For each expression, apply the distributive property and write an equivalent expression.

Lee las situaciones y realiza lo siguiente con cada una:

Julli [10]

Answer:

Part 1) see the explanation

Part 2) see the explanation

Part 3) see the explanation

Part 4) see the explanation

Step-by-step explanation:

<u><em>The question in English is</em></u>

Read the situations and do the following with each one:

Write down the magnitudes involved

Write which magnitude is the independent variable and which is the dependent variable

It represents the function that describes the situation

SITUATIONS:

1) A machine prints 840 pages every 30 minutes.

2) An elevator takes 6 seconds to go up two floors.

3) A company rents a car at S/ 480 for 12 days.

4) 10 kilograms of papaya cost S/ 35

Part 1) we have

A machine prints 840 pages every 30 minutes

Let

x ----> the time in minutes (represent the variable independent or input value)

y ---> the number of pages that the machine print (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=840\ pages\\x=30\ minutes$

substitute

$k=\frac{840}{30}=28\ pages/minute$

The linear equation is

$y=28x$

Part 2) we have

An elevator takes 6 seconds to go up two floors.

Let

x ----> the time in seconds (represent the variable independent or input value)

y ---> the number of floors (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=2\ floors\\x=6\ seconds$

substitute

$k=\frac{2}{6}=\frac{1}{3}\ floors/second$

The linear equation is

$y=\frac{1}{3}x$

Part 3) we have

A company rents a car at S/ 480 for 12 days.

Let

x ----> the number of days (represent the variable independent or input value)

y ---> the cost of rent a car (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=\$480\\x=12\ days$

substitute

$k=\frac{480}{12}=\$40\ per\ day$

The linear equation is

$y=40x$

Part 4) we have

10 kilograms of papaya cost S/ 35

Let

x ----> the kilograms of papaya (represent the variable independent or input value)

y ---> the cost (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=\$35\\x=10\ kg$

substitute

$k=\frac{35}{10}=\$3.5\ per\ kg$

The linear equation is

$y=3.5x$

6 0

3 years ago

Write the equation of the line that passes through the points (-3, 3) and (1, 2).

postnew [5]

Y=-1/4x+2.25

Slope: -1/4
Y-intercept: 2.25

5 0

3 years ago

Please help ASAP will give brainilest to best answer

kykrilka [37]

Answer: 100

Step-by-step explanation:

1 cubic inch would just be 100 because each cube is 1 cubic inch. So 100(number of cubes)/1(cubic inch)=100 I hope I'm right :)

3 0

3 years ago

A company with a fleet of 150 cars found that the emissions systems of only 4 out of the 32 they tested failed to meet pollution

lidiya [134]

Answer:

Yes

Step-by-step explanation:

First, we need to find how many cars out of the entire fleet fail the test

4/32 = x/150

Cross multiply to find x

32x = 150(4)

32x = 600

32x/32 = 600/32

x = 18.75

I'll round it to 19. So 19 out of 150 cars fail the test. Find the percentage of this and compare it to the 30% estimate

19 /150 = 0.127

0.127(100) = 12.7%

12.7% is obviously lower than 30% so yes it is strong evidence the percentage of the fleet out of compliance is different from their initial thought

8 0

4 years ago

Ethan sorts shapes into two groups as shown what mistakes did ethan make

nataly862011 [7]

Ethan's mistakes in sorting the shapes into two groups are:

Shape C does not belong to group 1 because it does not have square corners
Shape F does not belong to group 2 because it does not have any square corners

<h3>How to spot the mistakes?</h3>

From the complete question (see attachment), the shapes are grouped using the following criteria:

All the shapes in group 1 have 4 square corners
All the shapes in group 2 have exactly 1 square corner

Using the above rules, Ethan's mistakes are: shapes C and F are placed in the wrong groups