All Questions ⁺⁰236089 Questions

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38

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+1768

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

bader Apr 19, 2024

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41

0

+1768

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

bader Apr 19, 2024

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33

0

+1768

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

bader Apr 19, 2024

0

46

0

+1768

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

bader Apr 19, 2024

0

38

0

+1839

Geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

ABJeIIy Apr 19, 2024

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30

0

+1839

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

ABJeIIy Apr 19, 2024

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19

1

+20

answer pls

y=ax^2+bx+c is graphed as a parabola
The parabola is graphed below. Find a+b+c. (The grid lines are one unit apart.)
a+b+c=

gaberiellz Apr 19, 2024

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35

0

+1768

Algebra

The graph of y=f(x) is shown in red below. Find f(-2).

bader Apr 19, 2024

0

30

0

+1768

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

bader Apr 19, 2024

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29

0

+1768

Probability

Raina places the following balls into a bag. She then 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 3 orange balls and 2 purple read more ..

bader Apr 19, 2024

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21

1

+12

Geometry Problems

difficult questions!
1.

2.
<#> 3.<#> read more ..

wendigo Apr 19, 2024

Apr 18, 2024

0

30

0

+2653

Algebra

The function $f(x,y)$ gives an ordered pair as output. It is defined according to the following rules:
* If $x > 4$, $f(x,y) = (x - 4,y)$.
* If $x \le 4$ but $y > 4$, $f(x,y) = (x,y - 4)$.
* Otherwise, $f(x,y) = (x + y + 11, read more ..

LiIIiam0216 Apr 18, 2024

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33

0

+2653

Algebra

Find all real numbers $x$ such that $f(x) = f(f(x))$, where $f(x) = x^2 - 3x + x^3 - 7x^2 + 5x.$

LiIIiam0216 Apr 18, 2024

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29

1

+2653

Algebra

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

LiIIiam0216 Apr 18, 2024

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35

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+2653

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

LiIIiam0216 Apr 18, 2024

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18

1

+2653

Probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probablility that all three pieces are shorter than 2 units?

LiIIiam0216 Apr 18, 2024

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37

1

+2653

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

LiIIiam0216 Apr 18, 2024

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39

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+2653

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

LiIIiam0216 Apr 18, 2024

0

28

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+1234

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

Akhain1 Apr 18, 2024

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22

1

+1234

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

Akhain1 Apr 18, 2024

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37

1

+1234

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

Akhain1 Apr 18, 2024

0

25

1

+355

PLS HELP ASAP

Find the number of ordered pairs of integers such that

Lilliam0216 Apr 18, 2024

0

25

1

+1768

Algebra

Our badminton team has finished $60\%$ of its season. So far, we have won $40\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

bader Apr 18, 2024

0

31

1

+1768

Counting

Three adults and three children are to be seated at a circular table. In how many different ways can they be seated if each child must be next to at least one adult? (Two seatings are considered the same if one can be rotated to form the read more ..

bader Apr 18, 2024

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