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2 years ago

In the graph shown below, if lines land 12 are parallel, then the slope of line 12 is

Mathematics

1 answer:

Yanka [14]2 years ago

4 0

9514 1404 393

Answer:

Step-by-step explanation:

The slope of L1 is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (5 -1)/(-2 -(-3)) = 4/1 = 4

The slope of L2 is the same as the slope of L1. The slope is 4.

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What is the quotient in simplified form? State any restrictions on the variable? \frac{x^2-16}{x^2+5x+6} /\frac{x^2+5x+4}{x^2-2x

lora16 [44]

$\frac{x^2-16}{x^2+5x+6} / \frac{x^2+5x+4}{x^2-2x-8}$

We can begin by rearranging this into multiplication:

$\frac{x^2-16}{x^2+5x+6} * \frac{x^2-2x-8}{x^2+5x+4}$

Now we can factor the numerators and denominators:

$\frac{(x+4)(x-4)}{(x+3)(x+2)} * \frac{(x-4)(x+2)}{(x+4)(x+1)}$

The factors (x+4) and (x+2) cancel out, leaving us with:

$\frac{(x-4)}{(x+3)} * \frac{(x-4)}{(x+1)}$

Our answer comes out to be:

$\frac{(x-4)^{2} }{(x+3)(x+1)}$ or $\frac{ x^{2} -8x+16}{ x^{2}+4x+3 }$

Based on the numerator of the second fraction (since we used its inverse), the denominators of both, and the factors we canceled out earlier, the restrictions are x ≠ -4, -3, -2, -1, 4

4 0

2 years ago

Question 8 Find the unit vector in the direction of (2,-3). Write your answer in component form. Do not approximate any numbers

slamgirl [31]

Answer:

The unit vector in component form is $\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$ or $\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j$ .

Step-by-step explanation:

Let be $\vec u = (2,-3)$ , its unit vector is determined by following expression:

$\hat {u} = \frac{\vec u}{\|\vec u \|}$

Where $\|\vec u \|$ is the norm of $\vec u$ , which is found by Pythagorean Theorem:

$\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}$

$\|\vec u\| = \sqrt{13}$

Then, the unit vector is:

$\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)$

$\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$

The unit vector in component form is $\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$ or $\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j$ .

6 0

2 years ago

Plz help....................

BaLLatris [955]

The answer is 22.3 i hope that helped

3 0

3 years ago

As Venus revolves around the sun, it travels at a rate of approximately 22 miles per second. Convert this rate to kilometers per

Leona [35]

1 mile = 1.6 kms
22 miles / sec = 22*1.6 = 35.2 km / sec

Number of kms that Venus travel in 2 seconds = 70.4

4 0

2 years ago