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Mamont248 [21]
3 years ago
9

What is the solution to the following system of linear equations?

Mathematics
1 answer:
Lostsunrise [7]3 years ago
8 0
<span> x − 2y = −1 => x = 2y -1

2x + y = −12
2(2y - 1) + y = -12
4y - 2 + y = -12
5y = -10
y = -2
x = 2</span>·(-2) - 1
x = -4 - 1
x = -5

Answer <span>D (-5,-2)</span>
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13x−2=<br>  <br>  <br> −<br> 10<br> x<br> −<br> 2<br> −10x−2
Misha Larkins [42]

Answer:

x=0

Step-by-step explanation:

13x-2 = 10x-2

Subtract 10x from each side

13x-10x-2 = 10x-2 -10x

3x-2 = -2

Add 2 for each side

3x-2+2 = -2+2

3x= 0

divide by 3

3x/3 = 0/3

x =0

3 0
3 years ago
Find the distance between the points T(13, 1.6) and V(5.4.3.7).
11Alexandr11 [23.1K]

Find the distance between the points t(13, 1.6)t(13, 1.6) and v(5.4, 3.7)v(5.4, 3.7).

1

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The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

Thus the distance between points t(13, 1.6) and v(5.4, 3.7) is found using the formula as:

5 0
2 years ago
How do you find the arc length of a semi-circle?
ArbitrLikvidat [17]

the arc length is calculated by the formula                                                                    \displaystyle\bf C=\frac{2\pi r}{360} \cdot\alpha   then   \displaystyle\bf C=\frac{2\cdot 8 \pi }{360} \cdot180=8\pi=3,14\cdot8=25.12   or it can be calculated using the circumference of the circle since we have a semicircle the circumference 2πr must be divided by 2  С=2πr:2=πr =8π=<u>25,12</u>

4 0
3 years ago
Graph the line that passes through the points (2, -3)(2,−3) and (4, -3)(4,−3) and determine the equation of the line.
liraira [26]

Answer:

Step-by-step explanation:

7 0
3 years ago
Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random an
belka [17]

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2  

3. {S2, S3, S4, S5}

4. { }  OR  ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

<u>QUESTION 1</u>

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

<u>ANSWER TO QUESTION 1</u>

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only <em>two possible answers</em> (also known as options) while questions 3, 4 and 5 have <em>four possible answers</em>/<em>options</em> to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

<u>QUESTION 2</u>

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

<u>ANSWER TO QUESTION 2</u>

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5}     Set 2: {S2, S3, S4}     Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

<u>QUESTION 3</u>

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

<u>ANSWER TO QUESTION 3</u>

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

<u>QUESTION 4</u>

Find the ' of Set 1 and explain the notation in this sentence.

<u>ANSWER TO QUESTION 4</u>

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { }  or  ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

3 0
3 years ago
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