All Questions ⁺⁰236343 Questions

-4

22

1

+204

Algebra

Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___

BRAlNBOLT Jun 27, 2024

-3

13

1

+204

Graphing

The parabola y = ax^2 + bx + c is graphed below. Find a + b + c. (The grid lines are one unit apart.)
The parabola passes through (-2,8), (0,0), and (2,8).

BRAlNBOLT Jun 27, 2024

-3

22

1

+204

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

BRAlNBOLT Jun 27, 2024

0

16

2

+845

Algebra

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

gnistory Jun 27, 2024

0

11

1

+845

Algebra

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

gnistory Jun 27, 2024

0

19

1

+845

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 $a_6.$

gnistory Jun 27, 2024

0

12

3

+8

Difficult counting problem NEED HELP

Each square of a 4 × 4 gameboard is colored either red or black. Two colorings are considered equivalent if one can be obtained from the other by a rotation, but mirror images are not necessarily the same. How many different gameboard read more ..

mathlunatic Jun 27, 2024

0

25

1

+845

Algebra

Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.

gnistory Jun 27, 2024

0

19

1

+845

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

NotThatSmart ●

gnistory Jun 27, 2024

0

12

1

+868

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

NotThatSmart ●

eramsby1O1O Jun 27, 2024

0

14

1

+868

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

eramsby1O1O Jun 27, 2024

0

22

1

+868

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

AsianMathGuy ●

eramsby1O1O Jun 27, 2024

0

21

1

+868

Geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

eramsby1O1O Jun 27, 2024

0

19

1

+1560

Geometry

Two circles intersect at two points, $P$ and $Q$. The equations of the two circles are $x^2 + (y - 1)^2 = 1$ and $(x - 1)^2 + y^2 = 1$. Find the length PQ.

blackpanther Jun 27, 2024

0

17

0

+1560

Geometry

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

blackpanther Jun 27, 2024

0

11

1

+1560

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

NotThatSmart ●

blackpanther Jun 27, 2024

0

16

1

+1839

Algebra

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

ABJeIIy Jun 27, 2024

0

13

1

+1839

Algebra

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

NotThatSmart ●

ABJeIIy Jun 27, 2024

0

16

1

+1839

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

NotThatSmart ●

ABJeIIy Jun 27, 2024

0

16

3

+1839

Algebra

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

ABJeIIy Jun 27, 2024

0

16

1

+845

help help

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

gnistory Jun 27, 2024

0

22

0

+845

help algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

gnistory Jun 27, 2024

0

19

0

+845

need help

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

gnistory Jun 27, 2024

0

24

2

+845

help me

The roots of Ax^2+Bx+1 are the same as the roots of (x - 2)(x + 2). What is A+B?

gnistory Jun 27, 2024

0

11

2

+64

halp ASAP

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $a^2 b^3 = 24$. What is the value of B in this ordered pair?

ghistory Jun 27, 2024

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