37. Construct Arguments Luis and Raul are
riding their bicycles to the beach from their
respective homes. Luis proposes that they leave
their respective homes at the same time and
plan to arrive at the beach at the same time.
The diagram shows Luis's position at two points
during his ride to the beach.
Write an equation in slope-intercept form
to represent Luis's ride from his house to the
beach. If Raul lives 5 miles closer to the beach
than Luis, at what speed must Raul ride for the
plan to work?

37. Construct Arguments Luis And Raul Areriding Their Bicycles To The Beach From Theirrespective Homes.

Answers

Answer 1

Using the slope - intercept relation, the required equation which models the scenario and Raul's speed are ;

y = - 7.5x + 15 4 miles per hour

Time difference, Δt = 1.2 hours - 0.5 hours = 0.7 hours

Change in distance, Δd = 11.25 - 6 = 5.25 miles

Assuming a constant speed :

Speed = (Δd ÷ Δt) = (5.25 ÷ 0.7) = 7.5 mi/hr

Using the general form :

y = bx + c

At, x = 1.2 hours ;

Miles left, y = 6 miles

End point decreases by 7.5 mi/hr (-7.5 mi/hr)

Inputting the data into the equation :

6 = - 7.5(1.2) + c

6 = - 9 + c

c = 6 + 9 = 15 miles

The expression in slope intercept form becomes ;

y = -7.5x + 15

If Raul lives 5 miles closer to the beach ;

Time it will take Luis to get to the beach :

Time taken = (15 ÷ 7.5) = 2.5 hours

Distance Raul has to cover = 15 - 5 = 10 miles

To reach the beach after 2.5 hours ;

Speed required = (10 ÷ 2.5) = 4 mi/hr

Therefore, Raul has to ride at 4 miles per hour for the plan to work.

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Related Questions

Geometry please help me

Determining angle measures in context.

Answers

Answer:

d

Step-by-step explanation:

the corresponding angles are described by 2 parallel lines and a line that cross them all

pls help ASAPPPP11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

It's between 0 and 1

Step-by-step explanation:

1/64 = 0.015625

Write the equation of a line in slope-intercept form that has a slope of -1/4x and a y-intercept of 5

Answers

Answer:

Step-by-step explanation:

Slope = m = -1/4

y-intercept = b = 5

Slope intercept form = y = mx +b

[tex]y =\dfrac{-1}{4}x+5[/tex]

For brainily please help

Answers

Answer:

3

Step-by-step explanation:

It's the same on both sides

3 because the sides are the same

hhhhhhhhhhheeeeeeeeeeeelllllllllllllpppppppppp

Answers

Answer:

angle 4 is the alternate angle

Answer: (A) angle 1

Step-by-step explanation:

so i am struggling e

Answers

Answer:

17

Step-by-step explanation:

[tex]perimeter = 2(length + breadth) \\ breadth = (perimeter \div 2) - length[/tex]

[tex]72 \div 2 = 36 \\ 36 - 19 = 17[/tex]

Answer:

y is 17 mm

Step-by-step explanation:

perimeter formula is p= 2l +2w

19 is width

19+19 = 38

72-38=34

34/2= 17

17 is length

I hope it is right:)

(5a-4)(3a-1)
How do I do it?

Answers

Answer:

15a^2 -17a +4

5a x 3a = 15a^2 bc a times a makes it squared.

next, 5a x -1 = -5a

and then -4 x 3a = -12a

-5a -12a (bc they're like terms) = -17a

then, -4 x -1= 4 ( two negs cancel each other out)

I apologize for my mistake the first time

12 cm
14 cm
1

-
Find volume

Answers

Answer:

Volume of cylinder = 6,330.24 cm

Solution:

Volume of cylinder = area of base × altitude

Volume = πr² × altitude

V= 3.14 × 12² × 14

V = 3.14 × 144 × 14

V = 6,330.24 cm

The area of a rectangle is 42 square centimeters it's length is 7 centimeters.

Answers

Answer:

6 cm

Step-by-step explanation:

A = l · w                     Substitute what you know A = 42; l = 7

42 = 7 ·w                   Solve

42/7 = w

6 = w                        cm · cm = cm²

A number y is multiplied by -0.8. The product is -49.
What is the value of y?

Answers

(-0.8)y = -49

Divide both sides by -0.8

y=61.25

Movie tickets now average $9.75 per ticket, but are increasing 7% each year.
What is the growth factor?

Answers

Answer:

The Tickets grow approximately ¢68 or $0.68 each year

Step-by-step explanation:

7% of 9.75 = 0.68

A percentage is out of a fraction of 100; 7/100

Hope This Helps!

Problem 2) write an equation for the following situation.
Jacob raises goats. He spends $75 to set up his goat pen. He has to spend $12 per day to feed
his goats.

