All Questions ⁺⁰237795 Questions

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448

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+206

Quadratic Formula/Discriminant

If the roots of the quadratic equation $\frac12x^2+99x+c=0$ are $x=-99+\sqrt{8001}$ and $x=-99-\sqrt{8001}$, then what is the value of $c$?

oliviapow06 Feb 21, 2021

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458

1

+1662

floor function

Evaluate $$\lfloor\sqrt{1}\rfloor + \lfloor\sqrt{2}\rfloor + \lfloor\sqrt{3}\rfloor + \dots + \lfloor\sqrt{29}\rfloor$$

wiseowl Feb 21, 2021

+1

702

1

+502

Domain and Range

Find the largest value of $c$ such that $1$ is in the range of $f(x)=x^2-5x+c$.

ellapow Feb 21, 2021

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369

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+1662

domain

What is the domain of the real-valued function $f(x)=\dfrac{2x-7}{\sqrt{x^2-5x+4}}$?

wiseowl Feb 21, 2021

-1

452

1

+206

Rationalizing Denominators

Simplify the following expression to a simplified fraction:
$$\sqrt{\dfrac{\dfrac{5}{\sqrt{80}}+\dfrac{\sqrt{845}}{9}+\sqrt{45}}{\sqrt5}}.$$

oliviapow06 Feb 21, 2021

+1

474

1

+502

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?

ellapow Feb 21, 2021

+1

488

1

+148

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

450

1

+206

Domain and Range

Find the domain of the real-valued function
\[f(x)=\sqrt{-6x^2+11x-4}.\]
Give the endpoints in your answer as common fractions (not mixed numbers or decimals).

oliviapow06 Feb 21, 2021

-1

465

1

+206

Complex Number Arithmetic

Evaluate $i^6+i^{16}+i^{-26}$.

oliviapow06 Feb 21, 2021

+1

470

1

+502

Domain and Range

What is the domain of the real-valued function $f(x)=\frac{2x-7}{\sqrt{x^2-5x+6}}$?

ellapow Feb 21, 2021

+1

522

1

+502

Complex Number Arithmetic

Machiavelli added together $1+3i$ and $2-4i$. What number did he get?

ellapow Feb 21, 2021

+1

508

1

+148

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

-1

493

1

+206

Domain and Range

Lana defines a function $f(x)$ which is given by the formula
$$f(x) = x^2,$$
but only on a domain, she has specified which consists of finitely many values $x$; she leaves the function undefined for all other $x$.
Given read more ..

oliviapow06 Feb 21, 2021

+1

653

1

+502

Complex Number Arithmetic

William Sydney Porter tried to perform the calculation $\frac{-3+4i}{1+2i}$. However, he accidentally missed the minus sign, finding $\frac{3+4i}{1+2i}=\frac{11}{5}-\frac{2}{5}i$.
What answer should he have obtained?
<read more ..

ellapow Feb 21, 2021

+1

430

1

+148

Domain and Range

What is the range of the function $f(x) = \frac{1}{x^2}$?

powclaire Feb 21, 2021

0

496

1

+206

Complex Number Arithmetic

There are 3 complex numbers $a+bi$, $c+di$, and $e+fi$. If $b=3$, $e=-a-c$, and the sum of the numbers is $2i$, find $d+f$.

oliviapow06 Feb 21, 2021

+1

538

1

+502

Complex Number Arithmetic

If $Q = 11-5i$, $E = 11+5i$, and $D = 2i$, find $Q\cdot E \cdot D$.

ellapow Feb 21, 2021

+1

456

1

+148

Complex Number Arithmetic

Find the domain of the function $f(x)=\sqrt{\sqrt{x^2-16}-3}$.

powclaire Feb 21, 2021

-1

497

1

+206

Domain and Range

Find the domain of the function $f(x)=\sqrt{\sqrt{x^2-16}-3}$.

oliviapow06 Feb 21, 2021

+1

424

1

+502

Complex Number Arithmetic

Express $(4-5i)(-5+5i)$ in the form $a+bi$, where $a$ and $b$ are integers and $i^2 = -1.$

ellapow Feb 21, 2021

+1

440

1

+148

Domain and Range

Find the domain of the real-valued function
$$f(x)=\sqrt{-10x^2-11x+6}.$$
Give the endpoints in your answer as common fractions, not mixed numbers or decimals.

powclaire Feb 21, 2021

0

427

1

+206

Complex Number Arithmetic

If $z=3+4i$, find $z^2$. (Note that $i^2 = -1.$)

oliviapow06 Feb 21, 2021

0

454

1

+502

Domain and Range

The domain of the function $h(x) = \sqrt{25-x^2}+\sqrt{-(x-2)}$ is an interval of what width?

ellapow Feb 21, 2021

+1

622

1

+148

Complex Number Arithmetic

Kelly and Avril chose complex numbers to represent their songs' popularities. Kelly chose $508+1749i$$508+1749i$. Avril chose $-1322+1949i$. What is the sum of their numbers?

powclaire Feb 21, 2021

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529

2

+206

Complex Number Arithmetic

Evaluate $\left(\frac{i}{2}\right)^2$.

oliviapow06 Feb 21, 2021

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