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2 years ago

Find the slope of a line parallel to the given line. y=4/5x+5

Mathematics

1 answer:

xeze [42]2 years ago

3 0

Answer:

y = 4/5x

Step-by-step explanation:

Her ya go!

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...

Strike441 [17]

Answer:

The 13th term is 81x + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

$\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots$

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:

$\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}$

Find the common difference by subtracting the first term from the second:

$d = (4x+4) - (-3x - 1)$

Distribute:

$d = (4x + 4) + (3x + 1)$

Combine like terms. Hence:

$d = 7x + 5$

The common difference is (7x + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

$\displaystyle x_n = a + d(n-1)$

Where a is the initial term and d is the common difference.

The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:

$\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)$

To find the 13th term, let n = 13. Hence:

$\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)$

Simplify:

$\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}$

The 13th term is 81x + 59.

3 0

3 years ago

Rewrite the equation in standard form y - 3 = 4(x - 3)

kumpel [21]

Answer:

y=4x-9

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

4x^2-20=5 solve by using the square root property

riadik2000 [5.3K]

Step-by-step explanation:

4x^2 - 20 = 5

4x^2 -25 = 0

4x^2 = 25

2x = 5, or -5

x = 5/2 , or -5/2

7 0

3 years ago

Which of the following are equivalent to -7?

Scilla [17]

49/-7 and -21/3 are the only two equivalent to -7

3 0

3 years ago

A parking lot contains 100 cars , k of which happen to be lemons. we select m of these cars

Sunny_sXe [5.5K]

Given that a parking lot contains 100 cars, k of which happen to be lemons.

This is a conditional probability question.

Let event A be that a car is tested and event B be that a car is lemon.

The probability that a car is lemon is given by $\frac{k}{100}$

The probability that a car is tested is given by $\frac{m}{100}$

The probability that a car is lemon and it is tested is given by $\frac{n}{m}$

For a conditional probability, the probablility of event A given event B is given by:

$P(A|B)= \frac{P(A\cap B)}{P(B)}$

Therefore, the probability that a car is lemon, given that it is tested is given by.

$P(lemon|tested)= \frac{P(lemon\, and\, tested)}{P(tested)} \\ \\ = \frac{ \frac{n}{m} }{ \frac{m}{100} } = \frac{n}{m} \times \frac{100}{m} = \frac{100n}{m^2}$

4 0

3 years ago