All Questions ⁺⁰235690 Questions

0

28

1

+1768

Double root

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

bader Jan 16, 2024

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51

1

+0

Quadratic Functions 20-1; completing the square

Annette takes a jump on her snowmobile and lands on a level snowfield several meters from her takeoff point. Her path through the air could be described using the function y= -0.25x^2 + 2.5x where x and y are measured in meters.
Determine read more ..

DanStar Jan 16, 2024

0

6

0

+1364

Triangles

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 13$, $SU = 14$, $TU = 4$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

sandwich Jan 16, 2024

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3

1

+1364

Altitudes

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 20^\circ$, then what is $\angle ABH$ in degrees?

sandwich Jan 16, 2024

0

29

0

+1364

Triangle

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 62^\circ$ and $\angle STU = 29^\circ$, read more ..

sandwich Jan 16, 2024

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47

0

+1439

Counting question

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

kittykat Jan 16, 2024

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46

1

+1439

help with 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 ..

kittykat Jan 16, 2024

-1

49

0

+1443

Complex numbers

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

blackpanther Jan 16, 2024

0

4

1

+1443

Sequences

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 $a_6.$

blackpanther Jan 16, 2024

-1

43

1

+1443

Algebra

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

blackpanther Jan 16, 2024

-1

49

0

+1443

Help algebra

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

blackpanther Jan 16, 2024

0

43

1

+688

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

booboo44 Jan 16, 2024

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4

1

+688

Triangles

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

booboo44 Jan 16, 2024

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3

1

+688

Area

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 135^\circ$.

ElectricPavlov ●

booboo44 Jan 16, 2024

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4

1

+688

Altitudes

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

booboo44 Jan 16, 2024

0

39

0

+688

Triangle

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

booboo44 Jan 16, 2024

-1

30

1

+688

Triangle

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 135^\circ$.

booboo44 Jan 16, 2024

0

31

0

+688

Altitudes

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

booboo44 Jan 16, 2024

0

36

0

+688

Triangle

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

booboo44 Jan 16, 2024

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