All Questions ⁺⁰236027 Questions

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24

1

+773

Quadratic

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

booboo44 Jan 18, 2024

0

39

0

+773

Algebra

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

booboo44 Jan 18, 2024

0

40

0

+773

Problem on quadratic

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

booboo44 Jan 18, 2024

0

29

0

+862

Coordinates

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

magenta Jan 18, 2024

0

42

0

+862

Coordinates

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

magenta Jan 18, 2024

0

44

0

+862

Coordinates

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

magenta Jan 18, 2024

0

47

1

+862

Graphing question

Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.

magenta Jan 18, 2024

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24

3

+400

Probability

Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In other words, find the probability that XO is read more ..

omgitsrne Jan 18, 2024

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28

2

+400

Average

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is $4/3$. Find $n$.

omgitsrne Jan 18, 2024

0

39

0

+400

Probability

Raina places the following balls into a bag. She draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 6 orange balls and 6 purple read more ..

omgitsrne Jan 18, 2024

0

5

1

+1911

Operations

Let $x \mathbin{\spadesuit} y = \frac{x^2}{y}$ for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that $a\mathbin{\spadesuit} a = 1$. Write your answer as a list separated by commas.

tomtom Jan 18, 2024

-1

26

1

+1911

Functions

Suppose a(x) = 2x + 5 and b(x) = 2x - 5. Find (a\circ b)(3) - (b\circ a)(3).

tomtom Jan 18, 2024

-1

42

1

+1911

Functions

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

tomtom Jan 18, 2024

-1

40

1

+1911

Algebra

Find all real numbers x such that f(x) = f(f(x)) + 16x + 5, where f(x) = x^2 - 3x + 1.

tomtom Jan 18, 2024

Jan 17, 2024

-1

23

1

+1911

Functions

Let f(x) = px + q, where p and q are real numbers. Find p+q if f(f(f(x))) = 64x - 105 - 63x + 278.

tomtom Jan 17, 2024

-1

34

1

+1911

Functions

The function
f(x) = \frac{cx}{4x - 5 - 2x + 8}
satisfies f(f(x))=x for all real numbers x\neq -\frac{3}{2}. Find c.

tomtom Jan 17, 2024

-1

26

1

+1521

Coordinates

A line and a circle intersect at A and B. Find the coordinates of the midpoint of \overline{AB}.
The ilne is y = 3x - 2, and the circle is (x - 4)^4 + (y - 5)^2 = 68.

blackpanther Jan 17, 2024

-1

39

0

+1521

Quadratic Expressions

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 4x + 12y.$ Find the largest possible value of $x + y.$ Give your answer in exact form using radicals, simplified as far as possible.

blackpanther Jan 17, 2024

0

23

1

+15

Algebra help

Let be a monic cubic polynomial, and let p(x), q(x) and r(x) be polynomials such that f(x) = p(x)(x - 1) + 1 = q(x)(x - 2) + 1 = r(x)(x - 3) + 1
Find f(4)

LachrymoseMath Jan 17, 2024

0

34

1

+0

The amount of money Stephanie collected in tips in each of seven days is

The amount of money Stephanie collected in tips in each of seven days is
$107,
$74,
$86, read more ..

kenjen81 Jan 17, 2024

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