Two lines are perpendicular, and neither line is horizontal. Which of the following is not necessarily true of the lines?A.
The slopes of the two lines are opposite reciprocals.
B.
One line must have a positive slope.
C.
The y-intercepts are the same.
D.
One line must have a negative slope.

Answers

Answer 1

Answer: I think the correct answer from the choices listed above is option C. Two lines are perpendicular, and neither line is horizontal so it must be that the slopes of the lines are opposite reciprocals, one slope is positive and the other has a negative slope. Having different slopes so they should intersect the y-axis at different values.

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Solve the inequality 0 > –3x – 2x. A. x > –36
B. x > 1
C. x > 0
D. x > –28

Answers

Answer:

Option C is correct.

Step-by-step explanation:

Given Inequality,

0 > -3x - 2x

To Find: Solution of the inequality.

Consider,

0 > -3x - 2x

Group like terms in RHS

0 > ( -3 - 2 )x

0 > -5x

transpose RHS to LHS and LHS to RHS

-5x < 0

Divide both sides by -5

we know that in inequality multiplying and dividing negative number sign of inequality changes.

So,

x > 0/(-5)

x > 0

Therefore, Option C is correct.

0 > -3x - 2x...combine like terms
0 > - 5x ....divide both sides by -5
0/-5 < x
0 < x or x > 0

The product of (3+2i)and a complex number is (17+7i). The complex number is?

Answers

Hi there! Let x be the complex number. (3+2i)(x)=(17+7i), (x)=(17+7i)/(3+2i)=(17+7i)/(3+2i)*(3-2i)/(3-2i), (17+7i)*(3-2i)/(9+4), (51-34i+21i+14)/13), (65-13i)/13, 13(5-i)/13=(5-i). Therefore, the complex number is (5-i).

2x^2 + 108 = 42x NEED HELP SOLVING QUADRATIC EQUATION

Answers

Answer:

x = 18

x = 3

Step-by-step explanation:

2x² - 42x + 108 = 0

common factor is two, so take it out to simplify equation

2 (x² - 21x + 54) = 0

0/2 = 0

x² - 21x + 54 = 0

Factors of 54 which add up to 21 is 18 and 3

(x - 18)(x - 3) = 0

Hence,

x = 18

x = 3

Consider the sequence 51, 43, 35, 37, 19 which function describes the sequence.

Answers

The function f(n) = 8n - 5 + (-1)ⁿ × 3 indeed generates the given sequence 51, 43, 35, 37, 19.

The given sequence is 51, 43, 35, 37, 19. To identify the underlying function describing this sequence, let's analyze the pattern between the terms.

Subtraction: If we look at the differences between consecutive terms, we get the following sequence of differences: -8, -8, 2, -18.

Alternating Behavior: The differences between terms seem to alternate between subtracting 8 and adding 2.

Possible Linear Function: The alternating behavior suggests that this sequence might be generated by a linear function with some sort of periodic or alternating component.

Linear Function with Alternating Component: A possible function to describe this sequence could be:

f(n) = 8n - 5 + (-1)ⁿ × 3

Here, n represents the position in the sequence (starting from n = 1), and (-1)ⁿ introduces the alternating component. When n is even, (-1)ⁿ becomes 1, and when n is odd, (-1)ⁿ becomes -1.

Now, let's test this function with the given values:

- For n = 1: f(1) = 8(1) - 5 + (-1)¹ × 3 = 8 - 5 + (-1) × 3 = 3 - 3 = 0

- For n = 2: f(2) = 8(2) - 5 + (-1)² × 3 = 16 - 5 + 1 × 3 = 11 + 3 = 14

- For n = 3: f(3) = 8(3) - 5 + (-1)³ × 3 = 24 - 5 - 3 = 19 - 3 = 16

- For n = 4: f(4) = 8(4) - 5 + (-1)⁴ × 3 = 32 - 5 + 3 = 27 + 3 = 30

- For n = 5: f(5) = 8(5) - 5 + (-1)⁵ × 3 = 40 - 5 - 3 = 35 - 3 = 32

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