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All Questions
^{+0}
231651 Questions
+1
9
2
+177
Algebra
Compute
\frac{1}{1 \times 4} + \frac{1}{7 \times 10} + \frac{1}{37 + 40}
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siIviajendeukie
Mar 31, 2024
0
4
0
+177
Algebra
In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.
Fill in the blanks to make a true equation:
\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7}
read more ..
siIviajendeukie
Mar 31, 2024
0
8
1
+16
Geometry
Let the incircle of △ABC be tangent to AB, BC, AC at points M, N, P, respectively. If ∡BAC = 30◦ , find [BP C] [ABC] · [BMC] [ABC] , where [ABC] denotes the area of △ABC.
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Sxchen1110
Mar 31, 2024
0
8
2
+8
Help Quick
Let
f(x)=(x-1)(x-3)(x+5)+72
Find the sum of all values of x such that f(x)=72 .
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hearth222
Mar 31, 2024
0
14
0
+8
I need help
Let
p(x)=1-(1/x)
what is p^6(-1/2)
hearth222
Mar 31, 2024
0
8
0
+102
Counting
Find the number of positive integers that satisfy both the following conditions:
* Each digit is a 1 or a 2 or 3
* The sum of the digits is 5
cooIcooIcooI17
Mar 31, 2024
0
9
0
+102
Counting
Find the number of ways of choosing three circles below, so that no two circles are next to each other.
cooIcooIcooI17
Mar 31, 2024
0
6
0
+102
Counting
Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find
read more ..
cooIcooIcooI17
Mar 31, 2024
0
12
0
+102
Counting
Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find
read more ..
cooIcooIcooI17
Mar 31, 2024
0
7
0
+209
help 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?
fjeihqoO
Mar 31, 2024
0
3
0
+209
counting
Franklin the fly starts at the point (0,0) in the coordinate plane. At each step, Franklin takes a step to the right, left, up, or down. After 2 steps, how many different points could Franklin end up at?
fjeihqoO
Mar 31, 2024
0
5
0
+209
counting
Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)
fjeihqoO
Mar 31, 2024
0
5
0
+209
Counting
In how many ways can the numbers through be entered once each into the five boxes below so that all the given inequalities are true?
___ > ___ > ___ > ___ < ___
fjeihqoO
Mar 31, 2024
0
6
0
+1618
Series
Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 = 5 and a_2 + a_4 + a_6 + a_8 + a_{10} = 7, then find a_1.
bader
Mar 31, 2024
0
8
0
+1618
Counting
Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6 in a row so that the sum of any two adjacent numbers is even.
bader
Mar 31, 2024
-1
5
1
+357
Square
In the diagram, $ABCD$ is a square. Find $\sin \angle PAQ.$
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falafronk
Mar 31, 2024
-1
9
0
+357
Triangle
Find the area of triangle $ABC,$ given that $AH=11$ and $HD=5.$
falafronk
Mar 31, 2024
+1
10
1
+357
Semicircles
Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.
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falafronk
Mar 31, 2024
0
3
0
+357
geometry
In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.
falafronk
Mar 31, 2024
0
5
0
+952
Polynomial
There exists a polynomial f(x) and a constant k such that
(x^2 - 2x - 5) f(x) = 2x^4 - 4x^3 + kx^2.
What is k?
ABJeIIy
Mar 31, 2024
0
10
0
+952
Coefficient
What is the coefficient of x in (x^3 + x^2 + x + 1)(7x^6 + 8x^5 - 4x^4 - 10x^3 + 12x^2 - 2x - 8)?
ABJeIIy
Mar 31, 2024
0
4
0
+952
Polynomial
Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?
ABJeIIy
Mar 31, 2024
+1
2
1
+177
Fractions
Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator
read more ..
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siIviajendeukie
Mar 31, 2024
0
8
1
+177
Series
Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $2.$ The sum of the cubes of all the terms is $4.$ Find the common ratio.
●
siIviajendeukie
Mar 31, 2024
0
3
1
+177
Sum
Compute the sum
1 + \frac{1}{5} + \frac{4}{25} + \frac{8}{25} + \frac{16}{625}
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siIviajendeukie
Mar 31, 2024
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