All Questions ⁺⁰230619 Questions

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109

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quadratic

Let u and v be the solutions to 3x^2 + 5x + 7 = -2x^2 - 7x + 1. Find u/v +v/u.

Guest Dec 6, 2022

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107

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help trig

Calculate
\[ \arccos \sqrt{\cfrac{1-\sqrt{\cfrac{1-\sqrt{\cfrac{1-\sqrt{\cfrac{1+\cfrac{\sqrt{3}}{2}}{2}}}{2}}}{2}}}{2}}.\]
As usual, the output of an inverse trig function should be in radians.

Guest Dec 6, 2022

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115

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trig problem

Find the smallest positive -intercepts of the graph of
y = cos (12x) + cos(16x) + cos(20x)
and list them in increasing order.
Submit your answer as a list of x-coordinates from least to greatest.

Guest Dec 6, 2022

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136

1

The cost of a pair of soccer boots and a T-shirt is $175. The cost of the T-shirt and a cap is $64.

The cost of a pair of soccer boots and a T-shirt is $175. The cost of the T-shirt and a cap is $64. The cost of the pair of soccer boots is 4 times the cost of the cap. How much more does the pair of soccer boots cost than the T-shirt?

Guest Dec 6, 2022

Dec 5, 2022

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89

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Angle bisectors

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF, which intersect at I. If DI = 3, BD = 4, and BI = 8, then find the area of triangle ABC.

Guest Dec 5, 2022

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82

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Numbers

In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

Guest Dec 5, 2022

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129

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Expected value

The grid below is made up of line segments, like the line segment in red.
There are a number of paths that go from A to B in the grid, where every step goes to the right or up. If we choose a line segment at random, then what is the expected number of read more ..

Guest Dec 5, 2022

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135

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+4

53 - _____ = 56 - 27

53 - _____ = 56 - 27

paiterblader Dec 5, 2022

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127

2

Complex Numbers

Describe all solutions to zw - 3w - 2iw + 4z = 7iw + 5w + 11iz - 13 + 15i
where z and w are complex numbers.

Guest Dec 5, 2022

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139

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Algebra

Fill in the blanks to write this quadratic as the square of a binomial.

x^2 + 4x + ___

Guest Dec 5, 2022

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87

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Algebra question

Arrange the following numbers in increasing order (smallest first, biggest last):

A = 2*1/2*4*1/6
B = 12*128 read more ..

Guest Dec 5, 2022

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122

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Pascal's triangle

The entries in a certain row of Pascal's triangle are
1, n, ..., n, 1

The average of the entries in this row is 2. Find n. read more ..

Guest Dec 5, 2022

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87

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need help with identity

For a certain function f(n), the identity
(2n)/n - (2n)/(n + 1) = f(n) (2n)/n
for all nonnegative integers n. Find f(n).

Guest Dec 5, 2022

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81

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binomials

Simplify binom{100}{50}/binom{200}{51}*binom{100}{51}/binom{200}{50}

Guest Dec 5, 2022

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96

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binomials

Fill in the blanks to make the equation true (Each blank should contain a positive integer.)

\binom{n}{k} = \binom{n - 2}{k} + \binom{n - 2}{k - 1} + \binom{n - 1}{k} + \binom{n - 1}{k - 1} + \binom{n}{k - 1} + \binom{n}{k + read more ..

Guest Dec 5, 2022

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87

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binomials

For nonnnegative integers a and b, where a >= 2 and b >= 2, simplify
binom{a + b}{2} + binom{2a + b}{2} + binom{a + 2b}{2} - binom{a - b}{2}

Guest Dec 5, 2022

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137

2

help with probability

The following cards are dealt to three people at random, so that everyone gets the same number of cards. What is the probability that everyone gets a red card?

Guest Dec 5, 2022

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117

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Probability question

A bag contains five white balls and three black balls. Your goal is to draw two white balls.

(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls read more ..

Guest Dec 5, 2022

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102

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Factoring question

We are looking to factor 23x^2 + kx - 5 + x^2 - 3. Some values of k allow us to factor it as a product of linear binomials with integer coefficients. what are all such values of k?

Guest Dec 5, 2022

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117

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Probability Question

Jeffrey had a magic bag with colored rocks. There are 7 red rocks, 5 green rocks, 2 blue rocks and 6 orange rocks. If he picks 5 rocks without replacement, what is the probability of getting at least 1 blue, 1 red and 1 green rock?

Guest Dec 5, 2022

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100

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Algebra problem

A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 75% magical syrup by volume (and the rest is just water), and blue potion, which read more ..

Guest Dec 5, 2022

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124

2

help counting

Marvin the fly starts at (0,0). Each step, Marvin moves one unit right or one unit up. He is trying to get his home at (4,6). However, at (2,4) here is a frog that will eat him if he goes through that point. In how many ways read more ..

Guest Dec 5, 2022

-1

125

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help algebra

Assuming that p \neq 0 and q \neq 0, simplify pq^3^3 4p^2q^2 2pq^2^3

Assuming that and , simplify

Guest Dec 5, 2022

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107

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help algebra

If I give my brother 5 dolalrs, then we will have the same amount of money. If instead he gives me 14 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

Guest Dec 5, 2022

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