tomtom

478 Questions
15 Answers

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coordinates

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.

tomtom Apr 24, 2024

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coordinates

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.

tomtom Apr 24, 2024

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Coordinates

Two circles intersect at two points, $P$ and $Q$. The equations of the two circles are $x^2 + (y - 1)^2 = 1$ and $(x - 1)^2 + y^2 = 1$. Find the length PQ.

tomtom Apr 24, 2024

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coordinates

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = x + 3, and A = (7,1).

tomtom Apr 24, 2024

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help with coordinates

The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.

tomtom Apr 24, 2024

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Help geometry

In triangle PQR, M is the midpoint of \overline{QR}. Find PM.

tomtom Apr 10, 2024

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Need help

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

tomtom Apr 10, 2024

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Help trapezoid

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

tomtom Apr 10, 2024

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Help plz

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

tomtom Apr 10, 2024

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Constant term

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

tomtom Mar 31, 2024

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System

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

tomtom Mar 31, 2024

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Coefficient

Expand (x^2 + 1/x)*(x + x^4)^3.

tomtom Mar 31, 2024

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Expand

Expand (x^2 + 1/x)*(x + x^4)^3.

tomtom Mar 31, 2024

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counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

tomtom Mar 30, 2024

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counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

tomtom Mar 30, 2024

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help geometry

An isosceles triangle has side lengths $8$ cm, $10$ cm and $10$ cm. The longest side of a similar triangle is $20$ cm. What is the perimeter of the larger triangle, in centimeters?

tomtom Mar 30, 2024

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Algebra

Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.

tomtom Mar 25, 2024

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Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 4 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 40 miles per hour, the trip takes 5 hours. How many read more ..

tomtom Mar 25, 2024