All Questions ⁺⁰237321 Questions

0

36

2

+1729

Parabola

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a + b + c$. (The grid lines are one unit apart.)
The parabola passes through (-3,7), (-1,5), and (2,8).

parmen Jan 12, 2024

0

37

1

+1729

Algebra

Fill in the blanks with numbers to make a true equation
3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 = __ (x + __)^3 + __(x + __)^2 + __x + ___

parmen Jan 12, 2024

0

49

1

+4

Exponential word problem

There are 128 teams entered in a basketball tournament. Half of the teams are eliminated each round. How many teams are left after 4 rounds

yoshushplease Jan 12, 2024

0

43

1

+1556

Quadratic

Find the minimum value of the expression $x^2+y^2+2x-4y+8+10x-12y$ for real $x$ and $y$.

ElectricPavlov ●

kittykat Jan 12, 2024

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44

1

+1678

bisector

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

wiseowl Jan 12, 2024

-1

38

2

+1782

Probability question

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

blackpanther Jan 12, 2024

-1

47

1

+1678

Bisector

In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction. read more ..

wiseowl Jan 12, 2024

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59

2

+1678

Bisector

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.</ read more ..

wiseowl Jan 12, 2024

0

66

1

+15

Arithmetic Questions

I have three questions:
1. Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = -2$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 1$, then find $a_1$.
2. Find read more ..

NotACalculator123 Jan 12, 2024

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31

2

+1776

Rates

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $5$ km behind, and Foley is $6$ km behind. When Edith finishes the race, how far read more ..

bader Jan 12, 2024

0

63

1

+1776

Compute

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}

bader Jan 12, 2024

0

58

1

+1776

Compute

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3}

bader Jan 12, 2024

0

49

0

+1776

Logarithm

Find $x$ if \log_2 (\log_3 x) = 2 \log_2 x.

bader Jan 12, 2024

+1

57

1

+1348

Triangle Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

sandwich Jan 12, 2024

+1

40

1

+81

Number Theory

How many positive integers less than 2024 cannot be expressed as the difference of the squares of two positive integers?
What I have deduced so far is that the number cannot be a perfect square, it cannot be an odd number, and it has to be in the read more ..

moneydude242 Jan 12, 2024

0

41

1

+1348

Altitudes

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?

sandwich Jan 12, 2024

0

44

1

+1348

Angles

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

sandwich Jan 12, 2024

Jan 11, 2024

0

42

2

+1678

Domain

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

wiseowl Jan 11, 2024

0

39

1

+1678

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?

wiseowl Jan 11, 2024

0

43

4

+1678

Algebra

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

wiseowl Jan 11, 2024

0

40

1

+1930

help plz

Syd chooses two different primes, both of which are greater than 20, and multiplies them. The resulting product is less than 800. How many different products could Syd have ended up with?

ElectricPavlov ●

tomtom Jan 11, 2024

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