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3 years ago

If two lines are parallel and they are defined by the equations, y=4x-5 and y=ax+2, what is the value of a?

Mathematics

1 answer:

tino4ka555 [31]3 years ago

6 0

Answer:

$a=\dfrac{4x-7}{x}$

Step-by-step explanation:

The equations of lines are :

y=4x-5 and y=ax+2

From above equations,

4x-5 = ax+2

4x-ax = 5+2

4x-7 = ax

$a=\dfrac{4x-7}{x}$

So, the value of a is equal to $\dfrac{4x-7}{x}$ .

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If X²⁰¹³ + 1/X²⁰¹³ = 2, then find the value of X²⁰²² + 1/X²⁰²² = ?

enyata [817]

Step-by-step explanation:

$\bf➤ \underline{Given-} \\$

$\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\$

$\bf➤ \underline{To\: find-} \\$

$\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\$

$\bf ➤\underline{Solution-} \\$

Let us assume that:

$\rm: \longmapsto u = {x}^{2013}$

Therefore, the equation becomes:

$\rm: \longmapsto u + \dfrac{1}{u} = 2$

$\rm: \longmapsto \dfrac{ {u}^{2} + 1}{u} = 2$

$\rm: \longmapsto{u}^{2} + 1 = 2u$

$\rm: \longmapsto{u}^{2} - 2u + 1 =0$

$\rm: \longmapsto {(u - 1)}^{2} =0$

$\rm: \longmapsto u = 1$

Now substitute the value of u. We get:

$\rm: \longmapsto {x}^{2013} = 1$

$\rm: \longmapsto x = 1$

Therefore:

$\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 1 + 1$

$\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 2$

★ Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab

6 0

2 years ago

Factor-

Nastasia [14]

Hello from MrBillDoesMath!

Answer:

See Discussion section below

Discussion:

2x^2 + 5x + 3 = (2x+3)(x+1) which is Choice 3

3x^2+10x+4 =-1/3 (-3 x + sqrt(13) - 5) (3 x + sqrt(13) + 5)

I don't think any of the provided choices are right!

8x^2+10x-3 = (2x+3)(4x-1) which is Choice 2

6x^2-7x-4 = -1/24 (-12 x + sqrt(145) + 7) (12 x + sqrt(145) - 7)

I don't think any of the provided choices are right!

2x^2+x-28 = (2x-7)(x+4) which is Choice 2

Thank you,

MrB

4 0

3 years ago

If luke’s is 5 years younger than 3 times Syndey’s age , s. in this situation what does 3s represent

Ilya [14]

It should represent Sydney's age, right? The equation would be 3s-5 I'm 99% sure lol

6 0

3 years ago

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The width of a rectangle is 7 inches less than its length. The area of the rectangle is 120 square inches. Solve for the dimensi

lukranit [14]

A) w + 7 = L
B) w * L = 120
A) w = L -7 then substituting this into B)
(L-7) * L = 120
L² -7L = 120
L² -7L -120 = 0
Solving by quadratic Formula:
L1 = 15
L2 = -8

If length = 15, then width = 8

4 0

3 years ago

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Solve

goblinko [34]

The answer should be B

8 0

2 years ago

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