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3 years ago

Which equation models the linear relationship between the variables shown in the table?

Mathematics

1 answer:

Luda [366]3 years ago

4 0

Answer:

H) y = 2x -3

Step-by-step explanation:

Given the data on the table for the values of 'x' and 'y', you can find the slope by taking two points and subtracting the difference in 'y' values from the difference in 'x' values:

( $(x_{1},y_{1})and(x_{2},y_{2})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Using points (6, 9) and (2, 1): $\frac{9-1}{6-2}=\frac{8}{4}=2$

Given the slope (m)=2, you can use slope-intercept form to solve for 'b':

y = mx + b

y = 2x + b, use point (2, 1) for 'x' and 'y': 1 = 2(2) + b or 1 = 4 + b so b = -3

Put the values of m = 2 and b = -3 into your slope-intercept form:

y = 2x -3 (answer H)

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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.

QUESTION 1

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?

ANSWER TO QUESTION 1

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 two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options 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.

QUESTION 2

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

ANSWER TO QUESTION 2

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

QUESTION 3

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

ANSWER TO QUESTION 3

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.

QUESTION 4

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

ANSWER TO QUESTION 4

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

what is the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).

ioda

Answer:

The equation of the line would be y + 4 = -1/8(x + 6)

Step-by-step explanation:

To find the point-slope form of the line, start by finding the slope. You can do this using the slope formula below along with the two points.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-4 - -5)/(-6 - 2)

m = 1/-8

m = -1/8

Now that we have the slope, we can use that along with one of the points in the base form of point-slope.

y - y1 = m(x - x1)

y + 4 = -1/8(x + 6)

7 0

3 years ago

Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?

mezya [45]

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

<h3>What is a matrix?</h3>

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
For instance, consider a matrix with two rows and three columns.

To find the order of matrix:

We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.
Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.
Dimension is assigned to the provided matrix: 6 × 5
This means the given matrix contains six rows and five columns.
As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.
The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.

To prove:

In other words, the inner products of the dimensions should be equal.
That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.
The dimensions of the matrix are given by, row × column.

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

Know more about matrix here:

brainly.com/question/24079385

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7 0

2 years ago

Brandon is landscaping his backyard. He bought 2 7\8tons of decorative rock and 1 2\5 tons of boulders. How many total tons of r

Doss [256]

Answer:

4 11/40 hope this helps :)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Form a paragraph proof for the following. Make sure you include all the

timama [110]

Answer:

Line BD is Congruent to Line BD due to the Reflexive property. Angle Bad is congruent to angle BCD because of the third angle theorem therefore triangle ABD is congruent to triangle CBD because all angles and sides are congruent

I don't know if that will satisfy your teacher because some prefer different things but that leaves no ground to be inferred and explains everything word for word.

8 0

3 years ago