nathanl6656

17 Questions
0 Answers

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6

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+60

help with geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

nathanl6656 Apr 10, 2024

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5

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+60

help plz

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

nathanl6656 Apr 10, 2024

0

5

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+60

need help

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

nathanl6656 Apr 10, 2024

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5

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+60

Triangle

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?

nathanl6656 Apr 10, 2024

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6

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+60

math problem

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 $a + b$.

nathanl6656 Mar 24, 2024

0

7

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+60

Algebra

Let $x$ and $y$ be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

nathanl6656 Mar 24, 2024

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8

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+60

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

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10

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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

9

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+60

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

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4

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+60

Venn Diagram

I need a Venn Diagram for this
Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are $100$ dogs in the school.
$45$ read more ..

nathanl6656 Jan 13, 2024

-1

6

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Polygon

The regular polygon below is cut out of a flat piece of cardboard. The polygon is then placed back into the hole.
In how many ways can the polygon be placed back into the hole, if the polygon can be rotated, but not reflected? read more ..

nathanl6656 Jan 13, 2024

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13

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+60

Quadratic

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

nathanl6656 Jan 13, 2024

0

13

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+60

Quadratic

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?

nathanl6656 Jan 13, 2024

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15

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+60

Domain

Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2}} - \sqrt{5x+6-11}$.

nathanl6656 Jan 13, 2024

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12

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Function

Let $A(t) = 3 - 5t^3 \cdot 4 \cdot 2^t$. Find $A(2) - A(1)$.

nathanl6656 Jan 12, 2024

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10

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+60

Domain

Let
\[f(x) = \frac{2x + 3}{x^2 + 7}.\]
Find the domain of $f$. Give your answer using interval notation.

nathanl6656 Jan 12, 2024