All Questions ⁺⁰237313 Questions

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PLANE PROB, RATES

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 5 hours and 20 minutes, but when there is a wind blowing from Penthaven to Jackson at 75 miles per hour, the trip takes 6 hours. How many read more ..

Lilliam0216 Mar 2, 2024

0

37

1

+1729

Vertex

Find the vertex of the graph of the equation y = -2x^2 + 8x + 15 - 3x^2 + 7x - 25

parmen Mar 2, 2024

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38

0

+1729

Circle

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.

parmen Mar 2, 2024

0

50

1

+1729

Parabola

The graph of $y = ax^2 + bx + c$ has an axis of symmetry of $x = -1.$ If $a = 2,$ then find $b.$

parmen Mar 2, 2024

0

31

1

+1776

Function

Let $f(x) = px + q$, where $p$ and $q$ are real numbers. Find $p+q$ if $f(f(f(x))) = 64x - 105 - 30x + 70 + 32x - 12$.

bader Mar 2, 2024

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66

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+1776

Function

The function
\[f(x) = \frac{cx}{(4x - 5)(3x + 2)}\]
satisfies $f(f(x))=x$ for all real numbers $x\neq \frac{5}{4}$ and $x \neq -\frac{2}{3}$. Find $c$.

bader Mar 2, 2024

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65

0

+1776

Function

Find the real number k such that f(x) = f(k - x) for all real numbers x, where
f(x) = 3x^2 - 4x + 2x^2 + 15x.

bader Mar 2, 2024

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51

1

+1776

Polynomial

Let $b$ be a constant. What is the smallest possible degree of the polynomial $f(x) + b \cdot g(x)$, where $f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5$ and $g(x) = x^15 - 3x^14 - 2x^13 - 6x^12 + 14x - 10$?

bader Mar 2, 2024

Mar 1, 2024

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52

0

+921

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

booboo44 Mar 1, 2024

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44

1

+921

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

booboo44 Mar 1, 2024

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50

0

+1556

Probability

Triangle XYZ is equilateral, with O as its center. A point P is chosen at random. Find the probability that P is closer to point O than to any of the side lengths.

kittykat Mar 1, 2024

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64

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+1776

Polynomial

Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?

bader Mar 1, 2024

-1

27

1

+1782

Hexagon

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

blackpanther Mar 1, 2024

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37

1

+1782

Geometry

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

blackpanther Mar 1, 2024

Feb 29, 2024

+1

53

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+46

I'd like some help! Thank you

The product of four consecutive positive integers is less than . What is the least of these four numbers?
I've tried writing equations but that didn't work. Can someone help? Thank you! read more ..

greenplanet2050 Feb 29, 2024

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64

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+0

math

A consumer survey was conducted to examine patterns in ownership of tablet computers, cellular telephones, and Blu-ray players. The following data were obtained: 313 people had tablet computers, 236 had cell phones, 269 had Blu-ray players, 65 had all three, read more ..

yojoema Feb 29, 2024

+1

1

2

+1926

Roots

The solutions to
2x^2 - 10x + 13 = -17x^2 - 4x - 18
are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$

tomtom Feb 29, 2024

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