Question
Solve the real-world situation by using the substitution method.
Jen is riding her bicycle on a trail at the rate of 0.33 kilometer per minute. Michelle is 8
kilometers behind Jen when she starts traveling on the same trail at a rate of 0.43 kilometer
per minute. Let d represent the distance in kilometers the bicyclists are from the start of
the trail and t represent the time in minutes.
The system of equations
d = 0.33t + 8
d = 0.43t
can be used to represent this situation.
р.
How many minutes will it take Michelle to catch up to Jen? How far will they be from the
start of the trail? Use the substitution method to solve this real-world application.
Michelle will catch up to Jen in
of the trail.
minutes and they will be
km from the start

Answers

Answer 1

9514 1404 393

Answer:

80 minutes34.4 km

Step-by-step explanation:

Use the second equation to substitute for d in the first equation.

  0.43t = 0.33t +8

Subtract 0.33t from both sides

  0.10t = 8

Multiply by 10

  t = 80 . . . . . . Michelle will catch Jen in 80 minutes

The distance traveled will be ...

  d = 0.43t = 0.43×80 = 34.4 . . . . km

The girls will have traveled 34.4 km when they meet.


Related Questions

he length of the stretch (in millimeters) of a spring is proportional to the weight (in grams) attached to the end of the spring as shown in the graph. a) Label the points given (give the ordered pair). b) What is the unit rate? c) Plot and label the point whose ordered pair represents the unit rate. d) What are the coordinates of that point? e) Explain what the point that you plotted means in this context of this problem. f) Write an equation for this graph. ​

Answers

Answer:

a) Label the points given (give the ordered pair).

(2, 10), (3, 15), (7, 35)

b) What is the unit rate?

10/2 = 15/3 = 35/7 = 5

c) Plot and label the point whose ordered pair represents the unit rate.

Plot the point at 1 unit right, 5 units up

d) What are the coordinates of that point?

(1, 5)

e) Explain what the point that you plotted means in this context of this problem.

1 gram of weight is proportional to 5 mm stretch

f) Write an equation for this graph. ​

y = 5x

PLEASE HELP ME :(
(X+4)^2-3(x+4)-3=0
Select the solutions of the og equation

Answers

Answer:

[tex]\boxed{\textsf{ The value of x is }\bf{ \dfrac{-5\pm\sqrt{21}}{2}}.}[/tex]

Step-by-step explanation:

A quadratic equation is given to us and we need to find the Solutions of the quadratic equation . So the given equⁿ is ,

[tex]\sf\implies (x+4)^2 -3(x+4) -3 = 0 [/tex]

Firstly let's simpify the quadratic equation and then use the quadratic formula also known as " Shreedhacharya's Formula" .

Taking the given equation :-

[tex]\sf\implies (x+4)^2 -3(x+4) -3 = 0\\\\\sf\implies x^2 + 16 + 8x -3x -12 -3 = 0 \\\\\sf\implies x^2+5x +1 = 0 [/tex]

Now let's use the Quadratic formula ,

Quadratic Formula :-

[tex]\qquad\boxed{\boxed{ \sf x =\dfrac{ -b \pm \sqrt{ b^2-4ac}}{2a} }} [/tex]

With respect to Standard form ax² + bx + c form. Here a = 1 , b = 5 and c = 1 .

[tex]\sf\implies x = \dfrac{ -5\pm \sqrt{ (5)^2-4(1)(1)}}{2(1)} \\\\\sf\implies x = \dfrac{ -5 \pm \sqrt{ 25 -4 } }{2} \\\\\sf\implies \boxed{\pink{\sf x = \dfrac{-5+\sqrt{21}}{2}, \dfrac{-5-\sqrt{21}}{2} }}[/tex]

What is the surface area of this triangular right prism?
Below are the measurements
6.5 ft
6 ft-
11 ft
5 ft

Answers

Area of triangular prism = 1/2 times base times height times length

1/2 * 5 * 6 * 11 (6.5 is extra info)
2.5 * 6 * 11
15 * 11
165 cubic feet or ft^3

What is 13 divide 5 . And what is 2 divided 3

Answers

Decimal form:                                                         Fraction form                                                                                      

13/5 is 2.6                                                                     2 3/5.

