All Questions ⁺⁰237313 Questions

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73

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+1926

Counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that at all the freshmen are standing next to each other?

tomtom Jan 14, 2024

0

74

0

+1926

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

tomtom Jan 14, 2024

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77

0

+1926

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

tomtom Jan 14, 2024

0

67

1

+1729

system

The system of equations
\frac{xy}{x + y} = 0, \quad \frac{xz}{x + z} = 0, \quad \frac{yz}{y + z} = 1
has exactly one solution. What is $z$ in this solution?

parmen Jan 14, 2024

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68

1

+1729

system

For certain values of k and m, the system
3a + 2b = 12 - 5a + 7b
8a + 6b = k - a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

parmen Jan 14, 2024

0

69

1

+478

Simplify

Compute (1 + i)/(2 - i)(3 + i).

ChiIIBill Jan 14, 2024

0

69

1

+478

Simplify

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

ChiIIBill Jan 14, 2024

0

63

1

+478

Algebra

Factor x^2 - 8x + 15 + x^2 - 4x + 3

Find all values of x such that x^2 - 8x + 15 + x^2 - 4x + 3 = 0. If you find more than one value, then list your solutions, separated by commas.

ChiIIBill Jan 14, 2024

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68

0

+1729

System

For a certain value of $k$, the system
x + y + 8z = 10,
x + 5y + 3z = 7 + 7z - 4y,
kx + 2z = 3 - 4y
has no solutions. What is this value of $k$?

parmen Jan 14, 2024

-1

52

1

+1729

Percent

Our badminton team has finished $75\%$ of its season. So far, we have won $35\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

parmen Jan 14, 2024

+1

76

0

+291

Problem

Can someone find this? Show steps:

Sorry it's in Albanian, basically what it means is:
Find all positive read more ..

DS2011 Jan 14, 2024

+1

80

0

+291

IMO Problem

DS2011 Jan 14, 2024

+1

67

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+291

Suggestion

What if this site includes other subjects, such as Literature, Science, History, Geography, and other subjects? I think that would be a good idea and the website could get more popular.
The read more ..

DS2011 Jan 14, 2024

+1

66

0

+291

AIME Problem

The solid shown has a square base of side length s. The upper edge is parallel to the base and has length 2s. All other edges have length s. Given that , what is the volume of the solid?

So read more ..

DS2011 Jan 14, 2024

+1

53

1

+291

My Lock Puzzle

Find the 4-digit number given these clues:
2 7 1 3 Two numbers are correct but wrongly placed.
8 0 6 3 One number is correct and well placed.
6 4 3 1 Nothing is correct. read more ..

DS2011 Jan 14, 2024

+1

55

1

+291

Lock Puzzle

Find the 4-digit lock combination given these clues:

DS2011 Jan 14, 2024

+1

62

2

+291

Problem

In the figure AC and BC are radii of circles. The length of AB is 8. If AC = 4, what is BC? (BC is tangent to the circle with center A.)
read more ..

BuiIderBoi ●●

DS2011 Jan 14, 2024

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68

1

+1556

3d geo stuff

A rectangle with vertices A(0,0), B(5,0), C(5,3) and D(0,3) is graphed in a coordinate plane. The rectangular region determined by those points is rotated $360^\circ$ about the line $y=-2$, forming a geometric solid. The rectangular region is then rotated read more ..

kittykat Jan 14, 2024

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67

1

+1556

Coordinates

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-12)$ and $O(2,8)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

kittykat Jan 14, 2024

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70

1

+1556

Coordinates

In the diagram, the four points have coordinates $A(0,1)$, $B(1,3)$, $C(5,2)$, and $D(4.5,0)$. What is the area of quadrilateral $ABCD$?

kittykat Jan 14, 2024

0

39

1

+1678

Coordinates

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

wiseowl Jan 14, 2024

+1

76

0

+1678

Triangle

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

wiseowl Jan 14, 2024

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