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3 years ago

Which function has the same y-intercept as the line graphed below?

Mathematics

1 answer:

KatRina [158]3 years ago

8 0

Answer:

D. y + 4 = 2x

Step-by-step explanation:

The graph has a y-intercept at (0, -4).

A. y=16 - 3x/4

if x = 0, y = 16. FALSE.

B. 24 + 3y = 6x

If x = 0, 24 + 3y = 0

3y = -24

y = -8. FALSE.

C. 4y + x = 16

If x = 0, 4y = 16

y = 4. FALSE.

D. y + 4 = 2x

If x = 0, y + 4 = 0

y = -4. TRUE.

y = 4 + 2x has the same y-intercept as the graphed line.

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Which expressions are equivalent to 3(x + 3y + 2x − y)?

Irina-Kira [14]

3(x + 3y + 2x − y) = 3(3x + 2y)
= 9x + 6y
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8 0

3 years ago

Read 2 more answers

If x = (√2 + 1)^-1/3 then the value of x^3 + 1/x^3 is

Shtirlitz [24]

Step-by-step explanation:

Given: x = {√(2) + 1}^(-1/3)

Asked: x³+(1/x³) = ?

Solution:

We have, x = {√(2) + 1}^(-1/3)

⇛x = [1/{√(2) + 1}^(1/3)]

[since, (a⁻ⁿ = 1/aⁿ)]

Cubing on both sides, then

⇛(x)³ = [1{/√(2) + 1}^(1/3)]³

⇛(x)³ = [(1)³/{√(2) + 1}^(1/3 *3)]

⇛(x)³ = [(1)³/{√(2) + 1}^(1*3/3)]

⇛(x)³ = [(1)³/{√(2) + 1}^(3/3)]

⇛(x * x * x) = [(1*1*1)/{√(2) + 1)^1]

⇛x³ = [1/{√(2) + 1}]

Here, we see that on RHS, the denominator is √(2)+1. We know that the rationalising factor of √(a)+b = √(a)-b. Therefore, the rationalising factor of √(2)+1 = √(2) - 1. On rationalising the denominator them

⇛x³ = [1/{√(2) + 1}] * [{√(2) - 1}/{√(2) - 1}]

⇛x³ = [1{√(2) + 1}/{√(2) + 1}{√(2) - 1}]

Multiply the numerator with number outside of the bracket with numbers on the bracket.

⇛x³ = [{√(2) + 1}/{√(2) + 1}{√(2) - 1}]

Now, Comparing the denominator on RHS with (a+b)(a-b), we get

a = √2
b = 1

Using identity (a+b)(a-b) = a² - b², we get

⇛x³ = [{√(2) - 1}/{√(2)² - (1)²}]

⇛x³ = [{√(2) - 1}/{√(2*2) - (1*1)}]

⇛x³ = [{√(2) - 1}/(2-1)]

⇛x³ = [{√(2) - 1}/1]

Therefore, x³ = √(2) - 1 → → →Eqn(1)

Now, 1/x³ = [1/{√(2) - 1]

⇛1/x³ = [1/{√(2) - 1] * [{√(2) + 1}/{√(2) + 1}]

⇛1/x³ = [1{√(2) + 1}/{√(2) - 1}{√(2) + 1}]

⇛1/x³ = {√(2) + 1}/[{√(2) - 1}{√(2) + 1}]

⇛1/x³ = [{√(2) + 1}/{√(2)² - (1)²}]

⇛1/x³ = [{√(2) + 1}/{√(2*2) - (1*1)}]

⇛1/x³ = [{√(2) + 1}/(2-1)]

⇛1/x³ = [{√(2) + 1}/1]

Therefore, 1/x³ = √(2) + 1 → → →Eqn(2)

On adding equation (1) and equation (2), we get

x³ + (1/x³) = √(2) -1 + √(2) + 1

Cancel out -1 and 1 on RHS.

⇛x³ + (1/x³) = √(2) + √(2)

⇛x³ + (1/x³) = 2

Therefore, x³ + (1/x³) = 2

Answer: Hence, the required value of x³ + (1/x³) is 2.

Please let me know if you have any other questions.

3 0

3 years ago

NEED HELP WITH THESE QUESTIONS

amm1812

For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

$\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =$

Applying double C we have:

$\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =$

By definition of multiplication of powers of the same base we have to place the same base and add the exponents: $\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =$