Tell whether each equation represents a direct proportion. If so, identify the
constant of proportionality.

1. 0.4y = x

2. x = 1 - 2y

Answers

Answer 1

Answer:

Step-by-step explanation:

1. 0.4y = x is a direct proportion. It'd be more appropriate to write this as

y = x / 0.4, or y = 2.5x, in which case 2.5 is the constant of proportionality.

2. x = 1 - 2y is not a direct proportion because of the offset (1). A line representing a direct proportion must go through the origin (0, 0); this particular line does not do that.

Answer 2

The first equation, 0.4y = x, represents a direct proportion with the constant of proportionality being 2.5. The second equation, x = 1 - 2y, does not represent a direct proportion since it does not have the form y = kx.

When we talk about two quantities being directly proportional, we mean that as one quantity increases, the other increases by a constant rate, and vice versa. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.

For the first equation, 0.4y = x, this is rearranged as y = (1/0.4)x or y = 2.5x. This is indeed a directly proportional relationship, with the constant of proportionality being 2.5.

The second equation x = 1 - 2y does not describe a directly proportional relationship because it is not of the form y = kx. Instead, it shows that x decreases as y increases, which is suggestive of an inverse relationship, rather than a direct one.

Related Questions

Evaluate 3/2y - 3 + 5/3z when y=6 and z=3

Answers

Answer: 11

Step-by-step explanation:

3/2(6) - 3 + 5/3(3)= 11

Find the slope of the line through (2, -3) and (-4, 3).

-1
0
1

Answers

ANSWER

-1

EXPLANATION

The slope formula is given by

[tex]m = \frac{y_1-y_2}{x_1-x_2} [/tex]

The slope of the line through (2, -3) and (-4, 3) is found by substituting the points into the above formula;

[tex]m = \frac{ - 3 - 3}{2 - - 4} [/tex]

This simplifies to

[tex]m = \frac{ - 6}{ 6} = - 1[/tex]

The slope is -1

Answer:

-1

Step-by-step explanation:

The slope of a line is the ratio of its change in rise to its change in run. In the -xy-plane, this is the same as the ratio of the change in y coordinate to the change in x coordinate. In notation, we write this as

[tex]\frac{\Delta y}{\Delta x}[/tex]

and calculate it by finding the difference between y coordinates and dividing it by the difference between x coordinates. Here, our y coordinates are 3 and -3, and our x coordinates are -4 and 2, so our slope would be

[tex]\frac{3-(-3)}{-4-2}=\frac{3+3}{-6}=\frac{6}{-6}=-1[/tex]

Simplify the variable expression by evaluating its numerical parts and enter your answer m - 22 + 37 - 8

Answers

7 is the answer dddddddddddddddd

Answer:

M+7

Step-by-step explanation:

hoped it heped ^v^

tell whether the angles are complementary or supplementary. then find the value of x

Answers

Hello,

In Q5. Being a straight line the angles are supplementary to each other.

And x = 70°

In Q6.

The angles sum up to 90° , so 25x + 30° = 90

25x = 60°

x= 60°/25 = 2.4°

Hope this helps.

Answer:

see explanation

Step-by-step explanation:

x and 110 form a straight angle and are supplementary, thus

x + 110 = 180 ( subtract 110 from both sides )

x = 70

25x and 30 form a right angle and are complementary, thus

25x + 30 = 90 ( subtract 30 from both sides )

25x = 60 ( divide both sides by 25 )

x = [tex]\frac{60}{25}[/tex] = [tex]\frac{12}{5}[/tex]

A survey asks teachers and students whether they would like the new school mascot to be a shark or a moose . this table shows the results .
A person is randomly selected from those surveyed
Are being a student and preferring “shark” independent events ? Why or why not ?

Answers

The true statement about the events is (b) No, they are not independent because P(student)= 0.87 and P(student/shark)=0.95

How to determine the true statement?

Two events A and B are independent if

P(A∣B) = P(A)

Using the data entries in the table, we have:

P(Student) = 100/115

P(Student) = 0.87

Also, we have:

P(Student | Shark) = 90/95

P(Student | Shark) = 0.95

The probability values are not equal

i.e.

P(Student) ≠ P(Student | Shark)

Hence, the events A and B are not independent events because P(student)= 0.87 and P(student/shark)=0.95

Answers

Answer: $26

$40*.35=$14 off price of sweater

40-14=$26 sale price

$40*.65=$26 sale price

Answer:

The correct answer is $26.

Step-by-step explanation:

Well, we must first analyze the information we have.

We have a sweater that was marked down 35% off.

We know that the original price of the sweater is $ 40. Now we just have to find out the final price.

But to know that, we must first know what the discount was applied.

And we find out as follows:

[tex]Tax= 40 . 0,35[/tex]

[tex]Tax= 14[/tex]

In this way we show that the price discounted to the sweater was $ 14

Now we just have to make a subtraction between the original price and the discount :

40-14=26

The final price of the sweater is $ 26

Help please what is the answer?

Answers

Answer:

C) 5.6

Step-by-step explanation:

AC = sqrt(11^2 + 2^2) = sqrt(125)

(1/2)AC = (1/2)sqrt(125)

(1/2)AC = 5.6

Answer: C) 5.6

Answer:

C, 5.6

Step-by-step explanation:

A midsegment is half of the side it is parallel to. This means that it is half of BC. They give us the coordinates for B and C so we can just use the distance formula (the square root of the change in x squared plus the change in y squared)

If you simplify it, you get root 125 which is about 11.2. 11.2 divided by 2 is 5.6, so your answer would be C.

Martin can run 1 mile in 7 minutes. What proportions can be written from this information?

Answers

Answer:

[tex]\frac{1}{7}=\frac{3}{21}[/tex]

[tex]\frac{7}{1}=\frac{21}{3}[/tex]

Step-by-step explanation:

Verify each case

case 1) [tex]\frac{1}{7}=\frac{3}{21}[/tex]