All Questions ⁺⁰237991 Questions

0

58

3

+30

Algebra 2

1. The sequence a(n) satisfies a(1) = 3 and
a(n) = [a(n-1)-1]/a(n-1)+1
for all n ≥ 2. Find a(100).
(I'm sorry about the way I formatted this question. read more ..

Chadly Jun 17, 2024

-4

87

0

+216

counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \le 10
in nonnegative integers, where x_2 is even and x_5 is odd.

BRAlNBOLT Jun 17, 2024

Jun 16, 2024

-1

81

1

+1863

Algebra

When the same constant is added to the numbers 60, 120, and 140, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

ABJeIIy Jun 16, 2024

-1

95

0

+1863

Algebra

A geometric sequence has $400$ terms. The first term is $1000$ and the common ratio is $-\frac{8}{9}.$ How many terms of this sequence are greater than $1?$

ABJeIIy Jun 16, 2024

-1

66

0

+1863

Algebra

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 6 or 9.

ABJeIIy Jun 16, 2024

-1

85

1

+1863

Algebra

In a geometric sequence, the 23rd term is 16 and the 24th term is 1/4. What is the 30th term?

NotThatSmart ●

ABJeIIy Jun 16, 2024

0

60

1

+1044

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

Hi6942O Jun 16, 2024

0

92

0

+1044

Algebra

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

Hi6942O Jun 16, 2024

0

56

1

+1044

Algebra

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

Hi6942O Jun 16, 2024

0

69

1

+1044

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}

Hi6942O Jun 16, 2024

0

82

1

+363

Even harder

We introduced i as a square root of -1. Does i itself have any square roots among the complex numbers? If so, name one. If not, answer with "None."

Lilliam0216 Jun 16, 2024

0

79

1

+363

Super hard

Lilliam0216 Jun 16, 2024

-1

88

0

+1863

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

ABJeIIy Jun 16, 2024

-1

64

1

+1863

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

ABJeIIy Jun 16, 2024

0

71

1

+1536

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

learnmgcat Jun 16, 2024

0

102

0

+1536

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

learnmgcat Jun 16, 2024

+1

36

5

+52

Please help counting and probability

In how many ways can 4 balls be placed in 3 boxes if the balls are distinguishable, and the boxes are indistinguishable?

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MEMEGOD Jun 16, 2024

0

97

0

+1044

Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a.
The lines passes through (5,8) and (-4,17).

Hi6942O Jun 16, 2024

0

59

1

+1044

Algebra

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

Hi6942O Jun 16, 2024

0

77

0

+1044

Algebra

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 ..

Hi6942O Jun 16, 2024

0

51

2

+1044

Algebra

Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.

Hi6942O Jun 16, 2024

0

58

2

+1044

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

Hi6942O Jun 16, 2024

-1

51

1

+1863

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when \frac{1}{5} is expressed in base 3, the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When read more ..

ABJeIIy Jun 16, 2024

0

34

1

+363

$\frac{4}{1 - \sqrt[3]3 + \sqrt[3]9}.$

Lilliam0216 Jun 16, 2024

-1

56

1

+1863

Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 135 + 136 + 137 + 138 + 139 + 140.

ABJeIIy Jun 16, 2024

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