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All Questions
^{+0}
233895 Questions
0
1
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+452
Algebra
All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?
siIviajendeukie
5 hours ago
0
1
0
+452
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?
siIviajendeukie
5 hours ago
Aug 5, 2024
+1
1
1
+173
Algebra
A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45
read more ..
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onyuIee
Aug 5, 2024, 7:57:13 PM
+1
1
1
+173
Algebra
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 ..
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onyuIee
Aug 5, 2024, 7:56:49 PM
0
1
0
+465
Algebra
The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4
read more ..
AnswerscorrectIy
Aug 5, 2024, 6:51:58 PM
0
1
0
+465
Algebra
Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$
AnswerscorrectIy
Aug 5, 2024, 6:34:49 PM
0
1
1
+1582
Geometry
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.
●
ABJeIIy
Aug 5, 2024, 4:31:34 PM
0
1
0
+1582
Geometry
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.
ABJeIIy
Aug 5, 2024, 4:31:19 PM
0
1
0
+719
Algebra
Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.
RedDragonl
Aug 5, 2024, 3:42:43 PM
0
1
0
+452
Algebra
Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).
siIviajendeukie
Aug 5, 2024, 2:50:26 PM
0
1
0
+719
Algebra
For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.
RedDragonl
Aug 5, 2024, 2:21:26 PM
0
1
0
+452
Counting
Catherine rolls a standard 6-sided die six times. If the product of her rolls is 60 then how many different sequences of rolls could there have been? (The order of the rolls matters.)
siIviajendeukie
Aug 5, 2024, 2:02:19 PM
0
1
0
+213
Algebra
Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.
fjeihqoO
Aug 5, 2024, 2:01:35 PM
0
1
0
+4
Algebra
There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$
justarandornperson
Aug 5, 2024, 2:00:53 PM
0
1
1
+359
Algebra
What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?
●
falafronk
Aug 5, 2024, 2:00:21 PM
0
1
0
+1175
Algebra
Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.
Akhain1
Aug 5, 2024, 1:59:34 PM
0
1
0
+2382
Number Theory
You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from
read more ..
LiIIiam0216
Aug 5, 2024, 1:59:12 PM
0
1
0
+212
Number Theory
When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When
read more ..
cooIcooIcooI17
Aug 5, 2024, 1:58:42 PM
0
1
0
+17
Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$ has exactly
Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$ has exactly $22$ positive divisors, then how many divisors does $m^2 n^2$ have?
dogsrule
Aug 5, 2024
Aug 4, 2024
0
1
0
+212
Number Theory
Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.
cooIcooIcooI17
Aug 4, 2024
0
1
0
+212
Number Theory
Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.
cooIcooIcooI17
Aug 4, 2024
0
1
0
+1175
Number Theory
On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 2 confusions and the other worth 3 confusions. There are also some coins of smaller value, but each weighs over 10
read more ..
Akhain1
Aug 4, 2024
0
1
1
+2382
Number Theory
The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?
●
LiIIiam0216
Aug 4, 2024
0
1
0
+1582
Number Theory
How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$
ABJeIIy
Aug 4, 2024
0
1
1
+815
Geometry
In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?
●
Rangcr897
Aug 4, 2024
+1
1
1
+16
Probability
Three fair quarters are tossed, and a tail appears on at least one of them. What is the probability that at least one head appears? Express your answer as a common fraction.
●
DeluluSunshine
Aug 4, 2024
0
1
0
+719
Algebra
Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(x^3)$ are drawn, at how many points do they intersect?
RedDragonl
Aug 4, 2024
0
1
0
+719
Algebra
Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?
RedDragonl
Aug 4, 2024
0
1
1
+719
Algebra
The parabola $y = ax^2 + bx + c$ is graphed below. Find $a \cdot b \cdot c.$ (The grid lines are one unit apart.)
read more ..
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RedDragonl
Aug 4, 2024
0
1
1
+719
Algebra
The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a.
read more ..
●
RedDragonl
Aug 4, 2024
0
1
1
+815
Geometry
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
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Rangcr897
Aug 4, 2024
0
1
1
+452
Algebra
Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.
●
siIviajendeukie
Aug 4, 2024
0
1
1
+452
Algebra
Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions
●
siIviajendeukie
Aug 4, 2024
0
1
1
+2382
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?
●
LiIIiam0216
Aug 4, 2024
0
1
1
+2382
Algebra
Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.
●
LiIIiam0216
Aug 4, 2024
0
1
1
+2382
Algebra
Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator
read more ..
●
LiIIiam0216
Aug 4, 2024
0
1
1
+366
help 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?
●
gnistory
Aug 4, 2024
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