Which side is adjacent to

15 Points! Find the range of the functions: f(x) = (x + 1)^2 - 1 f(x) = 7x - 11

MakcuM [25]

In both cases you may well benefit from graphing the functions.

Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).

Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.

Thus the range includes all real numbers: (-infinity, infinity).

4 0

3 years ago

I might not respond for a little while, please don’t end the session! Need help on #3 and 4

slavikrds [6]

We have a right triangle with a 15m hypotenuse and a 8m leg. If we use x for the missing leg then the Pythagorean Theorem states that:

$15^2=8^2+x^2$

Then we have to solve that equation for x:

$\begin{gathered} x^2=15^2-8^2=225-64 \\ x^2=161 \\ x=\sqrt[]{161} \end{gathered}$

So the answer is the square root of 161.

3 0

1 year ago

Reuben bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $150 more than the desktop. He p

cupoosta [38]

Same case as Pablo's, more or less.

a = price for the desktop

b = price for the laptop

we know the laptop is 150 bucks more than the desktop, b = a + 150.

how much is 7% of a? (7/100) * a, 0.07a.

how much is 9.5% of b? (9.5/100) * b, 0.095b.

total interests for the financing add up to 303, 0.07a + 0.095b = 303.

$\bf \begin{cases}
\boxed{b}=a+150\\
0.07a+0.095b=303\\
----------\\
0.07a+0.095\left(\boxed{a+150} \right)=303
\end{cases}
\\\\\\
0.07a+0.095a+14.25=303\implies 0.165a=288.75
\\\\\\
a=\cfrac{288.75}{0.165}\implies a=1750$

how much was it for the laptop? well b = a + 150.

8 0

3 years ago

Which graph shows the solution to this system of inequalities? y>-1/3x+1 y>2x-3

Mademuasel [1]

Given:

The system of inequalities is:

$y>-\dfrac{1}{3}x+1$