( I think )

1. Consider this scatter plot.
Test Scores in Relation to Homework

Hours of Homework
(a) Is the relationship linear or not linear? Justify your response.
(b) Is the relationship increasing or decreasing?
(c) What is the domain and range of the data set?
(d) Draw a line of best fit, and find the slope of that line.

Answers

Answer:

(A) Not Linear

(B) Increasing

(C) Domain : 1,2,3,4,5,6 Range: all real numbers

Step-by-step explanation:

Not linear because not straight line

Increasing because its increasing

Domain is x and range is y

(PLEASE HELP I NEED TO ANSWER THIS) what is the volume of the compisite figure

Answers

Answer: V=381m³

Step-by-step explanation:

V1=(5m)x(3m)x(6m) over 2

V1=45m³

V2=(16m)x(3m)x(7m)

V2=336m³

V1+V2=

V=381m³

PLEASE ANSWER QUICK IM RUNNING OUTTA TIME!!!

Answers

Answer:

15

Step-by-step explanation:

4x^2 - 10

-----------------

 y

Calculate the expression.

Let x = 5 and y = 6.  Substitute into the expression.

4(5)^2 - 10

-----------------

 6

Exponents first.

4(25) - 10

-----------------

 6

Multiply next.

100 - 10

---------------

   6

Calculate the numerator

90

-----

6

Divide the numerator by the denominator.

15

Jace uses the data in the table to predict that if all 4,320 students at his school vote for a new school​ mascot, about 1,539 students will vote for Barracudas. Do you​ agree? Explain.

Answers

Without seeing the table, I cannot provide a specific answer to this question. Please provide me with the table or the necessary information so I can assist you better.

Solve the given inequality:
Karen is pumping water into a tank at a rate of 17 liters per minute. Since she started pumping water, 12 liters has splashed out of the tank. Her goal is given by 17x - 12 < 90, where x is the number of minutes, she pumps water into the tank.

Choose and complete the statement that best describes the solution.
A. To meet the goal, the tank will have less then _ liters of water in it. this will take more then _ minutes.
B. To meet the goal, the tank will have less then _ liters of water in it. this will take less then _ minutes.
C. To meet the goal, the tank will have more then _ liters of water in it. this will take less then _ minutes.

Answers

Answer:

B

Step-by-step explanation:

the answer is c it’s not b

Maria’s current car gets 24 miles per gallon. Last year she drove 15,000 miles. Last year gas cost an average of $3.35
solve 1. How much did Maria spend for gas for her car last year?
solve 2. Maria is buying a new car that averages 32 miles per gallon. If she drives the car 15,000 miles in the next year and gas prices stay the same, how much will she spend for gas in the next year?
solve. 3 ) How much money will Maria save in gas costs in the next year by driving her new car as opposed to her old one?
solve 4. What percent decrease in gas costs for one year will Maria realize by driving her new car?

Answers

1) Last year, Maria spent $2093.75. Here's the equation to find that answer:

(a ÷ b) × c

a = 15,000b = 24c = 3.35

(15,000 ÷ 24) × 3.35

2) Same equation. (15,000 ÷ 32) × 3.35. The answer of this equation is 1570.3125, but that rounds to $1570.31.

3) This part represents a simple difference/subtraction problem. Since she spent $2093.75 last year, and will spend $1570.31 with a new car, she will save 523.44.

4) Using percent of change, the percent decrease Maria will realize in one year is 33.333%, or [tex]\frac{1}{3}[/tex].

ANSWERS1) 2093.752) 1570.313) 523.444) 33.333%

1) 2093.75

2) 1570.31

3) 523.44

4) 33.333%

Please I need help with this question,look at the picture below,solve and show steps how to solve

Answers

Answer:6

Step-by-step explanation:

Because 4 gallons get drained every minute you need to find the difference in 50 1/2 and 26 1/2 which is 24, so 24 gallons need to be drained until the amount of water is 26 1/2. So 24 gallons will drain in 6 minutes as 4 gallons drain every minute. It will take 6 minutes for the amount of water to be 26 1/2

HELP ASAP!!
The interior angles formed by the sides of a hexagon have measures that sum to 720°.

What is the measure of angle F?

Enter your answer in the box.

​m∠F=​
°

Answers

I think the answer is angle f is 100 degrees

angle F is 100 degrees

Which expression uses the greatest common factor and the distributive property to write 18+24 as a product? circle the correct answer.
A 2(9+12)
B 8(10=16
C 6(3) + 6(4)
D 6(3+4

Answers

Answer:

D

Step-by-step explanation:

The expression that used the greatest common factor and the distributive property to write 18 + 24 as a product is 6(3 + 4).

Given that,

The expression is 18 + 24.

Based on the above information, the following information should be considered:

The common factor that lies between them is 2 & 4 & 3 & 4 & 6 in which the greater should be 6.

Now after factoring out the expression should be 6(3 + 4).

Therefore we can conclude that the expression that used the greatest common factor and the distributive property to write 18 + 24 as a product is 6(3 + 4).

Answer:  D

Step-by-step explanation:

Please, help me with this!

Answers

Answer:

D

Step-by-step explanation:

1/2 = 20/40, and 1 = 40/40. 36 is 4 away from 40, and 20 is 20 away from 40. Therefore, 36/40 is closer to 1 than it is 20/40, or 1/2. Hope this helps! Have a great day! :)

Answer:

D

Step-by-step explanation:

how much?




it's not 112.5 js saying....

Answers

Answer:

562.5

Step-by-step explanation:

Original price = 450 x 1.25 = 562.5

How did you get 112.5?

the correct answer is $337.50

Explain how to use the unit rate to make the table in the example

Answers

Answer:+8

Step-by-step explanation:

The answer is positive 8 or +8

Write the following in slope intercept form:
y + 2 = 3/4x

Answers

Answer:

The equation y + 2 = 3/4x can be written in slope-intercept form by isolating the y-term and rearranging the equation. The slope-intercept form of the equation is y = 3/4x - 2

Answer:

y = 3/4x - 2

Step-by-step explanation:

The slope intercept formula y = mx + b

so y + 2 = 3/4x

=> y + 2 -2 = 3/4x - 2

=> y = 3/4x - 2

y + 2 = x which choice is the slope-intercept form for y + 2= x

Answers

Answer: y = x - 2

Step-by-step explanation:

x - y - x = y + 2 - y - x

-y/-1 = (2 - x)/-1

y = -2 + x

y = x - 2

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