All Questions ⁺⁰235719 Questions

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42

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+743

Equation

Find all real numbers a that satisfy \frac{1}{64a^3 + 7} - 7 = 0.

bingboy Feb 20, 2024

0

17

1

+1364

Algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does read more ..

sandwich Feb 20, 2024

0

3

1

+1364

Real numbers

Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas. read more ..

sandwich Feb 20, 2024

0

2

0

+1439

Trapezoid

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

kittykat Feb 20, 2024

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28

1

+400

Algebra

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

omgitsrne Feb 20, 2024

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23

1

+400

System

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab^2 = 4. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)

omgitsrne Feb 20, 2024

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41

1

+1768

Coefficient

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.

bader Feb 20, 2024

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32

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+1768

Solutions

How many solutions are there to the equation
u + v + w + x + y + z = 7
where u, v, w, x, y, and z are nonnegative integers, and x is at most 2 or y is at least 3?

bader Feb 20, 2024

0

3

1

+1911

Rates

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

tomtom Feb 20, 2024

-1

19

1

+1911

Proportion

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

tomtom Feb 20, 2024

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17

1

+1533

Angles in Triangles

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 ..

EnormousBighead ●

parmen Feb 20, 2024

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3

1

+1533

Altitudes

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

parmen Feb 20, 2024

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15

1

+1533

triangles

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.

parmen Feb 20, 2024

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16

2

+50

Converting polar coordinates to Cartesian coordinates?

I have found two solutions to my problem in polar coordinates, but have to submit them to Cartesian coordinate form. How do I convert them?
Point
Point

helloworldhello Feb 20, 2024

+1

36

1

+0

Casework Problem!

Syd chooses two different primes, and multiplies them. If both primes are greater than 4, and the resulting product is less than 200 , then how many different products could Syd have ended up with?

ankitm1 Feb 20, 2024

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28

1

+50

Multiple polar coordinates for one coordinate?

I have a point with polar coordinates . What are three other possible polar coordinates , , and ?

helloworldhello Feb 20, 2024

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25

1

+50

How to read polar coordinates?

The following polar grid is centered at the origin, with concentric circles of positive integer radii starting at $1,$ and consecutive rays through the origin with angles of $\pi/12$ between them. How do I find the polar coordinates for the following points? read more ..

helloworldhello Feb 20, 2024

-1

39

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+1443

Lattice Points

Find the minimum distance from any lattice point to the line $y = \frac{5}{3} x + \frac{12}{7}.$

blackpanther Feb 20, 2024

-1

40

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+1443

Coordinate problem

What is the minimum possible perimeter of a triangle two of whose sides are along the $x$- and $y$-axes and such that the third contains the point $(1,1)$?

blackpanther Feb 20, 2024

-1

25

0

+1443

Coordinates

What is the area of the region bounded by the graphs of $y = |x + 2| - |x - 2|$ and $y = |x + 1| - |x - 5|$?

blackpanther Feb 20, 2024

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