All Questions ⁺⁰237827 Questions

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244

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help plz

Let a and b be the roots of 7x^2 - x - 3 = x^2 - 4x + 5. Find (1 + a + a^2 + a^3 +.....) (1 + b + b^2 + b^3 +.....).

Guest Oct 22, 2022

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228

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counting

How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable and the boxes are not distinguishable?

Guest Oct 22, 2022

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225

3

algebra

If x^5 - x^4 + x^3 - px^2 + qx + 14 is divisible by both x+2 and x-1, then find p and q.

Guest Oct 22, 2022

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233

1

Question

A function f is defined by for all complex numbers z, where and are complex numbers and i^2=-1. Suppose that f(1) and f(i) are both real. What is the smallest possible value of ?

Guest Oct 22, 2022

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232

2

question

Let andbe complex numbers such that
What is the product of the minimum and maximum possible values of

Guest Oct 22, 2022

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228

1

Help

A function f is defined by . How many values of z satisfy both |z| = 5 and f(z)=z?

Guest Oct 22, 2022

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265

2

help counting

Six children are each offered a single scoop of any of 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 each flavor of ice cream is selected by at least read more ..

Guest Oct 22, 2022

Oct 21, 2022

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239

2

sums

Let S = 1/2^3 - 1/4^3 + 1/6^3 - 1/8^3 + ...
and
T = 1/1^3 - 1/3^3 + 1/5^3 - 1/7^3 + ...
read more ..

Guest Oct 21, 2022

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231

1

function

If f(x) = (ax + b)/(cx + d), abcd \neq 0, and f(f(x)) = 2x/(1 - x) for all x in the domain of f, what is the value of a + d?

Guest Oct 21, 2022

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270

1

algebra

What is the largest value of k such that the equation 6x - x^2 = k has at least one real solution?

Guest Oct 21, 2022

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256

1

polynomial

Let a and b real numbers such that x^4+2x^3-4x^2+ax+b = (Q(x))^2 for some polynomial Q(x). What is the value of a + b?

Guest Oct 21, 2022

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208

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geometry

In the figure, DC is parallel to AB. We have DCA = 40 and ACB = 73. Find ABC.

Guest Oct 21, 2022

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251

1

help

Which of the following is the equation of the line that passes through the point begin ordered pair, negative 6, 1, end ordered pair and has a slope of -1/2?

Guest Oct 21, 2022

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233

2

number theory

In the prime factorization of 12! + 15! + 18! + 21! + 24!, what is the exponent of 3?

Guest Oct 21, 2022

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223

1

Question

Let be complex numbers such that What is the product of the min and max of z_3?
I dont know where to start here.

Guest Oct 21, 2022

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241

1

help

A function f is defined by . How many values of x satisfy both |x| = 5 and f(x) = x.
I got 0 but I don't think it was correct. Could someone help me out and tell me how I did it wrong

Guest Oct 21, 2022

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187

0

roots

Let r and s be the roots of 3x^2+4x-12=0=2x^2+6x-5. Find r^2 + s^2

Guest Oct 21, 2022

0

257

1

geometry

Let AB be a diameter of a circle, and let C be a point on the circle such that AC=8 and BC=4 The angle bisector of ACB intersects the circle at point M Find CM.

Guest Oct 21, 2022

0

269

2

Sale price and Discounts

The sales tax for an item was $11.40 and it cost $380 before tax. Find the sales tax rate. Write your answer as a percentage.

Guest Oct 21, 2022

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230

1

algebra

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

Guest Oct 21, 2022

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223

1

complex numbers

Simplify (1-3i)(1-i)(1+i)(1+2i)(1-4i).

Guest Oct 21, 2022

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221

1

number theory

For how many positive integers n less than 100 is 5^n+8^{n+1}+11^{n+2}+5^{n+2} a multiple of 6?

Guest Oct 21, 2022

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289

1

0.4 is mulitipled by something to make 4

0.4 is mulitipled by something to make 4

(what is the something?)

Guest Oct 21, 2022

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