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3 years ago

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

Mathematics

1 answer:

ollegr [7]3 years ago

5 0

Answer: Consistent and independent.

Step-by-step explanation:

We have the system of equations:

y = 4x - 4

y = -4x + 4.

Now, first let's define the terms used in the question.

consistent and independent: we have only one solution.

consistent and dependent: we have infinite solutions.

inconsistent: we do not have solutions.

Now, let's look at the system:

y = 4x - 4

y = -4x + 4.

Let's take the quotient between both the equations:

(y/y) = (4x - 4)/(-4x + 4)

1 = (4x - 4)/(-4x + 4)

let's see if we can solve this for x.

1*(-4x + 4) = 4x - 4

-4*x + 4 = 4x - 4

-4x - 4x = -4 - 4

-8*x = -8

x = -8/-8 = 1.

and to find the value of y, we can input this value of x in one of the equations:

y = 4*1 - 4 = 0.

Then we have only one solution, (1, 0).

(and will be the same if you input x in the other equation, as the right side is minus the right side of the first equation)

Then the system is consistent and independent.

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3 years ago

Read 2 more answers

Line E'F' has endpoints located at E'(1,0) and F'(1,3). Line EF was dilated by a scale of 1/2 from the orgin. Which statement de

Lerok [7]

Answer:

If line EF was dilated by a scale of 1/2 from the origin to get line E'F', then if line E'F' is dilated by a scale of 2 from the origin, EF is obtained. Also, the length of EF is double than the length of E'F'.

Dilation by a scale of 2 from the origin transforms point (x,y) into (2*x, 2*y)

E'(1,0) -> E(2,0)

F'(1, 3) ->F(2, 6)

length of E'F': 3

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3 years ago

Herber read a total of 36pages in 2 hours. Later on, he read 90 pages in 5 hours. How many pages did Herber read each hour.

Lady_Fox [76]

Answer:

18 pages per hour.

If you do 36 (the pages/amount) divided by 2 (The time), you get 18.

To double check, when you do 90 (The pages/amount) divided by 5 ( The time), then you get 18 again.

Therefore the answer is 18 pages per hour.

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3 years ago

You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.75. Wi

Dafna1 [17]

Answer:

0.2915

Step-by-step explanation:

Let W represent water and D represent Dying probability

W = water

D = die

->If with water, it will die with probability 0.4

P(W & D) = 0.82 x 0.4 = 0.328