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All Questions
^{+0}
233372 Questions
0
19
1
+506
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?
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booboo44
Jan 18, 2024
0
25
0
+506
Algebra
Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.
booboo44
Jan 18, 2024
0
30
0
+506
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
22
0
+563
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
25
0
+563
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
29
0
+563
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
21
1
+563
Graphing question
Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.
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magenta
Jan 18, 2024
0
10
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 ..
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omgitsrne
Jan 18, 2024
0
15
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 $n$.
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omgitsrne
Jan 18, 2024
0
22
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
+1859
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.
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tomtom
Jan 18, 2024
-1
17
1
+1859
Functions
Suppose a(x) = 2x + 5 and b(x) = 2x - 5. Find (a\circ b)(3) - (b\circ a)(3).
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tomtom
Jan 18, 2024
-1
22
1
+1859
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.
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tomtom
Jan 18, 2024
-1
10
1
+1859
Algebra
Find all real numbers x such that f(x) = f(f(x)) + 16x + 5, where f(x) = x^2 - 3x + 1.
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tomtom
Jan 18, 2024
Jan 17, 2024
-1
13
1
+1859
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.
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tomtom
Jan 17, 2024
-1
13
1
+1859
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.
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tomtom
Jan 17, 2024
-1
15
1
+1222
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.
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blackpanther
Jan 17, 2024
-1
22
0
+1222
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
12
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)
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LachrymoseMath
Jan 17, 2024
0
24
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 ..
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kenjen81
Jan 17, 2024
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