All Questions ⁺⁰237677 Questions

0

62

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+1662

Coordinates

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 4x + 12y.$ Find the largest possible value of $x + y.$ Give your answer in exact form using radicals, simplified as far as possible.

ElectricPavlov ●●●

wiseowl Jan 14, 2024

0

52

3

+4

help with analytical geometry

hi, sorry, I wasn't able to attend class and need some help with two questions that I'm struggling with.
1. Point is reflected over the line shown below to point B. Find the coordinates of B.
[asy]
usepackage("amsmath");read more ..

helpplease Jan 14, 2024

0

49

1

+417

Circle

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle?

nathanl6656 Jan 14, 2024

0

48

1

+417

Circle

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

ElectricPavlov ●

nathanl6656 Jan 14, 2024

0

74

0

+417

Triangle

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle BAC = 42^\circ$. Find $\angle PBC$ in degrees.

nathanl6656 Jan 14, 2024

Jan 13, 2024

+2

86

1

+17

Ordered pairs of primes

How many ordered pairs of primes (a,b) satisfy a+b=22?

ruiruima Jan 13, 2024

-1

55

1

+1808

Floor Function

Find all values of t such that \lfloor t\rfloor = 3t + 4 - \lfloor 2t \rfloor. If you find more than one value, then list the values you find in increasing order, separated by commas.

blackpanther Jan 13, 2024

-1

42

1

+1808

Floor Function

Let
f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.)

blackpanther Jan 13, 2024

-1

76

0

+1808

Inequality

(1) Let a_1, a_2, a_3 be real numbers such that
|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.
What is the largest possible value of |a_1 - a_2|?

(2) Let a_1, a_2, a_3, \dots, a_{10} be real numbers such that read more ..

blackpanther Jan 13, 2024

+13

52

2

+71

Help i am struggling a lot

Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 120 meters per hour when walking across flat ground, and 150 meters per hour when walking downhill. One day, Carissa walks across read more ..

Starry Jan 13, 2024

+1

74

1

+291

Problem

The surface area of a sphere in terms of is 3364. the radius of the sphere is . Find x.

DS2011 Jan 13, 2024

+1

55

3

+1932

Linear Graph

Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common divisor $1$.) read more ..

tomtom Jan 13, 2024

+1

72

1

+1932

Positive integers

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 13$, what is the minimal possible value of $|a - b|$?

tomtom Jan 13, 2024

+1

47

1

+1348

Sequence question

What is the 2009th term in the arithmetic sequence whose first four terms are 2, 10, 18, 26?

sandwich Jan 13, 2024

+1

46

2

+1348

Question on sequences

How many integers belong to the arithmetic sequence 13, 20, 27, 34, $\dots$, 97?

sandwich Jan 13, 2024

+1

57

2

+1348

Arithmetic sequence

The sequence 24, $a$, $b$, $c$, $d$ 60 is arithmetic. What is the value of $a+b+c+d$?

sandwich Jan 13, 2024

+1

87

1

+789

Help quadratic

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

ElectricPavlov ●

bingboy Jan 13, 2024

+1

46

2

+789

Roots of Quadratic

For what values of $j$ does the equation $(2x + 7)(x - 4) = -31 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

bingboy Jan 13, 2024

+1

58

1

+789

Quadratic Functions

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-13x+27$.

bingboy Jan 13, 2024

+1

68

0

+789

Absolute Value

Find the sum of all the values of $x$ that satisfy the system of equations $y=|x^2-6x+5|$ and $y=\frac{29}{4}-2x$.

bingboy Jan 13, 2024

+1

68

1

+1776

Domain

Help with domain plz

bader Jan 13, 2024

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