All Questions ⁺⁰235731 Questions

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Geometry

In the diagram below, $O$ is the center of the circle, and $\overline{UV}$ is a diameter. Find $\angle XYZ$, in degrees.

MeIdHunter Nov 14, 2024

Nov 13, 2024

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+834

Counting

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both contain read more ..

gnistory Nov 13, 2024

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+834

Counting

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 squares read more ..

gnistory Nov 13, 2024

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+544

Geometry

In triangle ABC, AB = BC = 3 and AC = 4. Find sin angle ACB.

cooIcooIcooI17 Nov 13, 2024

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+176

Algebra

Let x be an acute angle such that \tan x + \sec x = 3 \cos x. Find \cos x.

AUnVerifedTaxPayer Nov 13, 2024

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+176

Algebra

Let theta be an acute angle. If cos theta = 3*sqrt(5) + 7, then what is sin theta?

AUnVerifedTaxPayer Nov 13, 2024

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+30

Number Theory

What is the answer?

Sxchen1110 Nov 13, 2024

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+176

Algebra

Find the smallest real number $x$ in the domain of the function f(x) = \sqrt{(x-3)^2-(x+3)^2}.

AUnVerifedTaxPayer Nov 13, 2024

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+176

Algebra

Find the number of real numbers that are not in the domain of the function $$f(x) = \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}.$$

AUnVerifedTaxPayer Nov 13, 2024

Nov 12, 2024

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+337

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

MeIdHunter Nov 12, 2024

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+337

Algebra

Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.
(a) Is the number 1/7 in the set S?
(b) Is the number 1/4 in the set S? read more ..

MeIdHunter Nov 12, 2024

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+337

Algebra

Let $f(x) = x^2 + bx + 12 - 3x + 10$ for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.

MeIdHunter Nov 12, 2024

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+337

Algebra

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
f(p) = f(q) = f(r) = f(s) = 1
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

MeIdHunter Nov 12, 2024

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+337

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{36} + \sqrt{45}} + \frac{1}{\sqrt{39} +\sqrt{96}}

MeIdHunter Nov 12, 2024

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+176

Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find $a$.
The points are (0,8) and (0,6)

AUnVerifedTaxPayer Nov 12, 2024

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+176

Algebra

Find the sum of all real numbers $x$ that are not in the domain of the function $$f(x) = \frac{1}{x^2+7} + \frac{1}{x^3 - x^4} + \frac{1}{x^2 - 3x + 2}.$$

AUnVerifedTaxPayer Nov 12, 2024

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+176

Algebra

If $f(x)$ is a function whose domain is $[-8,8]$, and $g(x)=f\left((x^2 - 2)/(x + 1)\right)$, then the domain of $g(x)$ is an interval of what width?

AUnVerifedTaxPayer Nov 12, 2024

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+846

Geometry

Let $PQRSTUVW$ be a rectangular prism, as shown. The area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.

magenta Nov 12, 2024

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+846

Geometry

Find the total surface area and the volume of the conical frustum below.

magenta Nov 12, 2024

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+448

Geometry

The cone below has a lateral surface area of 16 \sqrt{10} \cdot \pi. Find the volume of the cone.

onyuIee Nov 12, 2024

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