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3 years ago

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The equation of a line is y = 3. write an equation in slope-intercept form of a line parallel to y = 3 that passes through (0,6)

. user: write the equation of the line that passes through the point (-6,2) and is parallel to the line whose equation is x=-10

1 answer:

egoroff_w [7]3 years ago

7 0

So first make it y-6=3(x-0) and distribute to make y-6=3X+0 than add the 6 to make Y=3x+6 do you see how I did that

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, <em>f</em> and <em>g</em> are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let <em>j</em> be the inverse function of <em>h</em>.

Function <em>h</em> is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for <em>y. </em>Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

2 years ago

Which is a perfect square?

velikii [3]

Answer:

6 squared

Step-by-step explanation:

The square root of a perfect square is a rational number.

4 0

3 years ago

Find the minimum and maximum values of the objective function z=3x+5y

Margarita [4]

3.15 addd all of them! Then divide

6 0

3 years ago

Read 2 more answers

the mean height was 69.9 inches with a standard deviation of 3.0 inches. Assume the height data is normally distributed. Zak’s h

sammy [17]

Answer:

snsnbsjskksnsnanammanz xnzkmz

5 0

2 years ago

Please help the questions are in the picture above

svp [43]

Not sure if I'm right but I think it's 3(x - 6) (x^2 + 5x)

Step-by-step explanation:

3x^3 - 3x^2 - 90x

Apply GCF: 3 (x^3 - x^2 - 30)

Split 30 into -6 and 5

(x^3 - 6x^2) (5x^2 - 30x)

GCF of both: x^2 (x - 6) and 5x (x - 6)

DON'T FORGET TO CARRY THE 3

And your answer is 3 (x - 6) (x^2 + 5x)

5 0

3 years ago