All Questions ⁺⁰235719 Questions

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help with geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

kittykat Jan 11, 2024

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27

1

+1439

Square in triangle

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

kittykat Jan 11, 2024

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26

1

+1439

Geometry problem

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 1 and QC = 4. Find sin angle PAQ.

kittykat Jan 11, 2024

+1

33

1

+290

Question ANSWER FAST PLS IM SERIOUS

Write a paragraph proof of the Corollary to Theorem 3-4.
Corollary to Theorem 3-4 if u dk:
Any rigid motion can be expressed as a composition of reflections.
If... M is a rigid motion read more ..

DS2011 Jan 11, 2024

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23

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+1678

Quadratic

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

wiseowl Jan 11, 2024

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44

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+1533

Need help with probability

The six faces of a cube are painted black. The cube is then cut into $3^3$ smaller cubes, all the same size.
(a) How many of the smaller cubes have exactly one black face?
(b) How many of the smaller cubes do not read more ..

parmen Jan 11, 2024

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18

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+1533

Digits

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability that Sam chooses read more ..

parmen Jan 11, 2024

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26

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+1533

Counting question

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $100,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

parmen Jan 11, 2024

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22

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+1911

Percent

In a store window, there was a box of berries having a total weight of $200$ kg. The berries were $95\%$ water, by weight. After two days in the sun, the water content of the berries was only $90\%$, by weight. What was the total weight read more ..

tomtom Jan 11, 2024

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24

1

+1911

help with algebra

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

tomtom Jan 11, 2024

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37

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+1443

Coordinates

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

blackpanther Jan 11, 2024

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37

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+1443

Intercepts

A line has a slope of $m,$ and its $y$-intercept is $(0,b)$. If $m = 8$ and $b = 14,$ then what is the $x$-intercept of the line?

blackpanther Jan 11, 2024

-1

28

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+1443

Numbers

Arrange the following numbers in increasing order (smallest first, biggest last):
A = 2*1/2*4*1/6
B = 12*128
C = 1*8*1/5^2 read more ..

blackpanther Jan 11, 2024

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17

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+1678

Angles

In the diagram below, we have $\overline{AB}\parallel\overline{CD}$ and $QP = QR$. If $\angle BPQ = 2x^\circ + 105^\circ$ and $\angle APR = 5x^\circ - 27^\circ$, then find $x$.

wiseowl Jan 11, 2024

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43

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+1678

Area

In triangle $ABE,$ $C$ and $D$ are points on sides $\overline{BE}.$ If $BD = 18$, $CE = 7$, $[ABC] = 13$, and $[ADE] = 22$, then find $[ACD]$.

wiseowl Jan 11, 2024

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15

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+1678

Area

In triangle $ABC,$ points $P$ and $Q$ are on side $\overline{AB},$ and point $R$ is on side $\overline{AC}.$ If $\frac{AP}{2} = \frac{PQ}{5} = \frac{QB}{11}$ and $\frac{AR}{8} = \frac{RC}{13},$ then find $\frac{[QBC]}{[CRQ]}.$

wiseowl Jan 11, 2024

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+1678

Rectangle

In rectangle $ABCD$, as shown below, $DX = XC$. Find the number of degrees in $\angle XDY.$

wiseowl Jan 11, 2024

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27

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+1364

Series

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$

sandwich Jan 11, 2024

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22

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+1364

Sequences

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 $20,$ Shirley runs screaming from the room. What number does Laverne say that read more ..

sandwich Jan 11, 2024

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