All Questions ⁺⁰236007 Questions

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Geometry

Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $CD = 34$, then find the minimum length of $CQ$.

RedDragonl May 14, 2024

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26

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+868

Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

eramsby1O1O May 14, 2024

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Geometry

In triangle PQR, M is the midpoint of \overline{QR}. Find PM.

eramsby1O1O May 14, 2024

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+868

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, and BC read more ..

eramsby1O1O May 14, 2024

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Geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

eramsby1O1O May 14, 2024

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Preclac

Let x and y be two perpendicular unit vectors.
(a) Find a formula for the magnitude of an arbitrary linear combination ax+by
of x and y in terms of a and b.
(b) Find the precise condition on a,b,c and d under which the linear combinations read more ..

LearningCat May 14, 2024

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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.

eramsby1O1O May 14, 2024

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Help me

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 $a + b$.

eramsby1O1O May 14, 2024

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quadratic roots

The quadratic has the following unexpected property: the roots, which are and , are one less than the final two coefficients. Now find a quadratic with leading term such that the final two coefficients read more ..

eramsby1010 May 14, 2024

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+1234

Quadratic Functions

What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?

Akhain1 May 14, 2024

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+1234

Quadratic Function

If s is a real number, then what is the smallest possible value of 2s^2 - 8s + 19 - 7s^2 - 8s + 20?

Akhain1 May 14, 2024

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+1234

Roots of Quadratic

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 5x + 12. Compute 1/(a^2 - 4) + 1/(b^2 - 4).

Akhain1 May 14, 2024

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Quadratic Functions

If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?

Akhain1 May 14, 2024

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+868

help with math

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

eramsby1O1O May 14, 2024

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Need help

A line has a slope of $m,$ and its $y$-intercept is $(0,b)$. If $m = 8$ and $b = 14,$ then what is the $x$-intercept of the line?

eramsby1O1O May 14, 2024

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Need help

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

eramsby1O1O May 14, 2024

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+868

Coordinates question

Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 8x - 3y$.

eramsby1O1O May 14, 2024

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Hard Trig

Among all pairs of real numbers such that with , Oleg randomly selected a pair . Compute the probability that .

eramsby1010 May 14, 2024

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+868

help with coordinates

A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

eramsby1O1O May 14, 2024

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+868

Algebra

The quadratic equation $x^2+4mx+m = 2x - 6$ has exactly one real root. Find the positive value of $m$.

eramsby1O1O May 14, 2024

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C&P Problem

Two distinct positive integers from 1 to 50 inclusive are chosen. Let the sum of the integers equal S and the product equal P. What is the probability that P + S is one less than a multiple of 5?

eramsby1010 May 14, 2024

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+68

Precalculus

LearningCat May 14, 2024

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Complex Number Arithmetic

eramsby1010 May 14, 2024

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Particle Speed

A particle moves so that it is at at time Find the speed of the particle, measured in unit of distance per unit of time.

eramsby1010 May 14, 2024

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Another Simon's Favorite Factoring Trick Problem

Two numbers are independently selected from the set of positive integers less than or equal to 5. What is the probability that the sum of the two numbers is greater than their product? Express your answer as a common fraction.

eramsby1010 May 14, 2024

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