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3 years ago

The lines below are perpendicular. If

Mathematics

1 answer:

RSB [31]3 years ago

5 0

Answer:

Correct answer: s₁ = - 2

Step-by-step explanation:

The relationship between the slope of two lines that are perpendicular is:

s₁ = - 1/s = - 1/(1/2) = - 2

God is with you!!!

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Solve the rational function of (check image) and check for extraneous solutions

Oxana [17]

Answer:

Option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

Step-by-step explanation:

Given the expression

$\frac{5}{x}=\frac{4x+1}{x^2}$

Solving the rational function

$\frac{5}{x}=\frac{4x+1}{x^2}$

Apply fraction across multiply: if $\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c$

$5x^2=x\left(4x+1\right)$

Subtract x(4x+1) from both sides

$5x^2-x\left(4x+1\right)=x\left(4x+1\right)-x\left(4x+1\right)$

Simplify

$5x^2-x\left(4x+1\right)=0$

5x² - 4x² - x = 0

x² - x = 0

Factor x² - x = x(x-1)

x(x-1) = 0

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$x=0\quad \mathrm{or}\quad \:x-1=0$

Thus, the solution to the equation is:

$x=0,\:x=1$

But, it is clear that if we substitute x = 0, the equation becomes undefined because we can not have the denominator to be 0.

In other words, the equation is undefined for x = 0

Thus, x = 0 is an extraneous solutions.

Therefore, option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

5 0

3 years ago

Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (−1, 0).

Hitman42 [59]

<span>The two points that are most distant from (-1,0) are exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3) approximately (0.3333333, 1.885618) and (0.3333333, -1.885618) Rewriting to express Y as a function of X, we get 4x^2 + y^2 = 4 y^2 = 4 - 4x^2 y = +/- sqrt(4 - 4x^2) So that indicates that the range of values for X is -1 to 1. Also the range of values for Y is from -2 to 2. Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis. So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So y = sqrt(4-4x^2) distance is sqrt((x + 1)^2 + sqrt(4-4x^2)^2) =sqrt(x^2 + 2x + 1 + 4 - 4x^2) =sqrt(-3x^2 + 2x + 5) And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving -3x^2 + 2x + 5 Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative. d = -3x^2 + 2x + 5 d' = -6x + 2 And set d' to 0 and solve for x, so 0 = -6x + 2 -2 = -6x 1/3 = x So the furthest point will be where X = 1/3. Calculate those points using (1) above. y = +/- sqrt(4 - 4x^2) y = +/- sqrt(4 - 4(1/3)^2) y = +/- sqrt(4 - 4(1/9)) y = +/- sqrt(4 - 4/9) y = +/- sqrt(3 5/9) y = +/- sqrt(32)/sqrt(9) y = +/- 4sqrt(2)/3 y is approximately +/- 1.885618</span>

7 0

3 years ago

How many atoms are in 0.44 mol of zinc metal

Flauer [41]

Multiply the number of atoms in 1 mole by .44 so...2.7x10^23 atoms

6 0

3 years ago

Dexter plans and records his spending. In the coordinate

Marrrta [24]

Answer:

<h2><u><em>mark me as brilliant ~_~</em></u></h2>

Step-by-step explanation:

5 0

3 years ago

Find all of the zeros of each function <br>x^3+9x^2+6x-16

dedylja [7]

Answer:

x = -8, -2, and 1

Step-by-step explanation:

The zeros of a function are another name for its x-intercepts. To find them, graph the function and examine its behavior near the x-axis. In the attached picture you can see that this function has the zeros, x = -8, -2, and 1.

6 0

3 years ago