Answers

Answer:

75 + 12d

Step-by-step explanation:

he pays $75 dollars up front. he then pays a rate of $12 per day

12X + 75 = Goat cost in all.
Reason: x is your days, 12 is cost per days, +75 is what he spent setting up his goat pen!

What is the answer for this question:12+2c+6d-8c+d

Answers

Answer:

12+10c+7d

Step-by-step explanation:

There is no possible way to really describe the value of the variables, so I simplified it.

ALL FELLOW PEOPLE I NEED HELP ASAP ! WILL MARK BRAINLIEST!!EXTRA POINTS !!!!

Answers

Answer: y = -5/3x + 4 and 5x + 2y = 4

Step-by-step explanation:

1. Firstly, we should substract 5x on both sides of the equation.

3y = -5x + 12

Then we divide by 3 on both sides of the equation. This would give us our answer.

y = -5/3x + 4

2. The answer is 5x + 2y = 4.

The slope of parallel lines should be the same. If we want to isolate y of the above the equation we should first substract 5x on both sides.

2y = -5x + 4

Then we should divide 2 on both sides of the equation.

y = -5/2x + 4

The equation above and y = -5/2x -7 have the same slope. Therefore, they are parallel.

The third answer is correct

If the line t is a transversal of lines I and m, NAME THE SPECIAL ANGLE PAIR RELATIONSHIP of the given angle pairs.

Answers

Answer:

a. <1 and <3

Step-by-step explanation:

5. The two figures are scaled copies of each other.
a. What is the
scale factor that
takes Figure 1
to Figure 2?
e
P
ס
R
С
A
A
b. What is the
scale factor that
takes Figure 2.
to Figure 1?
D
Figure 1
Figure 2
S

Answers

The quadrilaterals are similar and are related by a scale factor, taken from

a specific location, that maps the points on one figure to the other.

a. The scale factor that takes Figure 1 to Figure 2, is 3

b. The scale factor that takes Figure 2 to Figure 1 is [tex]\dfrac{1}{3}[/tex]

Reasons:

From the question, we have that Figure 1 is a scaled copy of Figure 2, therefore;

Let ABCD represent Figure 1, we have;

ABCD ~ PQRS

Length of [tex]\overline{AD}[/tex] = √(2² + 3²) = √(13)

Length of [tex]\overline{PS}[/tex] = √(6² + 9²) = √(117) = √(9 × 13) = 3·√(13)

Therefore;

a. The scale factor that takes Figure 1 to Figure 2, SF₁₂, is therefore;

[tex]SF_{12} = \mathbf{\dfrac{\overline{PS}}{\overline{AD}}}[/tex]

Which gives;

[tex]SF_{12} = \dfrac{3 \cdot \sqrt{13} }{\sqrt{13} } = 3[/tex]

The scale factor that takes Figure 1 to Figure 2, SF₁₂ = 3

(3 times the lengths of Figure 1 gives the lengths on Figure 2)

b. The scale factor that takes Figure 2 to Figure 1, SF₂₁, is given as follows;

[tex]SF_{21} = \mathbf{\dfrac{\overline{AD}}{\overline{PS}}}[/tex]

Which give;

[tex]SF_{21} = \dfrac{\sqrt{13} }{3 \cdot \sqrt{13} } = \mathbf{\dfrac{1}{3}}[/tex]

The scale factor that takes Figure 2 to Figure 1, SF₂₁ is [tex]\underline{\dfrac{1}{3}}[/tex]

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Given that
R
=
9
x
+
8
y

Find
x
when
y
=
3
and
R
=
5

Give your answer as an improper fraction in its simplest form.

Answers

Answer:

X = 19/9

Step-by-step explanation:

R = 9x + 8y

R = 5, Y = 3

5 = 9x + 8(3)

9x = 8(3) - 5

9x = 19

x = 19/9

6. There are only cars and trucks in the parking lot. Five out of every 13
vehicles are cars. If there are 143 vehicles in the parking lot, how many
are trucks?

Pls help me

Answers

Answer:

88 trucks

Step-by-step explanation:

Ratio of cars : vehicles = 5:13

Hence, the ratio of trucks : vehicles = 8:13

143/13 = 11

If the number of vehicles is 143,

we have to multiply both sides of the ratio by 11:

8*11 : 13* 11

88 : 143

Hence, there are 88 trucks for every 143 vehicles.

Hope this answers your question... Have a wonderful time ahead at Brainly!

what is the slope of the line that passes through the points (-3,1) and (7,14)​

Answers

The slope is 1.3. The whole equation is y=1.3x+4.9

A coffee shop sells lattes for $4 and cappuccinos for $3. Last Friday, they sold 78 drinks for a total of $252.



