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victus00 [196]
2 years ago
10

If x+2y=3 and xy=2 show that x³+8y³+9=0​

Mathematics
1 answer:
kicyunya [14]2 years ago
4 0

Step-by-step explanation:

<u>Given</u>

  • x + 2y = 3 and xy = 2
  • show that x³ + 8y³ + 9 = 0​

<u>Solution in steps:</u>

  • (x + 2y)³ = 3³
  • x³ + 3x²(2y) + 3x(2y)² + (2y)³ = 27
  • x³ + 6x(xy) + 12y(xy) + 8y³ = 27
  • x³ + 8y³ + 6(x + 2y)xy = 27                    ⇒  Substitute values
  • x³ + 8y³ + 6*3*2 = 27
  • x³ + 8y³  + 36 - 27 = 0
  • x³ + 8y³  + 9 = 0

Done

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4. What is the y-intercept of the line
vagabundo [1.1K]

Answer:

A) (0,0)

Step-by-step explanation:

Plug in 0 for x to solve for y. y=4(0).

4(0)=0, so y=0.

8 0
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Answer:

The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

  • y+2=\frac{3}{4}\left(x+4\right)
  • 3x - 4y = -4

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the line

3x - 4y = 7

writing in the slope-intercept form

4y = 3x - 7

dividing both sides by 4

4y/4 = 3/4x - 7/4

y = 3/4x - 7/4

Now, comparing with the slope-intercept form of the line equation

y = 3/4x - 7/4

The slope of the line m = 3/4

We know that parallel lines have the same slopes.

Therefore, the slope of the parallel line is: 3/4

now we have,

The point (-4, -2)

The slope m of parallel line = 3/4

Given the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting (-4, -2) and m = 3/4 in the point-slope form of line equation

\:y-\left(-2\right)=\frac{3}{4}\left(x-\left(-4\right)\right)

y+2=\frac{3}{4}\left(x+4\right)

Thus, the equation in the point-slope form of the line equation is:

y+2=\frac{3}{4}\left(x+4\right)

Simplifying the equation

y+2=\frac{3}{4}\left(x+4\right)

Subtract 3 from both sides

y+2-2=\frac{3}{4}\left(x+4\right)-2

y=\frac{3}{4}x+1

Multiplying the equation by 4

4y = 3x + 4

3x - 4y = -4

Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

  • y+2=\frac{3}{4}\left(x+4\right)
  • 3x - 4y = -4
7 0
2 years ago
What is the pre-image of vertex A' if the image shown on
lisov135 [29]

Answer: B. (-6, 8).

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
R varies directly as S and inversely as T. if R = 8 when S = 4 and T = 3, then R is equal to ​
Alex

Answer:

R = 6S/T

Step-by-step explanation:

R ∝ S/ T

》R = kS/ T

》k = RT/ S

If R = 8 when S = 4 and T = 3

then, k = (8 × 3)/ 4

k = 6

∴ R = (6 × S)/ T

5 0
3 years ago
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