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onyuIee
Username
onyuIee
Score
217
Membership
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Questions
54
Answers
1
54 Questions
1 Answers
0
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+217
Geometry
In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.
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onyuIee
23
mins ago
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+217
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 ..
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onyuIee
8 hours ago
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+217
Algebra
Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.
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onyuIee
Aug 13, 2024
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+217
Algebra
Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m.
read more ..
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onyuIee
Aug 13, 2024
0
1
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+217
Algebra
Solve the inequality 4t^2 \le -9t + 12 - 4t + 23 + (2t - 1)(2t + 1). Write your answer in interval notation.
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onyuIee
Aug 12, 2024
0
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+217
Algebra
Solve the inequality
\frac{3-z}{z+1} \ge 2(z + 4).
Write your answer in interval notation.
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onyuIee
Aug 12, 2024
0
1
1
+217
Algebra
When the same constant is added to the numbers $60,$ $120,$ and $140,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
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onyuIee
Aug 9, 2024
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+217
Algebra
A geometric sequence has $400$ terms. The first term is $1000$ and the common ratio is $-\frac{8}{9}.$ How many terms of this sequence are greater than $1?$
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onyuIee
Aug 9, 2024
0
1
1
+217
Algebra
Find the sum of all positive integers less than 1000 ending in 3 or 4 or 6 or 9.
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onyuIee
Aug 9, 2024
0
1
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+217
Geometry
A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.
onyuIee
Aug 8, 2024
0
1
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+217
Counting
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?
onyuIee
Aug 6, 2024
+1
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1
+217
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
+1
1
1
+217
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
0
1
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+217
Algebra
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.
onyuIee
Aug 3, 2024
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We need the numerator to be nonzero, so the largest possible value not in the domain is x = 2.
onyuIee
Aug 12, 2024