All Questions ⁺⁰236160 Questions

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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 18, it has the same three digits, in reverse order. What is N? (Express your answer in decimal read more ..

Rangcr897 Jun 15, 2024

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10

4

+22

Help

1. Let f(x)=ax^2 +bx+a,where a and b are constants and a≠0. If one of the roots of the equation f(x)=0 is x=4, what is the other root?
2. Find the sum of the coefficients of the product (x^50+x^49+x^48+···+x^2+x+1)(x^50−x^49+x^48 −···+x^2 −x+1).
(In read more ..

Chadly Jun 15, 2024

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17

1

+948

Number Theory

What is 100000_{16} * E21A8_{16} in base 16?

Rangcr897 Jun 15, 2024

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19

1

+948

Number Theory

Express 0.11012 as a base 10 fraction in reduced form.

Rangcr897 Jun 15, 2024

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15

2

+948

Number Theory

Express 0.\overline{2123} as a base 10 fraction in reduced form.

NotThatSmart ●●

Rangcr897 Jun 15, 2024

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33

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+948

Number Theory

Compute A710B_{16} * 5_{16} in base 16.

Rangcr897 Jun 15, 2024

0

15

1

+22

Need Help Please, Really Challenging

Find the asymptotes of the graph y = 1/(f)x. Format your answer as follows: list the x-coordinates of any vertical asymptotes of y=1/f(x), then the righthand side of the slope-intercept form of the equation of any horizontal read more ..

Chadly Jun 15, 2024

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22

0

+948

Number Theory

Compute 221_3 \cdot 12211021_3 in base 3.

Rangcr897 Jun 15, 2024

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28

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+948

Number Theory

Compute 25_6 \cdot 541302_6 in base 6.

Rangcr897 Jun 15, 2024

0

25

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+948

Number Theory

Compute 35A8_{11} - 27_{11} + 3BC_{11}. Give your answer as a base 11 integer.

Rangcr897 Jun 15, 2024

0

35

1

+948

Number Theory

Compute 11_2 + 10101_2 + 11_2 + 1100101_2 + 1001_2 + 1001101_2. Give your answer as a base 2 integer.

Rangcr897 Jun 15, 2024

0

19

1

+948

Number Theory

Compute 2A31_{12} + E2_{12}. Give your answer as a base 12 integer.

Rangcr897 Jun 15, 2024

0

10

1

+948

Number Theory

Compute 357_8 + 501_8. Give your answer as a base 8 integer.

NotThatSmart ●

Rangcr897 Jun 15, 2024

0

15

1

+1911

Algebra

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

tomtom Jun 15, 2024

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16

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+1911

Algebra

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

tomtom Jun 15, 2024

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22

0

+1911

Algebra

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

tomtom Jun 15, 2024

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21

1

+1911

Algebra

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.

tomtom Jun 15, 2024

0

18

1

+1911

Algebra

When the same constant is added to the numbers 60, 120, and 160, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

NotThatSmart ●

tomtom Jun 15, 2024

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6

1

+1911

Algebra

Let a_1, a_2, a_3, \dots, a_{10}, a_{11}, a_{12} be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = 0$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 0$, then find $a_1$.

NotThatSmart ●

tomtom Jun 15, 2024

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12

2

+1911

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 20, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

tomtom Jun 15, 2024

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19

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+1911

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$

tomtom Jun 15, 2024

0

28

0

+1911

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 $x$.

tomtom Jun 15, 2024

0

5

1

+1911

Algebra

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

NotThatSmart ●

tomtom Jun 15, 2024

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15

1

+1911

Algebra

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

tomtom Jun 15, 2024

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21

1

+1911

help geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

tomtom Jun 15, 2024

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