How many cappuccinos were sold?

Answers

Answer: 60 cappuccinos were sold.

Explanation:
x = number of lattes sold
y = number of cappuccinos sold

Two equations can be set up:
x + y = 78
4x + 3y = 252

The first equation can be rearranged and substituted into the other equation to find the value of a variable.

y = 78 - x
4x + 3(78 - x) = 252
4x + 234 - 3x = 252
x + 234 = 252
x = 18

To find y, the value of x can be substituted into either equation.

x + y = 78
18 + y = 78
y = 60

To check answers, substitute both values into the original equations and make sure they work.

x + y = 78
18 + 60 = 78
78 = 78

4x + 3y = 252
4(18) + 3(60) = 252
72 + 180 = 252
252 = 252

Number of sold cappuccinos will be 60.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

A coffee shop sells lattes for $4 and cappuccinos for $3.

Last Friday, they sold 78 drinks for a total of $252.

Now,

Let number of lattes = x

Number of cappuccinos = y

Since, Last Friday, they sold 78 drinks.

So, we can formulate;

x + y = 78   ... (i)

And, Last Friday, they sold 78 drinks for a total of $252.

So, we can formulate;

4x + 3y = 252 ... (ii)

Solve equation (i) and (ii) we get;

x + y = 78

4x + 3y = 252

Multiply by 4 in equation (i) and subtract from (ii) we get;

4x + 3y - 4x - 4y = 252 - 312

- y = - 60

y = 60

And, x + y = 78

x + 60 = 78

x = 18

Thus, Number of sold cappuccinos will be 60.

Learn more about the linear expression visit:

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plz help
Which of the algebraic expressions below is equal to 28?
Select all that apply.(ANSWER ONLY IF YOU KNOW!)

A) (34)(20)×2
B) (24÷4)(7)
C) 9(7−3)–8
D) (3+4)⋅(22+3)

Answers

Answer:

ITS C

Step-by-step explanation:

9(7−3)−8

=(9)(4)−8

=36−8

=28

Answer:

C.

Step-by-step explanation:

9(7-3)-8

according to PEMDAS, we have to do the parenthesis first. so

9(4) - 8

then

36 - 8

which gives us 28.

Hope this helped! (:

The radius of a sphere is increasing at a rate of 0.5 centimeters per minute. At a certain instant, the radius is 17 centimeters.


What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)?

Answers

Using implicit differentiation, it is found that the rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

In this problem, we have that [tex]\frac{dr}{dt} = 0.5, r = 17[/tex], thus:

[tex]\frac{dV}{dt} = 4\pi (17)^2(0.5) = 1815.84[/tex]

The rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.

A similar problem is given at https://brainly.com/question/11496075

HELP ME PLSS.....


Consider the function f (x) = – ⅔+5.

What is f (5/2)?

Enter your answer, as a simplified fraction, in the box

f (5/2) =​

Answers

Answer:

2.5 f

Step-by-step explanation:

5

F x —

2

5

— f

2

I hope it's help :)

Answer:

hi good morning friends

on average, what value is expected for the t statistic when the null hypothesis is true?

Answers

Answer:

0

Step-by-step explanation:

discrete or continuous ​

Answers

i think the answer is contionous

The ages of the members of a family are 65, 58, 27, 25, 5, and 2 years old. What is the total admission price for the family to visit the zoo?

A picture shows an admission price board for people of different ages at a zoo. The ages of people and their admission price per person in dollars are as follows: 12 and under, 8; 13-59, 12; 60 and older, 10.

Answers

Answer:$62

Step-by-step explanation: 62 becuase I took your formula and plugged it in. There are 2 kids under 12 so thats $16, then there are 3 people who are 12-59 that equals $52, then 1 person who is over 60. So $62.

Please help I will give Brainiest if correct!
What is the rate of change?

Answers

Answer: 2 is the correct answer I am 100% positive

Step-by-step explanation:

Answer: the rate of change is 2

Step-by-step explanation:

Please help
What is the measure of ∠ABC?

Answers

Answer:

180°

Step-by-step explanation:

1. What is 3/4 divided by 1/6

Answers

Answer:

9/2 or 4 1/2

Step-by-step explanation:

3/4 ÷ 1/6 = 3/4 × 63/4 × 6 = 18/418/4 = 9/29/2 = 4 1/2

Therefore, the answer is 9/2 or 4 1/2.

Answer: 3

Step-by-step explanation:

3/4 ÷ 1/6

3/4 × 6/1

Divide 4 and 6 by 2

3/2 × 3/1

3 × 3 / 2 × 1

6 / 2 = 3

Graph y= –3x+4.

i need a pic
5o points and brain thing

Answers

Refer to the attachment

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