2/3 is 0.666666667                                         I can' figure out for this, sorry!                      

Hope this helps!!

13 divide by 5 is 2.6 and 2 divided by 3 is 0.66666666666 or 0.6

6)
If h= n + 4, and if n = 7, what is h?
A)
3
B)
1
D)
12
What is h

Answers

Answer:

11

Step-by-step explanation:

If n=7, you would substitute n in the equation with 7.

h=7+4

h=11

Answer:

h=11

Step-by-step explanation:

h = n + 4

but n = 7

h = 7 + 4

h=11

Can you please help me

Answers

Answer:

x=14

Step-by-step explanation:

5x+3x+30 +2x+10 = 180 (angles on straight line add to 180)

10x+40 =180

10x=140

x=14

It usually takes you 1 1/4 hours to get home. One day, traffic was slowed by bad weather and it took you 2 1/2 hours to get home. How much longer did it take you to get home with bad weather?

Answers

Answer:

1 1/4 more hours

Step-by-step explanation:

To find this, we must subtract 2 1/2, the time it takes you to get home with bad weather by 1 1/4, the amount it usually takes you to get home. We can make 2 1/2 into 2 2/4, and now we can subtract and get 1 1/4.

Finding trigonometric ratios:

( ONLY QUESTIONS 10, 12 and 14)

Answers

Step-by-step explanation:

Sorry that they're sideways, it's the only way brainy would let me send them!!

What is the interest of an investment of $2,000 made at 6% simple interest per year for a time period of 9 mo.?

Answers

Answer:The answer would be $1080.

Please help me figure these out! Thanks!

Answers

For number 18 is c hope it helps

Jenna drank 2 3 liter of water Monday before going jogging. She drank 3 7 liter of water after her jog. How much water did Jenna drink altogether? Write your answer as a mixed number. Plzz i give brainly

Answers

Answer:

Step-by-step explanation:

57

Answer:

27 liter

Step-by-step explanation:

2 3 liter = 3+3= 6

3 7 liter = 7+7+7= 21

21+6=27

The length of the highway is 500 miles. If 1 inch represents 100 miles, what is
the length of the highway on the map?

Answers

Answer:

Its 5 inches

Step-by-step explanation:

This is because 1 inch is 100 miles and there are 500 miles so 1 inch times 5 is 5

could somebody help me please

Answers

Answer:

Step-by-step explanation:

A number squared is just the number times itself.

[tex]n(n)=n^2[/tex]

Answer:

A number squared is a number to the power of 2 or the number times itself.

Step-by-step explanation:

Lets say you have a 4 to the 2nd that would mean that the 4 is multiplied by 4. Dont get the exponent confused as the number to multiply it as. Look at [tex]9^{2}[/tex] for example, you would multiply the number 9 2 times not 9 times 2 so it would be 9x9.

Nevan's gross pay was $45,150 last year. The federal income tax withholding from his pay was 16% of his gross
pay. Nevan determined the federal income tax he owes is $6,150. Which of the following is true?
Nevan owes an additional $984 in federal tax.
• Nevan owes an additional $1,074 in federal tax.
Nevan will receive a refund of $984.
Nevan will receive a refund of $1,074.

Answers

Answer: Nevan will receive a refund of $1,074.

Step-by-step explanation:

I don't remember how I did it but I looked it up on Quizlet.

Nevan will receive a refund of $1,074.

What is the pattern?

Answers

Answer\Pattern for the right side will continue by 2 and the pattern on the other left side the pattern will continue by -2.

Step-by-step explanation:

On the right side each time it is an addition of two
On the left side it is a -2

3 women and 2 men are on a tv game show. What are the odds that a woman will win?

Answers

I don’t know what is - this is-

Answer:

3/5 or 60%

Step-by-step explanation:

given m||n fine the value of x

Answers

Answer:

153 im pretty sure

Step-by-step explanation:

use alternative interior angle rules which states that alternative interior angles are congruent (equal)

The answer is X=207°

Lisa is making her famous chocolate chip brownies. The recipe calls for 2 cups of chocolate chips, but Lisa can only find her LaTeX: \frac{1}{4}1 4 measuring cup. How many LaTeX: \frac{1}{4}1 4 cups will she need to get the 2 cups needed for her recipe?

