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3 years ago

Write a linear function in slope intercept form given the slope of the equation is -4 and the y intercept is 6.

Mathematics

1 answer:

hoa [83]3 years ago

4 0

Answer:

6=-4x+b

Step-by-step explanation:

You plug in the numbers but the formula that you use is y=mx+b with x being the number you don't know

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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, f and g are inverses, then:

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

So, we can let j be the inverse function of h.

Function h is given by:

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

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

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

Therefore, a = 1/3 and b = 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

3 years ago

Pls help me out and pls explain

LenKa [72]

Answer:

It is a function

Step-by-step explanation:

The x has only one y and that makes it a function

5 0

3 years ago

A river drops 12 ft vertically over a horizontal distance of 1500 ft.

elixir [45]

Answer:

Slope = rise / run

= -12 / 1500 (It's -12 and not 12 because a drop means it's decreasing)

= -0.008

4 0

3 years ago

a sleeping bag weighs 8 pounds. your backpack and sleeping bag together weigh 31 pounds. write an equation to determine whether

Luda [366]

31-8=23 pounds for the backpack.

8 0

3 years ago

(3x-8)(x+8) multiply

ohaa [14]

FOIL this out. 3x*x = 3x^2; 3x*8= 24x; -8*x = -8x; -8*8=-64. Combine like terms to get

7 0

3 years ago