1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wariber [46]
3 years ago
13

1. Which of the following systems is consistent and dependent?

Mathematics
1 answer:
Kamila [148]3 years ago
8 0

Answer:

Choice d.

Step-by-step explanation:

Consistent means the linear functions will have at least one solution.

Independent means the it will just that one solution.

Dependent means the system will have infinitely many solutions.

So we are looking for a pair of equations that consist of the same line.

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

If m and b are the same amongst the pair, then that pair is the same line and the system is consistent and dependent.

If m is the same and b is different amongst the pair, then they are parallel and the system will be inconsistent (have no solution).

If m is different, then the pair will have one solution and will be consistent and independent.

---------------------------

Choice A:

First line has m=1 and b=4.

Second line has m=1 and b=-4.

These lines are parallel.

This system is inconsistent.

Choice B:

First line is x+y=4 and it isn't in y=mx+b form.

Second line is 2x+2y=6 and it isn't in y=mx+b form.

These lines do have the same form though. This is actually standard form.

If you divide second equation by 2 on both sides you get:  x+y=3

The lines are not the same.

We are looking for the same line.

Now we could go ahead and determine to call this system.

If x+y has value 4 then how could x+y have value 3.  It is not possible. There is no solution. These lines are parallel.

Need more convincing. Let's put them into slope-intercept form.

x+y=4

Subtract x on both sides:

y=-x+4

m=-1 and b=4

x+y=3

Subtract x on both sides:

y=-x+3

m=-1 and b=3.

The system is inconsistent because they are parallel.

Choice c:

I'm going to go ahead in put them both in slope-intercept form:

3x+y=3

Subtract 3x on both sides:

y=-3x+3

So m=-3 and b=3

2y=6x+6

Divide both sides by 2:

y=3x+3

So m=3 and b=3

The m's are different so this system will by consistent and independent.

Choice d:

The goal is the same. Put them in slope-intercept form.

4x-2y=6

Divide both sides by -2:

-2x+y=-3

Add 2x on both sides:

y=2x-3

m=2 and b=-3

6x-3y=9

Divide both sides by -3:

-2x+y=-3

Add 2x on btoh sides:

y=2x-3

m=2 and b=-3

These are the same line because they have the same m and the same b.

This system is consistent and dependent.

You might be interested in
What is the measure of the angle
lutik1710 [3]
The angle would be 70 degrees because 180-110=70
6 0
3 years ago
Read 2 more answers
Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?
elixir [45]

Finding the equivalent angle of \theta, the correct statements are given as follows:

  • The Measure of the reference angle is 45.
  • \cos{\theta} = \frac{\sqrt{2}{2}}.
  • \tan{\theta} = 1
  • \sin{\theta} = \frac{\sqrt{2}{2}}.

<h3>What are equivalent angles?</h3>

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the given angle is as follows:

\theta = \frac{5\pi}{4}

It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:

\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}

The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:

  • The Measure of the reference angle is 45.
  • \cos{\theta} = \frac{\sqrt{2}{2}}.
  • \tan{\theta} = 1
  • \sin{\theta} = \frac{\sqrt{2}{2}}.

More can be learned about equivalent angles at brainly.com/question/24787111

#SPJ1

8 0
1 year ago
Find the values for a, b, and c that complete the simplification.
lisov135 [29]

Answer: A: 6

B: 4

C: 2

Step-by-step explanation:

8 0
3 years ago
Its 6 ya'll if you think it no it 6
snow_lady [41]

Answer:

HUH? What do you mean about that?

7 0
2 years ago
1. is this a function 7 8 2 9 3 10​
kow [346]
I need a lil more information
7 0
3 years ago
Other questions:
  • |-4a+10|=2 solve this eqation asasp 50 pts!
    11·2 answers
  • Jeremy mowed several lawns to earn money for camp. After he paid $17 for gas, he had $75 left over to pay towards camp. Write an
    12·1 answer
  • Simplify. (Note: x ≠ 0)
    11·2 answers
  • Solve each system of equations by graphing 4x-y=5 and. 2x+y=7
    9·1 answer
  • What is the area of rectangle DEFG shown below.
    10·1 answer
  • 2. A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.
    14·2 answers
  • Brian started with $300 in savings account. After 5 years he earned $18 in interest. What is the simple interest rate on his acc
    14·1 answer
  • Graph the linear equation y= 1/2x
    7·1 answer
  • Is 10, 20, 40, 80... an arithmetic sequence?
    5·1 answer
  • Write the rule for the table, use x for the input.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!