All Questions ⁺⁰235731 Questions

0

36

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+1533

Counting digits

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability that Sam chooses read more ..

parmen Mar 10, 2024

-1

15

1

+743

Polygon

Let P1 P2 P3 ... P10 be a regular polygon inscribed in a circle with radius 1. Compute
(P1 P2)^2 + (P2 P3)^2 + ... + (P1 P10)^2.
The sum includes all terms of the form (Pi Pi + 1)^2, where 1 <= i <= 9. We read more ..

bingboy Mar 10, 2024

0

9

1

+743

Semicircle

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $BC = \sqrt{3}$, then find $AB$. read more ..

bingboy Mar 10, 2024

-1

29

1

+1443

help solve

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $7$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

blackpanther Mar 10, 2024

-1

24

1

+1443

Algebra

If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

blackpanther Mar 10, 2024

-1

12

1

+1443

Algebra

Five times a number is divided by $2$ more than that number. If the result is $6,$ then what was the original number?

blackpanther Mar 10, 2024

-1

41

0

+1443

help algebra

Find all values of $a$ that satisfy the equation
\[\frac{a}{3} + 1 = \frac{a + 3}{a} - \frac{a^2 + 2}{a}.\]

blackpanther Mar 10, 2024

Mar 9, 2024

0

26

1

+479

Rotation

Let A1, A2, A3., ..., A15, A16 be a regular polygon. A rotation centered at A4 with an angle of X takes A3 to A5. Given that X < 180, find X in degrees.

ChiIIBill Mar 9, 2024

0

14

1

+479

dilation

A dilation with scale factor k takes figure A to figure B. Find the sum of all possible values of k.

Figure read more ..

ChiIIBill Mar 9, 2024

0

29

1

+479

Dilation

Point B is the image of point A under a dilation with center O. If OB = 60, and the scale factor of the dilation is 4, then what is OA?
O---A-----B

ChiIIBill Mar 9, 2024

0

23

1

+479

Parabola

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a \cdot b \cdot c.$ (The grid lines are one unit apart.)
The graph passes through (-3,5), (-1,7), and (2,-1).

ChiIIBill Mar 9, 2024

0

24

1

+704

Coordinates

Find the coordinates of the center of the circle.

booboo44 Mar 9, 2024

0

17

1

+704

Geometry

In trapezoid $EFGH,$ $\overline{EF} \parallel \overline{GH},$ and $P$ is the point on $\overline{EH}$ such that $EP:PH = 1:2$. If the area of triangle $EF = 3$ and $HG = 10$, and the height of the trapezoid is $6$, then find the area of triangle read more ..

booboo44 Mar 9, 2024

0

29

1

+704

Quadrilaterals

Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EAD$ is $9.$ If $AE:EB = 3:4$ and the height of parallelogram $ABCD$ is $10$, read more ..

booboo44 Mar 9, 2024

0

18

1

+704

Trapezoid

In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.

booboo44 Mar 9, 2024

0

29

1

+850

Line Equation

Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common divisor $1$.) read more ..

magenta Mar 9, 2024

0

20

0

+850

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.

magenta Mar 9, 2024

0

29

0

+850

Geometry

In the diagram, chords $\overline{XY}$ and $\overline{VW}$ are extended to meet at $U.$ If $\angle U = 30^\circ$, minor arc $XY$ is $180^\circ$, and minor arc $VW$ is $90^\circ$. Find arc $WY$, in degrees.

magenta Mar 9, 2024

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