All Questions ⁺⁰235721 Questions

-1

47

1

+1443

System

Find the ordered quintuplet $(a,b,c,d,e)$ that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 47
2a + 3b + 4c + 5d = 22
3a + 4b + 5c = -17 read more ..

blackpanther Jan 4, 2024

-1

21

1

+1443

System

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6 + 2ab,$ then what is $a^3 + b^3?$

blackpanther Jan 4, 2024

-1

24

1

+1443

Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.

blackpanther Jan 4, 2024

-1

43

1

+1443

Sum

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

blackpanther Jan 4, 2024

-1

32

0

+1443

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

blackpanther Jan 4, 2024

0

35

0

+1533

circle

A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Find the area of the circle.

parmen Jan 4, 2024

0

46

0

+1533

circle

Let TU and VW be chords of a circle, which intersect at $S$, as shown. Find $SW$.

parmen Jan 4, 2024

+1

30

4

+5

How to find the terminal point?

I was doing my homework and was stuck on a problem for a really long time, and eventually checked the answer key to try and see if I could understand the solution. This is the first part but I still don't understand what it is saying.
For read more ..

roomtempiq Jan 4, 2024

Jan 3, 2024

0

39

0

+1533

circle

Let AB and CD be chords of a circle, that meet at point $Q$ inside the circle. If $CD = 34$, then find the minimum length of $CQ$.

parmen Jan 3, 2024

0

31

0

+1533

Circle

Let $X$, $Y$, and $Z$ be points on a circle. Let line $XY$ and the tangent to the circle at $Z$ intersect at $W$. If $\overline{WY} \perp \overline{WZ}$, then find $YZ$.

parmen Jan 3, 2024

0

49

0

+1533

Chords

Chords AB and CD of a circle meet at $P$. If $AP = 3 \cdot PB$, then what is $AB$?

parmen Jan 3, 2024

0

52

1

+1533

Circle

Chords PR and QS of a circle are perpendicular. Find $RS$.

parmen Jan 3, 2024

0

42

1

+1533

Circle

Let $\overline{XY}$ be a tangent to a circle, and let $\overline{XBA}$ be a secant of the circle, as shown below. If $AX = 20$, then what is $AB$?

parmen Jan 3, 2024

+1

18

0

+1364

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

sandwich Jan 3, 2024

0

44

3

+8

Quick Question

Hi!! I am having a little trouble with the following question. Could someone help me out?
\(ABCDEFGHI\) is a regular nonagon with side length \(1\). Let \(M\) be the midpoint of \(\overline{EF}\). \(J\) is a point outside read more ..

ElemetraryQuestions Jan 3, 2024

0

36

0

+1364

Sum

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

sandwich Jan 3, 2024

0

29

1

+1364

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 ..

sandwich Jan 3, 2024

0

37

1

+1364

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 ..

sandwich Jan 3, 2024

0

26

0

+1364

Series

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $4.$ The sum of the cubes of all the terms is $10.$ Find the common ratio.

sandwich Jan 3, 2024

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