All Questions ⁺⁰238158 Questions

0

66

0

+1313

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?

AnswerscorrectIy Jan 28, 2025

0

40

2

+1313

Algebra

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

AnswerscorrectIy Jan 28, 2025

0

52

1

+1313

Algebra

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

AnswerscorrectIy Jan 28, 2025

Jan 27, 2025

0

58

1

+1757

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 $ABD$.

parmen Jan 27, 2025

0

72

0

+1757

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 $BX$?

parmen Jan 27, 2025

0

48

1

+1757

Geometry

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

parmen Jan 27, 2025

0

72

0

+1757

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 $ABC.$

parmen Jan 27, 2025

+1

43

1

+448

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

MEMEG0D Jan 27, 2025

+1

48

2

+448

Algebra

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

MEMEG0D Jan 27, 2025

+5

1

52

1

+122

algebra

what is the answer 2x-49y+21x=-7

thatgirlaj Jan 27, 2025

0

68

0

+448

Algebra

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

MEMEG0D Jan 27, 2025

+1

35

1

+789

Algebra

The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.

bingboy Jan 27, 2025

+1

40

1

+789

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

bingboy Jan 27, 2025

+1

27

1

+789

Algebra

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 98% water, by weight. After two days in the sun, the water content of the berries was only 95%, by weight. What was the total weight of the berries read more ..

bingboy Jan 27, 2025

Jan 26, 2025

0

30

1

+483

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

bIueb3rry Jan 26, 2025

+1

68

0

+483

Algebra

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

bIueb3rry Jan 26, 2025

+1

65

0

+483

Algebra

My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team read more ..

bIueb3rry Jan 26, 2025

+1

37

1

+5

help plsssss

The square below is dilated by a scale factor of 44. Find the perimeter of the dilated square. Figures are not necessarily drawn to scale. the area of the square is 100. the area is 100

saanvi Jan 26, 2025

0

45

1

+972

Geometry

Let
f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

Rangcr897 Jan 26, 2025

0

41

1

+972

Geometry

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
f(x) = 2x^2-8x+1.
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

Rangcr897 Jan 26, 2025

0

53

1

+972

Geometry

For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

Rangcr897 Jan 26, 2025

0

49

1

+972

Geometry

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

Rangcr897 Jan 26, 2025

0

53

1

+448

Geometry

Let $ABC$ be a triangle. Let $X$ be a point on $\overline{AC}$ such that $\angle BXA = 90^\circ.$ If $\angle ABC = 90^\circ,$ $AX = 15,$ and $CX = 15,$ then what is $BX?$

MEMEG0D Jan 26, 2025

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