All Questions ⁺⁰234646 Questions

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+162

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

MeIdHunter Sep 11, 2024

Sep 10, 2024

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1

+162

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

MeIdHunter Sep 10, 2024

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+864

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?

Rangcr897 Sep 10, 2024

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1

+96

Geometry

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 6 from one wall, and a distance of 6 from the other wall. Find the radius of the read more ..

bIueb3rry Sep 10, 2024

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+96

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

bIueb3rry Sep 10, 2024

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+484

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

gnistory Sep 10, 2024

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+484

Geometry

In triangle $ABC$, $AB = 10$ and $AC = 15$. Let $D$ be the foot of the perpendicular from $A$ to $BC$. If $BD:CD = 1:3$, then find $AD$.

gnistory Sep 10, 2024

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+1055

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

learnmgcat Sep 10, 2024

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2

+1055

Geometry

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

learnmgcat Sep 10, 2024

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1

+32

Geometry

Two circles are drawn, with the same center. A chord of the large circle is drawn, so that it is tangent to the small circle. If the chord has a length of 10, then find the area of the ring-shaped region that is inside the large circle but outside read more ..

surfz Sep 10, 2024

Sep 9, 2024

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+1323

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 12}

blackpanther Sep 9, 2024

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+1323

Algebra

Fill in the blanks to make a true equation:
1/(n(n + 3)(n + 5)) = __/n + ___/(n + 3) + ___/(n + 5)

blackpanther Sep 9, 2024

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+523

Geometry

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

siIviajendeukie Sep 9, 2024

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+523

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

siIviajendeukie Sep 9, 2024

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+864

Geometry

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 ..

Rangcr897 Sep 9, 2024

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+772

Need help

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 ..

RedDragonl Sep 9, 2024

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+355

Math help

Consider the set of all fractions of the form $\frac{2^m}{3^n},$ where $m$ and $n$ are integers such that $0 \le m \le n.$ For example, 1/9 and 8/27 would be included in this set, but not 32/81. What is the sum of all the numbers in this set?
<read more ..

Lilliam0216 Sep 9, 2024

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+617

Geometry

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

AnswerscorrectIy Sep 9, 2024

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2

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+617

Geometry

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

AnswerscorrectIy Sep 9, 2024

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1

+556

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

booboo44 Sep 9, 2024

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