All Questions ⁺⁰235615 Questions

0

48

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+743

Proportion

All members of our painting team paint at the same rate. If $4$ members can paint a specific wall in $40$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

bingboy Dec 14, 2023

0

23

1

+1678

Inequalities

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

wiseowl Dec 14, 2023

0

39

1

+1678

Inequality

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $1500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. Based read more ..

wiseowl Dec 14, 2023

0

35

1

+1678

Help with inequality

Jeri finds a pile of money with at least 200. If she puts 150 of the pile in her left pocket, gives away $\frac35$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away 200 of read more ..

wiseowl Dec 14, 2023

0

35

1

+1678

Linear Inequality

Find a linear inequality with the following solution set. Each grid line represents one unit.
(Give your answer in the form $ax+by>c$ or $ax+by\geq c$ where $a,$ $b,$ and $c$ are integers with no common factor other than $1$.) read more ..

wiseowl Dec 14, 2023

0

38

1

+1678

Linear Inequality

Find a linear inequality with the following solution set. Each grid line represents one unit.
(Give your answer in the form $ax+by>c$ or $ax+by\geq c$ where $a,$ $b,$ and $c$ are integers with no common factor other than $1$.) read more ..

wiseowl Dec 14, 2023

-1

46

1

+1427

Triangle

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

blackpanther Dec 14, 2023

-1

29

1

+1427

Altitudes

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

blackpanther Dec 14, 2023

-1

43

1

+1427

Area

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 135^\circ$.

blackpanther Dec 14, 2023

-1

33

1

+1427

Right triangles

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 $BX$?

blackpanther Dec 14, 2023

-1

24

1

+1427

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 $ABD$.

blackpanther Dec 14, 2023

0

34

1

+1348

Function with Integer

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

sandwich Dec 14, 2023

0

42

1

+1348

Algebra

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

sandwich Dec 14, 2023

0

41

1

+1348

sequence question

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 $a_6.$

sandwich Dec 14, 2023

0

40

1

+1348

System

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a+2b+3c+4d+5e=1
2a+3b+4c+5d+e=2
3a+4b+5c+d+2e=3 read more ..

sandwich Dec 14, 2023

0

50

0

+1348

Complex numbers

Let $a$ and $b$ be complex numbers. If $a + b = 0$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

sandwich Dec 14, 2023

0

42

1

+1348

Fraction

Find the value of
\[\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4}}}}}.\]

sandwich Dec 14, 2023

0

11

1

+1348

Sum

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{42} +\sqrt{45}} + \frac{1}{\sqrt{45} + \sqrt{49}}

sandwich Dec 14, 2023

0

49

0

+1348

Complex numbers

Let $x$ and $y$ be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

sandwich Dec 14, 2023

0

24

1

+817

help counting

Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c read more ..

maximum Dec 14, 2023

0

26

1

+817

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

maximum Dec 14, 2023

0

30

1

+817

Counting problem

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

maximum Dec 14, 2023

0

45

0

+688

Angles

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 62^\circ$ and $\angle STU = 29^\circ$, read more ..

booboo44 Dec 14, 2023

0

23

1

+688

Altitudes

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 20^\circ$, then what is $\angle ABH$ in degrees?

booboo44 Dec 14, 2023

0

26

0

+688

Altitudes

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 13$, $SU = 14$, $TU = 4$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

booboo44 Dec 14, 2023

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