All Questions ⁺⁰231330 Questions

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Pls help

Marcus saved $400 more than Joshua. After Joshua had given 1/5 of his savings to Marcus, Marcus had $480 more than Joshua. How much did Joshua save at first?

sugabreaddoughman May 7, 2024

May 6, 2024

0

2

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+269

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

rtsdylifdts May 6, 2024

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+269

Geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

rtsdylifdts May 6, 2024

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3

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+85

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 4 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 40 miles per hour, the trip takes 5 hours. How many read more ..

Rangcr897 May 6, 2024

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+85

Counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

Rangcr897 May 6, 2024

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4

1

+44

geometry help

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$ [asy] unitsize(1 cm); pair P, Q, R; P = (1,3); Q = (0,0); R = (4,0); draw(P--Q--R--cycle); label("$P$", P, N); label("$Q$", Q, SW); label("$R$", R, SE); label("$5$", (P + Q)/2, NW, red);read more ..

rtsdyhfdts May 6, 2024

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4

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+85

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

Rangcr897 May 6, 2024

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2

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+85

Algebra

Find all values of t such that \lfloor t\rfloor = 3t + 4 - \lfloor 2t \rfloor. If you find more than one value, then list the values you find in increasing order, separated by commas.

Rangcr897 May 6, 2024

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2

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+85

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} = 4 and a_{10} = 1, then find a_6.

Rangcr897 May 6, 2024

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2

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+85

Geometry

Two lines $p$ and $q$ intersect at $X$. The angle between lines $p$ and $q$ is $45^\circ$. Let $A$ be a point inside the $45^\circ$ angle formed by $p$ and $q$. Let $B$ be the reflection of $A$ through line $p,$ and let $C$ be the reflection read more ..

Rangcr897 May 6, 2024

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3

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+85

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BC$.

Rangcr897 May 6, 2024

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3

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+1246

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 May 6, 2024

0

2

3

+1246

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

LiIIiam0216 May 6, 2024

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2

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+1246

Counting

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

LiIIiam0216 May 6, 2024

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2

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+1246

Geometry

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x - 8y + 17x - 5y + 25,
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

LiIIiam0216 May 6, 2024

0

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1

+77

Please help me to solve this problem .

Aloysius had some money at first. He spent $360 on a suit. He then spent 1/7 of his remaining money on shoes and had 2/5 of his money left. How much money did he have at first?

sugabreaddoughman May 6, 2024

0

2

1

+291

Algebra

Find the domain of the function \[f(x)=\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}}.\]

Pythagorearn May 6, 2024

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2

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+291

Algebra

Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

Pythagorearn May 6, 2024

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+291

Function

Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.

Pythagorearn May 6, 2024

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+291

Algebra

Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.

Pythagorearn May 6, 2024

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+48

Can't Understand The Question

Let f(x) be an odd function defined for all real numbers x, and let g(x)=f(x+3)-5. You are told that the graph of y=g(x) passes through the point (2, -2). Then the graph of y=g(x) must also pass through two other points (a,b) and (c,d) Enter your answer read more ..

IWantToHelp May 6, 2024

May 5, 2024

0

2

1

+1246

Geometry

The line y = mx bisects the angle between the two lines shown below. Find $m$.
read more ..

LiIIiam0216 May 5, 2024

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3

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+1246

Geometry

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

LiIIiam0216 May 5, 2024

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