All Questions ⁺⁰237321 Questions

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43

1

+1930

Integers

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 5} = \frac{3b}{5}.

tomtom Dec 19, 2023

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43

1

+1930

Complex numbers

We can represent complex numbers geometrically by plotting them on the "complex plane", just like we plot points on the Cartesian plane. The real part of the complex number is the horizontal coordinate and the imaginary part is the vertical coordinate. read more ..

tomtom Dec 19, 2023

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39

3

+1930

Factoring

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 21m + 6n + 15m - 5n + ___

tomtom Dec 19, 2023

0

43

2

+1930

Algebra

Fill in the blanks with real numbers:
(sqrt(3) + i)*6*(6 + i)^4 = ___ + ___ i.

tomtom Dec 19, 2023

+1

49

3

+77

Probability Question, Please Help ASAP!

Peeyuu is giving out 8 identical chocolates to her 5 friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly 1 chocolate?
Thanks a whole lot for the help guys...
<read more ..

NotLatePY Dec 19, 2023

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37

3

+14

Hi please help!

Write the number "five hundredths, six thousandths, forty-two millionths" as a decimal.

Ayobruh Dec 19, 2023

Dec 18, 2023

0

56

1

+1348

Angle bisectors

Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees.

sandwich Dec 18, 2023

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64

1

+1348

Angle bisectors

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BZ$.

sandwich Dec 18, 2023

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65

1

+1348

Angle bisectors

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BC$.

sandwich Dec 18, 2023

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25

3

+14

The entries in a certain row of Pascal's triangle are

The entries in a certain row of Pascal's triangle are
1, n,...,n,1
The average of the entries in this row is 2048. Find n
i originally got 2047 but that was wrong

Galactic Dec 18, 2023

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39

1

+1348

triangle

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ read more ..

sandwich Dec 18, 2023

0

33

3

+14

Pascal’s triangle is suffering, please send help

For the positive integer n, the rational number r satisfies Express r in terms of n (your problem should be as simplified as possible).

Galactic Dec 18, 2023

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57

1

+1348

triangle

Find the inradius of trianlge ABC.
Find the circumradius of triangle ABC.

sandwich Dec 18, 2023

0

46

1

+1348

triangle

For the triangle below, let $x$ be the area of the circumcircle, and let $y$ be the area of the incircle. Compute $x - y.$ read more ..

sandwich Dec 18, 2023

0

40

1

+1678

Simplify

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} + \frac{1}{\sqrt{18}}.

wiseowl Dec 18, 2023

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25

1

+1678

Quadratic

Let $r$ and $s$ be the roots of $2x^2 + 5x - 13 = x^2 - 4x + 7.$ Find $r^2 + s^2.$

wiseowl Dec 18, 2023

0

53

1

+1678

Simplify

Simplify the expression
\frac{3}{\sqrt{2}} + \frac{1}{\sqrt{18}} - \frac{6}{\sqrt{3}} + \frac{9}{\sqrt{2}}

wiseowl Dec 18, 2023

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