All Questions ⁺⁰235756 Questions

+1

22

2

+637

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{7 \times 10} + \frac{1}{37 + 40}

siIviajendeukie Mar 31, 2024

0

30

0

+637

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

19

1

+30

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.

Sxchen1110 Mar 31, 2024

0

20

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 .

hearth222 Mar 31, 2024

0

35

0

+8

I need help

Let
p(x)=1-(1/x)
what is p^6(-1/2)

hearth222 Mar 31, 2024

0

26

0

+544

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

40

0

+544

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

32

0

+544

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

37

0

+544

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

36

0

+279

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

24

0

+279

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

22

0

+279

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

25

0

+279

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

33

0

+1768

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

29

0

+1768

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

-3

12

1

+359

Square

In the diagram, $ABCD$ is a square. Find $\sin \angle PAQ.$

falafronk Mar 31, 2024

-1

30

0

+359

Triangle

Find the area of triangle $ABC,$ given that $AH=11$ and $HD=5.$

falafronk Mar 31, 2024

+1

33

1

+359

Semicircles

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

falafronk Mar 31, 2024

0

18

0

+359

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

28

0

+1839

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

29

0

+1839

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

23

0

+1839

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

20

1

+637

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 ..

siIviajendeukie Mar 31, 2024

0

22

1

+637

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

26

1

+637

Sum

Compute the sum
1 + \frac{1}{5} + \frac{4}{25} + \frac{8}{25} + \frac{16}{625}

siIviajendeukie Mar 31, 2024

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