All Questions ⁺⁰235489 Questions

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Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

AnswerscorrectIy Oct 27, 2024

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+788

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

AnswerscorrectIy Oct 27, 2024

Oct 26, 2024

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+271

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

MeIdHunter Oct 26, 2024

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+271

Algebra

Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.

MeIdHunter Oct 26, 2024

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+271

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

MeIdHunter Oct 26, 2024

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+271

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

MeIdHunter Oct 26, 2024

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+271

Algebra

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

MeIdHunter Oct 26, 2024

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+936

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

Rangcr897 Oct 26, 2024

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+936

Algebra

The parabola y = ax^2 + bx + c is graphed below. Find a + b + c. (The grid lines are one unit apart.)
The parabola passes through (-2,8), (0,0), and (2,8).

Rangcr897 Oct 26, 2024

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+936

Algebra

Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___

Rangcr897 Oct 26, 2024

Oct 25, 2024

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+217

Algebra

Find all values of $a$ such that $\frac{a-3}{\sqrt{a}} = a$.

bIueb3rry Oct 25, 2024

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+217

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $5$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $9$ hours. How read more ..

bIueb3rry Oct 25, 2024

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+217

Algebra

All members of our painting team paint at the same rate. If $20$ members can paint a $1500$ square foot wall in $30$ minutes, then how long would it take 15 members to paint a $1200$ square foot wall, in minutes?

bIueb3rry Oct 25, 2024

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+217

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

bIueb3rry Oct 25, 2024

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+217

Algebra

At a math convention, a poll is taken about cable news. It turns out that $5$ out of every $8$ people are bored by cable news. If there are $120$ people at the convention, then how many people at the convention are bored by cable news?
<read more ..

bIueb3rry Oct 25, 2024

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+217

Algebra

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 40 minutes, then how long would it take the 20 members to paint a 6000 square foot wall, in minutes?

bIueb3rry Oct 25, 2024

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+217

Algebra

I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons read more ..

bIueb3rry Oct 25, 2024

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+217

Algebra

I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons read more ..

bIueb3rry Oct 25, 2024

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+217

Algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does read more ..

bIueb3rry Oct 25, 2024

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+1507

Algebra

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?

parmen Oct 25, 2024

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+1507

Algebra

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

parmen Oct 25, 2024

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+1507

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

parmen Oct 25, 2024

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