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faust18 [17]
3 years ago
13

use the substitution method to solve the system of equations choose the correct orderd pair. 3x-y=7 2x-2y=2

Mathematics
1 answer:
sergey [27]3 years ago
6 0

Answer:

(3,2)

Step-by-step explanation:

We are given the system:

3x-y=7

2x-2y=2.

We are asked to solve this by substitution.  We need to pick an equation and pick a variable from that equation to solve for that variable.

I really like either for this.  Some people might go with the first one though. Let's do that.  I will solve the first one for y.

3x-y=7

Subtract 3x on both sides:

   -y=-3x+7

Divide both sides by -1:

     y=3x-7

Now we are ready for substitution.  We are going to plug this equation into the second equation giving us:

2x-2y=2 with y=3x-7 gives us:

2x-2(3x-7)=2

Distribute:

2x-6x+14=2

Combine like terms:

-4x+14=2

Subtract 14 on both sides:

-4x      =2-14

Simplify:

-4x       =-12

Divide both sides by -4:

  x       =-12/-4

Simplify:

 x         =3

So using y=3x-7 and x=3, I will find y now.

y=3x-7 if x=3

y=3(3)-7   (I inserted 3 for x since we had x=3)

y=9-7       (Simplified)

y=2           (Simplified)

The answer is (x,y)=(3,2).

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The director of the library calculates that 29% of the library's collection is checked out. If the director is right, what is th
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Answer:

The probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4% is P=0.9255.

Step-by-step explanation:

The population's proportion is \pi=0.29

If we take a sample of 412 books (n=412), we have a standard deviation of the sampling distribution of:

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We have to calculate the probabilty that the sample proportion will be between 0.25 and 0.33.

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8 0
3 years ago
Write the congruency statement for the triangles. _______In triangles MNO and JKL, there are two congruent sides and included an
mafiozo [28]

Answer:

ΔJKL ≅ ΔMNO by SAS

Step-by-step explanation:

The question is incomplete, the question is as following:

ΔMNO is shown.

Which Δ below can be shown to be congruent to ΔMNO with only the given information?

Name the postulate that justifies your answer (SAS, AAS, HL, ASA or SSS).

Write the congruency statement for the triangles.

And see the attached figure which represent ΔMNO

==========================================================

Check the given options to see which triangle from the option will be congruent to ΔMNO

1. In triangles MNO and ABC, there are two congruent sides and non-included angle - which mean (angle - side - side)

The (angle - side - side) Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent.

2. In triangles MNO and DEF, there are two congruent sides - there is not enough information

3. In triangles MNO and GHI, there are three congruent angles - which mean AAA (angle - angle - angle)

The AAA Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. This postulate is used to prove the similarity between the triangles.

4. In triangles MNO and JKL, there are two congruent sides and included angle - SAS (side - angle - side)

MN ≅ JK , MO ≅ JL , ∠M ≅ ∠J

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