All Questions ⁺⁰237779 Questions

+1

13

1

+823

Algebra

Evaluate \sum_{n = 1}^{33} (5n + 2 - 4n + n^2 + 17).

crimefightingvigiI Mar 2, 2025

0

8

2

+823

Algebra

Evaluate 21 + 27 + 33 + ... + 267 + ... + 6021.

crimefightingvigiI Mar 2, 2025

0

11

1

+36

Algebra

Let be real numbers such that
Find the maximum value of in terms of
I originally got the answer of 1 but it was wrong! Thanks for helping!

crimefightingvigil Mar 2, 2025

0

11

1

+36

HELP Pls

Thanks for helping!
Let be real numbers such that
and is minimized. Find

crimefightingvigil Mar 2, 2025

0

4

2

+972

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 $S_{70}.$

Rangcr897 Mar 2, 2025

0

10

1

+972

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 ..

Rangcr897 Mar 2, 2025

0

1

8

1

+1524

Algebra

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

learnmgcat Mar 2, 2025

0

7

12

1

+1580

Algebra

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

kittykat Mar 2, 2025

0

11

1

+823

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 15$, find $BZ$.

crimefightingvigiI Mar 2, 2025

0

22

1

+823

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 15$, find $BC$.

crimefightingvigiI Mar 2, 2025

0

16

2

+351

help with counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

jaekg Mar 2, 2025

0

1

2

+34

Counting and Probability

Each face of a cube is painted randomly one of the colors red, orange, yellow, green, blue or purple. What is the probability that the cube has at least one pair of faces that share an edge and are the same color? Express your answer as a decimal to the read more ..

colinqiu Mar 2, 2025

0

5

1

+1844

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 2.

blackpanther Mar 2, 2025

0

14

1

+1844

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.

blackpanther Mar 2, 2025

0

21

1

+1844

Algebra

Let a, b, c be the roots of p(x) = x^3 + 7x^2 + 10x - 13 - 5x^3 + 25x^2 + 44x - 15. Find the value of
1/(ab + ac) + 1/(ab + bc) + 1/(ac + bc)

blackpanther Mar 2, 2025

+1

1

9

1

+417

Algebra

Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 0, what is b?

nathanl6656 Mar 2, 2025

0

1

12

1

+417

Algebra

Find all (real or nonreal) x satisfying
(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).

nathanl6656 Mar 2, 2025

0

12

1

+417

Algebra

Express x^8 + x^4 y^4 - x^6 y^2 + x^3 y^5 - 4xy^7 - y^8 as the product of two polynomials of degree 2, and a polynomial of degree 4.

nathanl6656 Mar 2, 2025

0

1

18

1

+417

Algebra

Find the constant k so that
2x^2 + 5xy - 8y^2 + 7x + 25y + k
can be expressed as the product of two linear factors of the form ax + by + c.

nathanl6656 Mar 2, 2025

+1

2

14

1

+498

Algebra

Let
p(a, b, c) = a^5 + b^5 + c^5 + k(a^3 + b^3 + c^3)(a^4 + b^4 + c^4 - 2a^2 b^2 - 2a^2 c^2 - 2b^2 c^2).
Find the constant k so that p(a,b,c) is divisible by a + b + c.

MeIdHunter Mar 2, 2025

0

1

16

0

+498

Algebra

If z is a complex number satisfying
z + \frac{1}{z} = \sqrt{5},
calculate
z^{10} + \frac{1}{z^{10}}. read more ..

MeIdHunter Mar 2, 2025

0

2

16

1

+498

Algebra

In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of read more ..

MeIdHunter Mar 2, 2025

0

1

13

0

+498

Algebra

In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of read more ..

MeIdHunter Mar 2, 2025

0

1

19

0

+1022

Algebra

If (x,y) satisfies the simultaneous equations
3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.
x^2 - y^2 = 7 + 4xy
where x and y may be complex numbers, determine all possible values of y^2.

gnistory Mar 2, 2025

0

2

12

0

+1022

Algebra

Factor 3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.

gnistory Mar 2, 2025

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