All Questions ⁺⁰236341 Questions

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Triangle

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

blackpanther Mar 22, 2024

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36

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+1560

Triangle

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

blackpanther Mar 22, 2024

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33

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Equilateral triangle

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

blackpanther Mar 22, 2024

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39

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+2653

Inequality

Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.

LiIIiam0216 Mar 22, 2024

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30

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Inequality

Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.

LiIIiam0216 Mar 22, 2024

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21

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Circles

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius read more ..

blackpanther Mar 22, 2024

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22

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+2653

System

For certain values of k and m, the system
3a + 2b = 12 - 5a + 7b
8a + 6b = k - a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

LiIIiam0216 Mar 22, 2024

Mar 21, 2024

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27

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help quick

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

blackpanther Mar 21, 2024

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33

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need help

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

blackpanther Mar 21, 2024

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38

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+2653

Simplify

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

LiIIiam0216 Mar 21, 2024

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27

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Complex numbers

Compute (1 + i)/(2 - i)(3 + i).

LiIIiam0216 Mar 21, 2024

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24

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+28

class arrangements

A speech class has 4 freshmen and 3 sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that at least two of the freshmen are standing next to each other?

coolcoolcool17 Mar 21, 2024

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29

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letter arrangements

In the array below, in how many different ways can we start with the letter and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
read more ..

coolcoolcool17 Mar 21, 2024

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27

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+28

Syd chooses prime numbers

Syd chooses two different primes, and multiplies them. If both primes are greater than 4, and the resulting product is less than 200, then how many different products could Syd have ended up with?

coolcoolcool17 Mar 21, 2024

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15

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arranging bookshelves

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 psychology textbook exactly in the middle, and there must be a mathematics read more ..

coolcoolcool17 Mar 21, 2024

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25

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Coefficient

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

LiIIiam0216 Mar 21, 2024

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19

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Coefficient

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?

LiIIiam0216 Mar 21, 2024

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34

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Algebra

There exists a polynomial $(x) and a constant 7k such that
(x^2 - 2x - 5) f(x) = x^4 - 2x^3 + kx^2
What is k?

LiIIiam0216 Mar 21, 2024

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47

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+2653

Polynomials

Find t if the expansion of the product of 2x^3 + x^2 - 3x + 5 and x^4 - 7x^3 + tx^2 - 11x + 15 has no x^2 term.

LiIIiam0216 Mar 21, 2024

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29

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help algebra

In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.
Fill in the blanks to make a true equation:
\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7} read more ..

LiIIiam0216 Mar 21, 2024

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23

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Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}

hasAquestion ●

LiIIiam0216 Mar 21, 2024

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28

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Series

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $4.$ The sum of the cubes of all the terms is $10.$ Find the common ratio.

LiIIiam0216 Mar 21, 2024

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41

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+2653

Function problem

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

LiIIiam0216 Mar 21, 2024

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44

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+2653

Algebra

Evaluate a^3 - \dfrac{1}{a^3} if a^2 - a - 1 = 0.

LiIIiam0216 Mar 21, 2024

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21

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+2653

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} = 4 and a_{10} = 1, then find a_6.

LiIIiam0216 Mar 21, 2024

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