All Questions ⁺⁰230590 Questions

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Algebra

Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

ABJeIIy 6 hours ago

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+757

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.

ABJeIIy 6 hours ago

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+757

Algebra

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

ABJeIIy 6 hours ago

Apr 24, 2024

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+757

Algebra

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

ABJeIIy 9 hours ago

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+757

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?

ABJeIIy 9 hours ago

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+757

Algebra

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?

ABJeIIy 10 hours ago

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+757

Algebra

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

ABJeIIy 10 hours ago

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+757

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.

ABJeIIy 10 hours ago

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+757

Algebra

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

ABJeIIy 10 hours ago

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+182

Algebra

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

ABJelly 10 hours ago

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+1791

coordinates

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.

tomtom Apr 24, 2024, 9:07:10 PM

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+1791

coordinates

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.

tomtom Apr 24, 2024, 9:04:41 PM

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+1791

Coordinates

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.

tomtom Apr 24, 2024, 6:45:01 PM

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+1791

coordinates

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = x + 3, and A = (7,1).

tomtom Apr 24, 2024, 5:29:03 PM

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+1791

help with coordinates

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

tomtom Apr 24, 2024, 3:36:26 PM

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+112

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

Pythagorearn Apr 24, 2024, 3:05:43 PM

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+112

pls help

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

Lilliam0216 Apr 24, 2024, 3:01:19 PM

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+112

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.

Pythagorearn Apr 24, 2024, 2:17:08 PM

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+631

need help

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

LiIIiam0216 Apr 24, 2024, 2:09:15 PM

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+112

Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

Pythagorearn Apr 24, 2024, 1:45:27 PM

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+112

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

Pythagorearn Apr 24, 2024, 1:45:14 PM

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+4

HELP ME PLS

a.Given the polynomial function y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
a. Use the definition of derivative to differentiate y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
b. Find the points on the graph where the tangent line is horizontal read more ..

aoas123 Apr 24, 2024, 1:13:08 PM

Apr 23, 2024

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+112

Geometry

Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$, read more ..

Pythagorearn Apr 23, 2024

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+11

PLEASE HELP

I could use the help

justtryinpass Apr 23, 2024

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+112

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 $EFGH$

Pythagorearn Apr 23, 2024

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+112

Geometry

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

Pythagorearn Apr 23, 2024

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+631

help plz

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 Apr 23, 2024

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+631

help counting

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

LiIIiam0216 Apr 23, 2024

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+631

help help

The six faces of a cube are painted black. The cube is then cut into $3^3$ 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 read more ..

LiIIiam0216 Apr 23, 2024

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+631

need help quick

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability read more ..

LiIIiam0216 Apr 23, 2024

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+466

help geo

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

booboo44 Apr 23, 2024

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+466

help plz

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

booboo44 Apr 23, 2024

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+909

Geometry

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 ..

Akhain1 Apr 23, 2024

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+909

Geometry

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 $a + b$.

Akhain1 Apr 23, 2024

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+909

Geometry

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

Akhain1 Apr 23, 2024

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+631

i need help

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

LiIIiam0216 Apr 23, 2024

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