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Post New Question
All Questions
+0
236075 Questions
0
47
0
+1348
Algebra
Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = 0$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 0$, then find $a_1$.
sandwich
Jan 11, 2024
0
41
1
+1348
3d problem
Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is , then find the volume of the resulting polyhedron.
read more ..
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sandwich
Jan 11, 2024
+2
42
1
+43
I really dont get this
Four circles of unit radius are drawn with centers (1,0), (-1,0),(0,1), and (0,-1). A circle with radius 2 is drawn with the origin as its center. What is the area of all points that are contained in an odd number of these 5 circles? ( express
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Solarblade
Jan 11, 2024
0
44
1
+1457
Angles
In triangle $ABC$, the angles $\angle A$, $\angle B$, $\angle C$ form an arithmetic sequence. If $\angle A = 45^\circ$, then what is $\angle C$, in degrees?
DS2011
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kittykat
Jan 11, 2024
0
50
1
+1457
Geometry
In the diagram below, $\overline{AB}$ and $\overline{EF}$ are parallel. If $\angle ABC = 155^\circ$, $\angle BCD = 180^\circ$, and $\angle ECD = 37^\circ$, then what is $\angle CEF$, in degrees?
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kittykat
Jan 11, 2024
0
57
0
+1457
Triangle
Let $ABC$ be a triangle. If $\angle A = \angle B + 2 \angle C - 60^\circ$ and $\angle B = 3 \angle A + 7 \angle C - 35^\circ$, then among all three exterior angles of triangle $ABC,$ what is the measure in degrees of the smallest exterior angle?
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kittykat
Jan 11, 2024
0
35
2
+1457
Angles
In a certain triangle, the exterior angles are in the ratio $3:5:10.$ What is the measure of the smallest interior angle of the triangle, in degrees?
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kittykat
Jan 11, 2024
0
49
1
+4
Help pls
let
Find the domain of . Give your answer using interval notation.
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ChillBill
Jan 11, 2024
0
55
0
+1457
Triangle
Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.
kittykat
Jan 11, 2024
0
48
1
+1768
Quadratic
For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 6x^2 + 12x + 18$ have nonreal roots? Enter your answer as an interval.
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bader
Jan 11, 2024
Jan 10, 2024
0
54
2
+1768
Algebra
Find all ordered pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 32 + 2xy$.
For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).
ElectricPavlov
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bader
Jan 10, 2024
+1
49
1
+1768
Quadratic
The roots of the quadratic equation $z^2 + bz + c = 0$ are $4 + 2i$ and $-5 + 8i$. What is $b+c$?
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bader
Jan 10, 2024
+1
48
1
+290
Question
DS2O11 Stop copying my username pls dont post questions with my username I don't want that. And don't copy my avatar that's even worse.
What is x?
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DS2011
Jan 10, 2024
0
46
2
+1768
Complex numbers
We can represent complex numbers geometrically by plotting them on the "complex plane", just like we plot points on the Cartesian plane. The real part of the complex number is the horizontal coordinate and the imaginary part is the vertical coordinate.
read more ..
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bader
Jan 10, 2024
+1
54
1
+290
Question
Find the ordered pair in this system of equations:
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DS2011
Jan 10, 2024
+1
52
1
+290
Question
What is ^
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DS2011
Jan 10, 2024
0
21
1
+1768
Integer solutions
Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.
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bader
Jan 10, 2024
0
53
0
+1768
Counting
Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC
read more ..
bader
Jan 10, 2024
+1
48
1
+1911
Series
Let $r$ be the positive real solution to $x^3 + \frac{2}{5} x - 1 = x^3 - 3x + 7.$ Find the exact numerical value of
\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.\]
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tomtom
Jan 10, 2024
+1
34
0
+1911
Series
Find the value of $k$ so that
3 + \frac{3 + k}{4^2} + \frac{3 + 2k}{4^4} + \frac{3 + 4k}{4^6} + \dotsb = 8.
tomtom
Jan 10, 2024
+1
56
1
+1911
Algebra
Compute the unique positive integer $n$ such that
2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.
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tomtom
Jan 10, 2024
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