All Questions ⁺⁰237321 Questions

0

21

0

+900

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

eramsby1O1O Dec 7, 2024

0

17

0

+900

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

eramsby1O1O Dec 7, 2024

Dec 6, 2024

0

15

1

+4

Discriminants for 2 variable equation.

Looking for the discriminants and interpretation for x and z for this equation: -(z^3)+6*z^2+(12*x)*z-(12*z)+6*x^2-(12*x)+6=0.
I tried it with the quadratic and cubic discriminants but not sure if I actually did it right or not. Thanks. read more ..

cwstevens71 Dec 6, 2024

0

14

1

+921

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

booboo44 Dec 6, 2024

0

21

0

+921

Counting

Each square below is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the squares?

booboo44 Dec 6, 2024

0

19

0

+921

Counting

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 3 or a 5.
The sum of the digits is 7.

booboo44 Dec 6, 2024

0

25

0

+802

Algebra

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

crimefightingvigiI Dec 6, 2024

0

28

0

+802

Algebra

Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.

crimefightingvigiI Dec 6, 2024

0

22

0

+802

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
\[a_n = a_{n - 1} + a_{n - 2}\]
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

crimefightingvigiI Dec 6, 2024

0

18

0

+821

Algebra

Find all c such that |c + 5| - 3c = 10 + 2|c - 4| - 6|c|. Enter all the solutions, separated by commas.

cooIcooIcooI17 Dec 6, 2024

0

9

1

+821

Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.

cooIcooIcooI17 Dec 6, 2024

0

12

0

+821

Algebra

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

cooIcooIcooI17 Dec 6, 2024

0

18

0

+802

Counting

Syd chooses two different primes, and multiplies them. If both primes are greater than 3, and the resulting product is less than 500 , then how many different products could Syd have ended up with?

crimefightingvigiI Dec 6, 2024

0

23

0

+802

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 7
where u, v, w, x, y, and z are nonnegative integers, and x is at most 2 or y is at least 3?

crimefightingvigiI Dec 6, 2024

0

17

0

+802

Counting

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.

crimefightingvigiI Dec 6, 2024

0

25

0

+750

Counting

Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c read more ..

siIviajendeukie Dec 6, 2024

0

18

0

+750

Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

siIviajendeukie Dec 6, 2024

0

17

0

+750

Counting

In how many ways can the numbers through be entered once each into the five boxes below so that all the given inequalities are true?
___ > ___ > ___ > ___ < ___

siIviajendeukie Dec 6, 2024

0

15

1

+750

Counting

A baking club wants to form an executive committee. There are $20$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $7$ people, including Mark?

siIviajendeukie Dec 6, 2024

0

26

0

+750

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

siIviajendeukie Dec 6, 2024

+1

19

2

+5

help

Let $f$ be a cubic polynomial such that $f(0) = 5$, $f(1) = -5$, $f(2) = 8$, and $f(3)=13$. What is the sum of the coefficients of $f$?

frozensssss Dec 6, 2024

Dec 5, 2024

0

22

0

+413

Counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways read more ..

nathanl6656 Dec 5, 2024

0

21

0

+413

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?

nathanl6656 Dec 5, 2024

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