All Questions ⁺⁰235552 Questions

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Algebra

For a certain value of k, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3
has no solutions. What is this value of k?

ChiIIBill Apr 17, 2024

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26

0

+479

Algebra

Ruth has a beaker containing a solution of $800$ mL of acid and $200$ mL of water. She thinks the solution is a little strong, so she drains $150$ mL from the beaker, adds $150$ mL of water, and stirs the solution. Ruth thinks the solution is read more ..

ChiIIBill Apr 17, 2024

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22

1

+195

Algebra

In a store window, there was a box of berries having a total weight of $200$ kg. The berries were $99\%$ water, by weight. After two days in the sun, the water content of the berries was only $80\%$, by weight. What was the total weight read more ..

Boseo Apr 17, 2024

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23

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+1768

Geometry

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

bader Apr 17, 2024

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31

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+1768

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

bader Apr 17, 2024

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41

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+1768

Geometry

In cyclic quadrilateral $PQRS,$
angle P = angle Q = angle R
Find the largest angle in quadrilateral $PQRS,$ in degrees.

bader Apr 17, 2024

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27

1

+1768

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

bader Apr 17, 2024

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36

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+1768

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

bader Apr 17, 2024

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27

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+1768

Geometry

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

bader Apr 17, 2024

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38

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+1439

Geometry

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

kittykat Apr 17, 2024

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25

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+1439

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.

kittykat Apr 17, 2024

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18

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+1439

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?

kittykat Apr 17, 2024

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31

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+1439

Algebra

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

kittykat Apr 17, 2024

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24

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+1439

Algebra

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

kittykat Apr 17, 2024

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38

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+1439

Algebra

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

kittykat Apr 17, 2024

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19

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+1439

Probability

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 ..

kittykat Apr 17, 2024

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36

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+1439

Probability

Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In other words, find the probability that XO is read more ..

kittykat Apr 17, 2024

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28

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+1439

Probability

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 ..

kittykat Apr 17, 2024

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33

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+4

How do I do this?

You spin each spinner, roll a die, and find the sum. How many different sums are possible? Spinner 1: 1,2,3,4,5,6 Die: 1,2,3,4,5,6 Spinner 2: 2,3,4

CatsVsDogs Apr 17, 2024

+1

20

1

+279

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

fjeihqoO Apr 17, 2024

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25

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+279

Probability

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

fjeihqoO Apr 17, 2024

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27

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+279

Geometry

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

fjeihqoO Apr 17, 2024

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27

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+279

help inequality

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

fjeihqoO Apr 17, 2024

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+51

dice. many dice. roll. painted.

The six faces of a cube are painted black. The cube is then cut into 6^3 smaller cubes, all the same size.
a. How many of the smaller cubes have exactly one black face?
b. How many of the smaller cubes do not have any black faces?
c. read more ..

fjeihqo0 Apr 17, 2024

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