All Questions ⁺⁰237734 Questions

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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

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95

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 ..

sandwich Jan 11, 2024

+2

80

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+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 read more ..

Solarblade Jan 11, 2024

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88

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+1585

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?

kittykat Jan 11, 2024

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108

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+1585

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?

kittykat Jan 11, 2024

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119

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+1585

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? read more ..

kittykat Jan 11, 2024

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66

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+1585

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?

kittykat Jan 11, 2024

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113

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+4

Help pls

let
Find the domain of . Give your answer using interval notation.

ChillBill Jan 11, 2024

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120

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+1585

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

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105

1

+1776

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.

bader Jan 11, 2024

Jan 10, 2024

0

105

2

+1776

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 ●●

bader Jan 10, 2024

+1

107

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+1776

Quadratic

The roots of the quadratic equation $z^2 + bz + c = 0$ are $4 + 2i$ and $-5 + 8i$. What is $b+c$?

bader Jan 10, 2024

+1

111

1

+291

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?

DS2011 Jan 10, 2024

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90

2

+1776

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 ..

bader Jan 10, 2024

+1

113

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+291

Question

Find the ordered pair in this system of equations:

DS2011 Jan 10, 2024

+1

118

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+291

Question

DS2011 Jan 10, 2024

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74

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+1776

Integer solutions

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

bader Jan 10, 2024

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112

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+1776

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

98

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+1940

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
\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.\]

tomtom Jan 10, 2024

+1

99

0

+1940

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

113

1

+1940

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.

tomtom Jan 10, 2024

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