All Questions ⁺⁰232819 Questions

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Reflections

Let $ABCD$ be a square with side length $1.$ A laser is located at vertex $A,$ which fires a laser beam at point $X$ on side $\overline{BC},$ such that $BX = \frac{1}{2}.$ The beam reflects off the sides of the square, until it ends up at another read more ..

Hi6942O May 23, 2024

+1

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+897

Temperature question!

The equation above shows how temperature 𝐹, measured in degrees Fahrenheit, relates to a temperature 𝐶, measured in degrees Celsius. Based on the equation, which of the following must be true?
(I) A temperature increase read more ..

NotThatSmart May 23, 2024

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THIS IS NOT COLLATZ!

There are a couple rules to this problem.
1. If the number is even, please divide by 2.
2. If the number is odd, please multiply by 3 and add 1.
Now, let's have an example. 6.
6 is even, so we divide by 2 to get 3. 3 is odd so we read more ..

NotThatSmart May 23, 2024

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+628

Logarithms

Suppose $a\neq 0$. Compute $\log_{8a} b$ in terms of $a$ and $b$.

learnmgcat May 23, 2024

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+628

Logarithm

Find $x$ if $\log_2 (\log_3 x) = \log_3 (\log_2 x).$

learnmgcat May 23, 2024

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+628

Absolute value

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

learnmgcat May 23, 2024

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+657

Algebra

Let $x$, $y$, and $z$ be nonzero real numbers. Find all possible values of
\frac{x}{|x|} + \frac{y}{|y|} + \frac{z}{|z|} + \frac{x + y + z}{|x + y + z|}

eramsby1O1O May 23, 2024

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Counting

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

eramsby1O1O May 23, 2024

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Counting

At a meeting, 4 mathematicians, 3 scientists, and 2 journalists are to be seated around a circular table. How many different arrangements are possible if the mathematicians must all sit together (in 4 consecutive seats) and the 3 scientists must read more ..

eramsby1O1O May 23, 2024

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+657

Counting

My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between read more ..

eramsby1O1O May 23, 2024

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+4

HELPPP

There exists a polynomial f(x) and a constant k
(x^2+4x-2) f(x)=3x^4+11x^3+kx^2+18x-8
What is K?

abusivephat May 23, 2024

May 22, 2024

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Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $300,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

eramsby1O1O May 22, 2024

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+657

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

eramsby1O1O May 22, 2024

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+657

Counting

Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $2$ steps, how many different points could Franklin end up at?

eramsby1O1O May 22, 2024

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Counting

Joanna has six beads that she wants to assemble into a bracelet. Four of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

eramsby1O1O May 22, 2024

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Algebra

Let a and b be the roots of the quadratic x^2 - 5x + 3 = -2x^2 + 11x - 14. Find the quadratic whose roots are a^2 and b^2.
x^2 + ___x + ___

eramsby1O1O May 22, 2024

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+16

pls help

jjtseng May 22, 2024

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+16

Help pls

The roots of the quadratic equation are 5 + 3i and 5-3i. What is b+c?

jjtseng May 22, 2024

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PLS help!

Find all solutions to the equation

jjtseng May 22, 2024

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+1774

Algebra

For a certain value of k, the system
x + y + 3z = 10 - x + 5y,
4x + 2y + 5z = 7 + 11y + 19z,
kx + z = 3 + 5y
has no solutions. What is this value of k?

LiIIiam0216 May 22, 2024

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+1774

Algebra

Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

LiIIiam0216 May 22, 2024

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+1774

Algebra

Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

LiIIiam0216 May 22, 2024

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+1774

Algebra

Solve the inequality
\frac{3-z}{z+1} \ge 2 + 7z.
Write your answer in interval notation.

LiIIiam0216 May 22, 2024

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+1774

Algebra

Arrange the following numbers in increasing order (smallest first, biggest last)
A = 2^(1/2)*4^(1/6)
B = (128)^(1/12)/64^(1/3)
C = (8^(1/5))^(2^2) read more ..

LiIIiam0216 May 22, 2024

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+1774

Algebra

Let $f(x) = x^2 + bx + 2 - 3x + 8$ for all real numbers $x$. For what real values of $b$ is $-2$ not in the range of the function $f(x)$? Express your answer in interval notation.

LiIIiam0216 May 22, 2024

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