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2 years ago

Which equations can pair with y = 3x – 2 to create a consistent and independent system?

Mathematics

2 answers:

S_A_V [24]2 years ago

4 0

Answer:

1, 2, and 5

Step-by-step explanation:

just did it on edg

Oduvanchick [21]2 years ago

3 0

Answer:

x=3y-2

y=-3x-2

3y-x=-2

Step-by-step explanation:

we know that

To create a consistent and independent system, the slope of the other equation must be different at the slope of the given equation.

A consistent and independent system has only one solution

we have

y=3x-2

The slope of the given equation is m=3

Verify the slope of each case

case 1) we have

x=3y-2

isolate the variable y

3y=x+2 ------> y=(1/3)x+(2/3)

The slope is m=1/3

therefore

This equation can pair with the given equation to create a consistent and independent system, because their slopes are different

case 2) we have

y=-3x-2

The slope is m=-3

therefore

This equation can pair with the given equation to create a consistent and independent system, because their slopes are different

case 3) we have

y=3x+2

The slope is m=3

Parallel lines with different y-intercepts (The system has no solution)

therefore

This equation cannot pair with the given equation to create a consistent and independent system, because their slopes are the same

case 4) we have

6x-2y=4

isolate the variable y

2y=6x-4

y=3x-2

The slope is m=3

Is the same given equation (is a consistent and dependent system, has infinitely solutions)

therefore

This equation cannot pair with the given equation to create a consistent and independent system, because their slopes are the same

case 5) we have

3y-x=-2

isolate the variable y

3y=x-2

y=(1/3)x-(2/3)

The slope is m=1/3

therefore

This equation can pair with the given equation to create a consistent and independent system, because their slopes are different

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Select the locations on the number line to plot the points 10/2 and −9/2 .

tresset_1 [31]

Answer:

5 and -4.5

Step-by-step explanation:

10/2=5

and -9/2=-4.5

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2 years ago

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An ostrich can run 6 mph faster than a giraffe. An ostrich can run 7 miles in the same time that a giraffe can run 6 miles. Find

LUCKY_DIMON [66]

NOTE THIS IS AN EXAMPLE:

Let t = time, s = ostrich, and g = giraffe.

Here's what we know:

s = g + 5 (an ostrich is 5 mph faster than a giraffe)

st = 7 (in a certain amount of time, an ostrich runs 7 miles)

gt = 6 (in the same time, a giraffe runs 6 miles)

We have a value for s, so plug it into the first equation:

(g + 5)t = 7

gt = 6

Isolate g so that we can plug that variable value into the equation:

g = 6/t

so that gives us:

(6/t + 5)t = 7

Distribute:

6 + 5t = 7

Subtract 6:

5t = 1

Divide by 5:

t = 1/5 of an hour (or 12 minutes)

Now that we have a value for time, we can plug them into our equations:

1/5 g = 6

multiply by 5:

g = 30 mph

s = 30 + 5

s = 35 mph

Check by imputing into the second equation:

st = 7

35 * 1/5 = 7

7 = 7

5 0

2 years ago

C) look at the scale factor for parts a and b. do they represent a reduction or enlargement of the empire state building? How do

ruslelena [56]

Answer:

Enlargement

Step-by-step explanation

It is enlargement, because it went up by three. Instead of reducing.

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2 years ago

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a new coffee shop can hold no more than 50 seats the owner wants at least 20 of the seats to be stools and the remaining seats t

Snezhnost [94]

Attached

Step-by-step explanation:

From the question x is the number of stools and y is the number of recliners

Given that the coffee shop can hold no more than 50, then the inequality for number of seats will be;

x+y≤ 50

Also, the owner wants at least 20 of the seats to be stools, this can be written as;

x≥20

Using a graph tool to visualize the inequalities, you get the attached graph;

Learn More

Inequalities graph : brainly.com/question/11234618

Keyword : graph, inequalities

#LearnwithBrainly

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2 years ago

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Tan 235° = 2tan20°+ tan215°

Mariulka [41]

Given : tan 235 = 2 tan 20 + tan 215

To Find : prove that

Solution:

tan 235 = 2 tan 20 + tan 215

Tan x = Tan (180 + x)

tan 235 = tan ( 180 + 55) = tan55

tan 215 = tan (180 + 35) = tan 35

=> tan 55 = 2tan 20 + tan 35

55 = 20 + 35

=> 20 = 55 - 35

taking Tan both sides

=> Tan 20 = Tan ( 55 - 35)

=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)

Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1

=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)

=> Tan 20 = (Tan 55 - Tan 35) /2

=> 2 Tan 20 = Tan 55 - Tan 35

=> 2 Tan 20 + Tan 35 = Tan 55

=> tan 55 = 2tan 20 + tan 35

=> tan 235 = 2tan 20 + tan 215

QED

Hence Proved

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2 years ago