powclaire

34 Questions
3 Answers

+1

432

1

+147

Piecewise-Defined Functions

For real numbers $x$, let
\[f(x) = \left\{
\begin{array}{cl}
x+2 &\text{ if }x>3, \\
2x+a &\text{ if }x\le 3.
\end{array} <#> \right.\]
What must the value of $a$ be to make the piecewise function read more ..

powclaire Feb 24, 2021

+1

476

2

+147

domain and range

If $f(x)$ is a function whose domain is $[-1,9]$, and $g(x)=f(x^2)$, then the domain of $g(x)$ is an interval of what width?

powclaire Feb 24, 2021

+2

815

1

+147

Given that the absolute value of the difference of the two roots of $ax^2 + 5x - 3 = 0$ is $\frac{\sqrt{61}}{3}$, and a is positive, what

Given that the absolute value of the difference of the two roots of $ax^2 + 5x - 3 = 0$ is $\frac{\sqrt{61}}{3}$, and a is positive, what is the value of a?

powclaire Feb 24, 2021

0

517

2

+147

Advanced System of Equations

The sum of three numbers a, b, and c is 99. If we increase a by 6, decrease b by 6 and multiply c by 5, the three resulting numbers are equal. What is the value of b?

powclaire Feb 24, 2021

+1

505

1

+147

Quadratic Formula/Discriminant

There are two ${\bf positive}$ integers $c$ for which the equation
$$5x^2+11x+c=0$$
has rational solutions. What is the product of those two values of $c$?

powclaire Feb 22, 2021

+1

418

1

+147

rationalizing denominators

Simplify $\frac{\sqrt{72}}{\sqrt{10}}$. Your answer should have an integer denominator.

powclaire Feb 22, 2021

+1

511

1

+147

Graphing Functions

If $f(x)=f(2-x)$ for all $x$, then what line is necessarily an axis of symmetry of the graph of $y=f(x)$? (Give the simplest equation of this line.)

powclaire Feb 22, 2021

+1

429

1

+147

graphing functions

Suppose the function $f(x)$ is defined on the domain $\{x_1,x_2,x_3\}$, so that the graph of $y=f(x)$ consists of just three points. Suppose those three points form a triangle of area $32$.
The graph of $y = 2f(2x)$ also read more ..

powclaire Feb 21, 2021

0

427

1

+147

Advanced System of Equations

Jerry is presently twice as old as his brother and six years older than his sister. How many years from now will Jerry's age be $\frac{2}{3}$ of the combined ages of his brother and sister at that time?

powclaire Feb 21, 2021

0

407

1

+147

Graphing Functions

Suppose the function $f(x)$ is defined on the domain $\{x_1,x_2,x_3\}$, so that the graph of $y=f(x)$ consists of just three points. Suppose those three points form a triangle of area $32$.
The graph of $y = 2f(2x)$ also read more ..

powclaire Feb 21, 2021

+1

430

1

+147

Complex Number Arithmetic

Karl was attempting to calculate economic figures. He found the following equation to be true:
\[fp-w=10000\]
If $f=5$ and $w=5+125i$, what is $p$?

powclaire Feb 21, 2021

+1

448

1

+147

Domain and Range

Find the greatest integer value of $b$ for which the expression $\frac{9x^3+4x^2+11x+7}{x^2+bx+8}$ has a domain of all real numbers.

powclaire Feb 21, 2021

+147

+1

First I simplified the equation. Then I used the quadratic formula and added the two solutions. I got 1/2 as the answer.

powclaireFeb 22, 2021

+147

0

-1/4

powclaireFeb 21, 2021

+147

+1

The y coordinates are 3 and 1.

3 - 1 = 2

1 - 3 = -2

2 is greater so the answer is 2.

powclaireFeb 15, 2021