On a round trip over the same roads, Sophia averaged 24 mi/hr going and 30 mi/hr coming back. If the whole trip took 13.5 hours, what is the distance one way? (Hint: Find the time for each part of the round trip)

Answer:

d = rt.  In this problem we are looking for the distance, but we will have to go about it indirectly.  If she's traveling the same exact road going and returning, then the distance traveled both ways is exactly the same.  Since d = rt, and d is the same, by the substitution property, if and , then , and .  So we need to rt for the trip going, rt for the trip returning and set them equal to each other and solve for t.  Going is a rate of 24, and the time is t (since we don't know t), and returning is a rate of 30, and the time is 13 1/3-t.  (If the whole trip takes 13 1/3 hours, and t is the time going, then the time returning is the difference between the total time and the going time.  That concept is one that baffles most algebra students!). So our r1t1 is 24t, and our r2t2 is 30(13 1/3 - t).  Set them equal to each other and that will look like this:    That fraction of 40/3 is 13 1/3 made into an improper fraction.  Distributing that we will have and 54t = 400.  That means that t = 7.407.  We have time, and that's great, but we need distance!  Go back to one of your equations for distance and sub in t and solve for d.  d = 24t, and d = 24(7.407), so d = 177.768 miles.

9x - 4 = ??

show step by step btw

use implicit differentation to determine dy/dx for the equation

Josh wants to simplify the expression (-8)(10+(-5)+(-8)). To get the fully simplified expression, Josh must multiply 10, -5, and -8 by some number and then add the resulting products.

By what number must Josh Multiply?

During the hottest week of the summer, the water level of the Muskrat river was 5/6 below normal. The following week, the level was 1/3 foot below normal. what is the overall change in the water level?


start at - 1/3 number line.


step 1 | find - 1/3 - (5/6)


step 2 | start at - 1/3


step 3 | move -5/6 = 5/6 to the right because ur subtracting a negative number.


the result is 1/2


so the water increased 1/2 foot.


now, compare the methods used to solve example 1 and 2.

please solve questions 4-8!! please solve by multiplying the decimals!! please and thank you :)

At the market, Joey buys 3 avocados for $.40 each and 5 lemons for $0.40 each. The cashier in training rings up 3 × 0.40 and then 5 × 0.40 to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8 × 0.40.

What property says that these two totals would be the same?

1. Associative property of multiplication
2. Commutative property of multiplication
3. Multiplicative identity
4. Distributive property

Please use the y = mx + b form, i have y = 3/2x but i don't know the y intercept.
through: (4, 3), SLOPE = 3/2
please provide an explanation i am really struggling.

I need help please this is about ratios

Please help me. Thank you.

HOW DO I SOLVE THIS??????!!!!!! 8.418 into a fraction pls show how you got the answer or just explain pls help

help please????????????

63 is 90% of what number? pls help

what is the value of 2.6+0.9=−(−−2.1)

what is the answer to this one because this is confusing

You buy the same pair of pants in 3 different colors for $89.85. How much does each pair of pants cost?​

..................................help please?......................................................

Please help me ASAP


*please don’t post links they don’t work*

A punch recipe that serves 24 people calls for 4 liters of lemon-lime soda, 2 pints of sherbet, and 6 cups of ice. How much of each ingredient would you need to make an identical recipe that serves 36 and 18 people

(jk−1)÷j when j=−4 and k=−0.7

Sam has saved 200 sand dollars and wants to give them away equally to n friends. Write an expression to show how many sand dollars each of Sam's friends will receive.

What is the difference between income and expenses?


Income is the money going out; expenses are the money coming in.

Income is the money coming in; expenses are the money going out.

Income is the amount paid in payroll taxes; expenses are the amount before payroll taxes.

Income is the amount paid in payroll taxes; expenses are the amount before payroll tax.

please help
find all points on the curve…

Mia is 6.92784 × 10^6 minutes old. Convert her age to more appropriate units using years, months, and days. Assume a year has 365 days and a month has 30 days.

what is the sum of (-0.4) with an exponent on the outside of 2

The graph below models the value of a $20,000 car t years after it was purchased.

Value of Car

A graph titled Value of Car has years on the x-axis and Dollars on the y-axis. A line curves down and goes through points (0, 20,000), (4, 10,000), and (14, 2,000).

Which statement best describes why the value of the car is a function of the number of years since it was purchased?
Each car value, y, is associated with exactly one time, t.
Each time, t, is associated with exactly one car value, y.
The rate at which the car decreases in value is not constant.
There is no time, t, at which the value of the car is 0.

Jordy is working on her homework. She has a total of 5 assignments to complete by Friday. If Jordy has completed 1 1/3 assignments, how many assignments does she have left to complete.

If the custodian finds 4 rotting bananas in the dumpster in her first 13 weeks of work, how many rotting bananas would she expect to find in 26 weeks? Write a proportion to represent the problem. Use a variable, such as x, to represent the unknown quantity. rotting banana(s) week(s) Enter the number of rotting bananas that she expects to find in 26 weeks. *see picture for much better explanation* ​​

Angle MNO is formed by segments MN and NO on the following coordinate grid:

Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. Which statement shows the measure of angle M′N′O′? (1 point)

Group of answer choices

m∠ M′N′O′ = 90 degrees

m∠ M′N′O′= 180 degrees

m∠ M′N′O′ = 2 ⋅ m∠MNO

m∠ M′N′O′ = m∠MNO

To avoid a storm, a passenger-jet pilot descended 0.38 mile in 0.4 minute. What was the plane's average change of altitude per minute?

1. Matt is going to create a graph of the equation y = -0.75x + 6. Which of the following will be true about the graph? a. The graph will contain the origin. b. The graph will increase from left to right. c. The graph will cross the x-axis at (6,0). d. The graph will have a slope of -0.75.​