Answers

Answer:

I think the answer is 8

Step-by-step explanation:

The bank charges 4 dollars a day for accounts under $100. Lisa's account had a balance of $15. What would the y-intercept be?

Answers

Answer:

her y intercept would be $15.

Which sentence is true?
All whole numbers are also natural numbers.
b All integers are also rational numbers.
All rational numbers are also integers.
d. All integers are also whole numbers.

Answers

Answer:

Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.

Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4…

Integers include all whole numbers and their negative counterpart e.g. …-4, -3, -2, -1, 0,1, 2, 3, 4,…

All integers belong to the rational numbers. A rational number is a number

ab,b≠0

Where a and b are both integers.

Example

The number 4 is an integer as well as a rational number. As it can be written without a decimal component it belongs to the integers. It is a rational number because it can be written as:

41

or

82

or even

−8−2

Whereas

15=0.2

is a rational number but not an integer.

A rational number written in a decimal form can either be terminating as in:

15=0.2

Or repeating as in

56=0.83333...

All rational numbers belong to the real numbers.

If you look at a numeral line

picture05

You notice that all integers, as well as all rational numbers, are at a specific distance from 0. This distance between a number x and 0 is called a number's absolute value. It is shown with the symbol

|x|

If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites. Opposites have the same absolute value since they are both at the same distance from 0.

|10|=10=|−10|

Step-by-step explanation:

Ellen drove 277.2 miles. For each gallon of gas, the car can travel 21 miles. How many gallons of gas did Ellen use?

Answers

Answer:

the answer is 13.2

Step-by-step explanation:

Answer:

13.2

Step-by-step explanation:

277.2÷21=13.2 gallons

True or False: A function must have a different output for each input. A True B False ​

Answers

Answer:

true

Step-by-step explanation:

Independent Practice


Determine whether the relation is a function. Explain why or why not.


{(6, –7), (5, –8), (1, 4), (5, 5)}


A.
Yes; the domain value 5 corresponds to two range values, –8 and 5.


B.
No; the domain value 5 corresponds to two range values, –8 and 5.


C.
Yes; the range values are all different.


D.
No: 5 is both in the domain and in the range.

Answers

The answer you’re looking for is a yes the domain value five corresponds to two range values -8 and five

what are all the composite numbers from 1 to 100

Answers

Answer:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81,82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Step-by-step explanation:

its pretty simple...

Sandy's dad just finished working and was paid $8000 for his work. Her dad gave her mom 5/8 of his salary to pay for household expenses. Her mom gave her brother 1/15 of the amount she received as allowances for her brother. Her brother gave Sandy 2/3 of his allowances because he owed her money. How much money did Sandy get from her brother?

a) Write an equation for this scenario

b) Solve the scenario and find out how much money Sandy got from her brother

Answers

Answer:

Sandy got (approximately) $222.22 from her brother.

Step-by-step explanation:

5/8 (8000) = 5000

1/15 (5000) = 333.33

2/3(333.33) = 222.22

PLS 100 points...?
10. Mary wants to do a cheesecake. She needs 4 4 12 cups of sweet cream. She knows that 1
cup = 8 ounces How many ounces does she need?

Answers

She needs 4 1/2 cups of sweet cream.

That’s the same as 4.5 cups.

If 1 cup = 8 ounces, you need to find 4.5 cups.

Just multiply 4.5 by 8.

The answer is 36 ounces.

Please help will give Brain

Answers

AA





Because you know the two angles

Answer:

by brain... do you mean top at the red light?

Step-by-step explanation: she gave me top at the red light

A U.S. penny has a mass of 2.5 grams. A U.S. quarter has a mass of 5.67 grams. What is the total mass of the two coins (pls help lol)

Answers

Answer:

8.17 grams

Step-by-step explanation:

To find the total mass of the two coins add the masses together.

[tex]5.67+2.5=8.17[/tex]

What is the distance between (8,-3) and (4,- 7)?

Answers

Answer:

5.66 units

Step-by-step explanation:

base: 8-4 = 4

rise: -3-(-)7 = 4

4^2+4^2 = d^2

d^2 = 32

d=5.66 units

Find the domain and range of f(x)=4*(1/2)^x

Answers

domain is the set of x-values and range is the set of y-values.
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