Member: wizzymath

76 Questions
9 Answers

479

+230

help me pls - clever algebraic manipulations

If $3a + b + c = -3, a+3b+c = 9, a+b+3c = 19$, then find $abc$.

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wizzymath Mar 19, 2021

528

+230

Hey besties, help pls

If $3a + b + c = -3, a+3b+c = 9, a+b+3c = 19$ then find $abc$.

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wizzymath Mar 16, 2021

526

+230

hey besties I could use some help

The vertices of a triangle are the points of intersection of the line $y = -x-1$, the line $x=2$, and $y = \frac{1}{5}x+\frac{13}{5}$. Find an equation of the circle passing through all three vertices.
read more ..

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wizzymath Mar 16, 2021

660

+230

help with analytic geometry

Let $A = (0, 0),$ $B = (1, 2),$ $C=(3, 3),$ and $D = (4, 0).$ Quadrilateral $ABCD$ is cut into two pieces with the same area by a line passing through $A$. What are the coordinates of the point where this line intersects $\overline{CD}$? read more ..

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wizzymath Mar 10, 2021

456

+230

Help with algebraic manipulations

Given
\begin{align*}
px+qy+rz&=1,\\
p+qx+ry&=z,\\
pz+q+rx&=y,\\
py+qz+r&=x,\\ <#> p+q+r&=-3, <#> \end{align*}
find $x+y+z$.

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wizzymath Mar 10, 2021

504

+230

hey besties i need help

Let
\[f(x) =
\begin{cases}
k(x) &\text{if }x>2, \\
2+(x-2)^2&\text{if }x\leq2.
\end{cases} <#> \]
Find the function $k(x)$ such that $f$ is its own inverse.

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wizzymath Mar 10, 2021

527

+230

Hey besties help me pls

Let $f$ be defined by
\[f(x) = \left\{
\begin{array}{cl}
2-x & \text{ if } x \leq 1, \\
2x-x^2 & \text{ if } x>1.
\end{array} <#> \right.\]
Calculate $f^{-1}(-3)+f^{-1}(0)+f^{-1}(3)$.

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wizzymath Mar 10, 2021

1033

+230

hey besties could use some help here thx ;)

Two angles of a triangle measure 30 and 45 degrees. If the side of the triangle opposite the 30-degree angle measures $6\sqrt2$ units, what is the sum of the lengths of the two remaining sides? Express your answer as a decimal to the nearest tenth. read more ..

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wizzymath Mar 9, 2021

608

+230

Piecewise-defined functions

Let
\[f(x) =
\begin{cases}
|\lfloor{x}\rfloor| &\text{if }x\text{ is rational}, \\
\lceil{x}\rceil^2 &\text{if }x\text{ is irrational}.
\end{cases} <#> \]
Find $f(\sqrt[3]{-8})+f(-\pi)+f(\sqrt{50})+f\left(\frac{9}{2}\right)$ read more ..

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wizzymath Mar 9, 2021

567

+230

Help pls

On an old-fashioned bicycle, the front wheel has a radius of $2.5$ feet and the back wheel has a radius of $4$ inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes $100$ revolutions?

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wizzymath Mar 8, 2021

463

+230

Help pls

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wizzymath Mar 8, 2021

533

+230

Help pls

Each of $\triangle PQR$ and $\triangle STU$ has an area of $1$. In $\triangle PQR,$ $U,$ $W,$ and $V,$ are the midpoints of the sides. What is the area of parallelogram $UVRW?$
read more ..

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wizzymath Mar 8, 2021

434

+230

help pls

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 continuous (which read more ..

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wizzymath Mar 6, 2021

416

+230

hey hey help pls

Given that $m \angle A= 60^\circ$, $BC=12$ units, $\overline{BD} \perp \overline{AC}$ and $m \angle DBC = 3m \angle ECB$, the length of segment $EC$ can be expressed in the form $a(\sqrt{b}+\sqrt{c})$ units where $b$ and $c$ have no perfect-square read more ..

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wizzymath Mar 6, 2021

501

+230

help me pls

If an arc of $45^{\circ}$ on circle $A$ has the same length as an arc of $30^{\circ}$ on circle $B$, then what is the ratio of the area of circle $A$ to the area of circle $B$? Express your answer as a common fraction.

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wizzymath Mar 6, 2021

486

+230

help pls

Let $g(x)$ e a function piecewise defined as
\[g(x) = \left\{
\begin{array}{cl}
-x & x\le 0, \\
2x-41 & x>0.
\end{array} <#> \right.\]
If $a$ is negative, find $a$ so that $g(g(g(10.5)))=g(g(g(a)))$. read more ..

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wizzymath Mar 5, 2021

+230

I don't think that is right because that circle looks like this and it doesn't go through the vertices of the triangle.

wizzymathMar 17, 2021

+230

Wow. Good job!

wizzymathMar 10, 2021

+230

Really close it was (25/8, 15/8) but thanks for the help :)

wizzymathMar 10, 2021

+230

Ummmmm never mind you were right thanks

wizzymathMar 6, 2021

+230

That's wrong because g(g(g(10.5))) equal -1 so g(g(g(a))) also neede to equal -1 but g(g(g(30.5))) equals 1 not -1. But thanks

wizzymathMar 6, 2021

+230

thats wrong but thanks

wizzymathMar 5, 2021

+230

Nevermind guys, I did it. The answer is 0.

wizzymathFeb 22, 2021

+230

Oops sorry, the fourth term is 8!

wizzymathFeb 20, 2021

Username	wizzymath
Score	230
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Questions	76
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