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Post New Question
All Questions
+0
236340 Questions
0
21
1
+844
Geometry
In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid
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RedDragonl
Jun 25, 2024
0
16
4
+40
math writing problem
Consider the two expressions and
a) Show that the two expressions represent equal numbers when
b) Explain why these two expressions do not represent equal numbers when
c) Show that these two expressions represent
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onyulee
Jun 25, 2024
0
19
1
+911
Number Theory
A positive integer is called terrific if it has exactly $12$ positive divisors. A positive integer is called good if it has exactly 4 positive divisors. Which numbers are good?
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magenta
Jun 25, 2024
0
10
1
+911
Number Theory
A positive integer is called terrific if it has exactly $12$ positive divisors. A positive integer is called fine if it has exactly 2 positive divisors. Which numbers are fine?
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magenta
Jun 25, 2024
0
23
1
+911
Counting
Catherine rolls a standard $6$-sided die three times. If the product of her rolls is $600,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
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magenta
Jun 25, 2024
0
14
1
+911
Counting
Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC
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magenta
Jun 25, 2024
0
28
0
+1379
Algebra
A geometric sequence has $400$ terms. The first term is $1000$ and the common ratio is $-\frac{8}{9}.$ How many terms of this sequence are greater than $1?$
learnmgcat
Jun 25, 2024
0
16
1
+1379
Algebra
When the same constant is added to the numbers 60, 120, and 140, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
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learnmgcat
Jun 25, 2024
-1
22
1
+331
Need help
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
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Stanry
Jun 25, 2024
-1
28
1
+331
Algebra
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.
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Stanry
Jun 25, 2024
-1
15
1
+331
Geometry
Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $15.$ Also, the sum of all the edges of the prism is $17.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.
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Stanry
Jun 25, 2024
Jun 24, 2024
0
27
1
+948
Geometry
The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.
shmewy
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Rangcr897
Jun 24, 2024
+1
25
1
+5
Trigonometry PLZ HELPPP!!!
Consider the following points on the graph of y=sin(x)
https://docs.google.com/document/d/1aHUVqjrIYnITSuw5MIPSvx_XD-0UItgdCAeLTALxebo/edit?usp=sharing
Say that the terminal points of angles a and b are as follows:
Terminal
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savvyylee
Jun 24, 2024
0
19
0
+948
Geometry
Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.
Rangcr897
Jun 24, 2024
0
19
1
+948
Geometry
Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find
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Rangcr897
Jun 24, 2024
0
13
1
+948
Geometry
Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square.
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shmewy
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Rangcr897
Jun 24, 2024
0
21
1
+948
Geometry
In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.
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Rangcr897
Jun 24, 2024
0
16
1
+63
Polynomials I think
Find all positive integers n for which is a perfect square.
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MeldHunter
Jun 24, 2024
0
23
1
+948
Geometry
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
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Rangcr897
Jun 24, 2024
0
29
2
+911
circle
Find the coordinates of the center of the circle.
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magenta
Jun 24, 2024
0
29
2
+911
Graph
Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+14x-14y+28
CPhill
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magenta
Jun 24, 2024
0
27
2
+84
vewy anoying sequence sereis problem
For a positive integer , define to be the minimum value of the sum
where are positive real numbers whose sum is 17. There is a unique positive integer for which is also an integer. Find
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shmewy
Jun 24, 2024
0
16
5
+63
Polynomials
Find all roots of the polynomial
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MeldHunter
Jun 24, 2024
0
15
2
+911
Algebra
For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.
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magenta
Jun 24, 2024
0
18
2
+911
Algebra
Expand (x^2 + 1/x)*(x + x^4)^3.
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magenta
Jun 24, 2024
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