All Questions ⁺⁰235278 Questions

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+1407

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 read more ..

blackpanther Jul 8, 2024

0

10

0

+1407

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

blackpanther Jul 8, 2024

0

11

1

+4

Help

solve the equation cos^2(x)-sin^2(x)=sin(x) given the domain (0,2pi]

Gus123456 Jul 8, 2024

0

6

1

+1796

Algebra

In an arithmetic sequence, the 23rd term is $\frac{1}{4},$ and the $33$rd term is $-\frac{1}{5}$. What is the $43$rd term?

ABJeIIy Jul 8, 2024

+1

13

1

+1796

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 Jul 8, 2024

0

15

0

+1796

Algebra

If x and y are positive integers for which 3x + 2y + xy = 115 + 11x + 2y, then what is x + y?

ABJeIIy Jul 8, 2024

0

10

0

+1796

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 = 22$ and $a_2 + a_4 = 17$, then find $a_1$.

ABJeIIy Jul 8, 2024

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10

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+1405

Algebra

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

kittykat Jul 8, 2024

0

4

1

+1405

Algebra

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

kittykat Jul 8, 2024

0

7

1

+1405

Algebra

Let f(x) = \sqrt{x}
Find the largest three-digit value of x such that f(x) is an integer.

kittykat Jul 8, 2024

0

17

1

+1405

Algebra

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

kittykat Jul 8, 2024

0

4

1

+458

Counting

Catherine rolls a standard $3$-sided die six times. If the product of her rolls is $600,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

cooIcooIcooI17 Jul 8, 2024

0

7

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+458

Counting

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

cooIcooIcooI17 Jul 8, 2024

0

10

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+458

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?

cooIcooIcooI17 Jul 8, 2024

0

7

0

+1405

Algebra

Let a be a real number such that a - \frac{1}{a} = 4 + a^2 + \frac{1}{a^2}. Compute a^3 - \frac{1}{a^3}.

kittykat Jul 8, 2024

0

9

1

+1405

Algebra

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

kittykat Jul 8, 2024

0

10

1

+1405

Algebra

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

kittykat Jul 8, 2024

0

14

0

+1405

Algebra

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

kittykat Jul 8, 2024

Jul 7, 2024

0

14

0

+458

Number Theory

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

cooIcooIcooI17 Jul 7, 2024

0

10

0

+458

Number Theory

What are the first $5$ digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{17}$ is written in base $16$?
(Express your answer as a five digit hexadecimal number. You do not need to read more ..

cooIcooIcooI17 Jul 7, 2024

0

6

1

+458

Number Theory

Jon teaches a fourth grade class at an elementary school where class sizes are always at least $20$ students and at most $60$. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately read more ..

cooIcooIcooI17 Jul 7, 2024

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