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ValentinkaMS [17]
2 years ago
8

E. Find the slope of the line that passes through the points (1, 3) and (9,7),

Mathematics
2 answers:
Zolol [24]2 years ago
8 0

Answer:

0.5

Step-by-step explanation:

→ Find the difference in y

7 - 3 = 4

→ Find the difference in x

9 - 1 = 8

→ Divide the results

4 ÷ 8 = 0.5

leva [86]2 years ago
6 0

Answer:

The slope is 1/2 (m=1/2)

Step-by-step explanation:

Use the slope formula: \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  } to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. \frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}

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Q1W7 Learning Task 1 (Introduction)
Tatiana [17]

Answer:

Column A                                            Column B

1. x² + 6x + 8                                        x-3,x+2

2. x³ - 7x + 6                                       x+1, x+2, x+3

3. x³ - 2x² - 5x + 6                              x-1, x+2, x-3

Step-by-step explanation:

Column A                                            Column B

1. x² + 6x + 8                                        x-3,x+2

2. x³ - 7x + 6                                       x+1, x+2, x+3

3. x³ - 2x² - 5x + 6                              x-1, x+2, x-3

Using Factor theorem we put values of x = ±1,±2,±3 in each of the polynomials unless we get a zero.

1. x² + 6x + 8      

= 1+6(1) +8= 15

1. x² + 6x + 8

  4+ 12+8 = 24

1. x² + 6x + 8

 (-1)² + 6(-1)+ 8

= 1-6+8= 3

1. x² + 6x + 8

 (-2)² + 6(-2)+ 8

= 4-12+8= 0

1. x² + 6x + 8

(3)²+ 6(3) +8

= 9+18+8 ≠ 0

1. x² + 6x + 8

(-3)²+ 6(-3) +8

= 9-18+8 =-1

For this polynomial we have x+2= 0 or x=-2, x-3= 0 , x=3

2. x³ - 7x + 6

1-7+6= 0

2. x³ - 7x + 6

(-1)³-7(-1) +6

= 13-1≠0

2. x³ - 7x + 6

(2)³-7(2) +6

= 8-14+6= 0

2. x³ - 7x + 6

(-2)³-7(-2) +6

= -8 +14+6

2. x³ - 7x + 6

(-3)³-7(-3) +6

= -27+21+6 = 0

For this polynomial we have x+1= 0 , x+2 = 0  and x+3= 0, or x=-1,-2,-3

3. x³ - 2x² - 5x + 6

(1)³-2(1)²-5(1)+6

= 0

3. x³ - 2x² - 5x + 6

(-1)³-2(-1)²-5(-1)+6

= -1 -2 +5+6

=8

3. x³ - 2x² - 5x + 6

(2)³-2(2)²-5(2)+6

= 8-8-10+6

=-4

3. x³ - 2x² - 5x + 6

(-2)³-2(-2)²-5(-2)+6

= -8-8+10+6

=0

3. x³ - 2x² - 5x + 6

(3)³-2(3)²-5(3)+6

= 27-18-15+6

=0

3. x³ - 2x² - 5x + 6

(-3)³-2(-3)²-5(-3)+6

= -27-18+15+6

=-14

For this polynomial we have x-1= 0 ,x+2=0, x-3= 0or x=1,-2,3

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
How do I solve for the solution??<br>y = 3x +2<br>y = x + 1​
Elis [28]

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−1/2,1/2)

Equation Form:

x=−1/2,y=1/2

Step-by-step explanation:

7 0
3 years ago
How do Solve these equations
arsen [322]

I can’t do these right off hand but look them up on google and google will tell you exactly how to do and if you type in the problem it will explain how to the the problem as well , I hope you understand and this helped you.

4 0
3 years ago
Which statement about the scenario represented in the table is true? Assume time is the independent variable
Verizon [17]

Answer:B

Step-by-step explanation:

5 0
3 years ago
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