Hi6942O

199 Questions
13 Answers

0

1

0

+820

Algebra

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

Hi6942O Sep 8, 2024

0

1

0

+820

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

Hi6942O Sep 8, 2024

0

1

1

+820

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

Hi6942O Sep 6, 2024

+1

1

1

+820

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

Hi6942O Sep 6, 2024

0

1

0

+820

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
\[a_n = a_{n - 1} + a_{n - 2}\]
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

Hi6942O Sep 5, 2024

0

1

1

+820

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

Hi6942O Sep 5, 2024

0

2

0

+820

Number Theory

Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{2}{17},
without a calculator.

Hi6942O Sep 2, 2024

0

1

0

+820

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 = 22$ and $a_2 + a_4 = 17$, then find $a_1$.

Hi6942O Aug 28, 2024

0

2

1

+820

Algebra

Let x and y be complex numbers. If x + y = 2 and xy = 5 - x^2 - y^2, then what is x^2 + y^2?

Hi6942O Aug 28, 2024

0

1

1

+820

Algebra

Let a and b be complex numbers. If a + b = 4 and a^2 + b^2 = 6 + ab, then what is a^3 + b^3?

Hi6942O Aug 28, 2024

0

1

0

+820

Algebra

Find x if \log_2 (\log_3 x) = \log_3 (\log_2 x).

Hi6942O Aug 23, 2024

0

4

0

+820

Algebra

Suppose a\neq 0. Compute \log_{8a} b in terms of a and b.

Hi6942O Aug 23, 2024

0

1

1

+820

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

Hi6942O Aug 21, 2024

0

2

1

+820

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

Hi6942O Aug 21, 2024

0

3

0

+820

Geometry

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

Hi6942O Aug 17, 2024

0

1

1

+820

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

Hi6942O Aug 16, 2024

0

3

1

+820

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

Hi6942O Aug 16, 2024

0

1

1

+820

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

Hi6942O Aug 13, 2024

0

4

1

+820

Geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Hi6942O Aug 13, 2024