All Questions ⁺⁰236007 Questions

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+868

Algebra

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

eramsby1O1O May 16, 2024

-1

24

0

+868

Algebra

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?

eramsby1O1O May 16, 2024

-1

24

0

+868

Algebra

There exists a polynomial f(x) and a constant k such that
(x^2 - 2x - 5) f(x) = x^4 - 2x^3 + kx^2
What is k?

eramsby1O1O May 16, 2024

-1

34

0

+868

Algebra

Determine all of the following for f(x) \cdot g(x), where f(x) = -7x^4-3x^2 + 2 and g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.
Leading term:
Leading coefficient:
Degree: read more ..

eramsby1O1O May 16, 2024

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24

0

+868

Algebra

Let f be a cubic polynomial such that f(0) = 5, f(2) = 8, f(3)=13, and f(7) = -5. What is the sum of the coefficients of f?

eramsby1O1O May 16, 2024

0

16

0

+868

Algebra

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^6 - 17x^5 + 2x^4 + 6x^3 + 11x^2 - 8x + 1.

eramsby1O1O May 16, 2024

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29

1

+868

Geometry

A circle is inscribed in a quarter-circle, as shown below. If the radius of the quarter-circle is $4,$ then find the radius of the circle.

eramsby1O1O May 16, 2024

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27

0

+868

Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

eramsby1O1O May 16, 2024

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39

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+868

Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

eramsby1O1O May 16, 2024

May 15, 2024

0

32

0

+868

Algebra

Consider the two expressions $\frac{6x^3+19x^2-4x+5}{2x+1}$ and $5x^2-8+\frac1{2x+1}.$
a) Show that the two expressions represent equal numbers when $x=10.$
b) Explain why these two expressions do read more ..

eramsby1O1O May 15, 2024

+1

14

1

+86

Extremely Hard Algebra Question. please help!

I've been working on this problem a while and I'm quite stuck. Could somebody please help me?
Suppose are all linear functions, and and are defined by
This read more ..

eramsby1010 May 15, 2024

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15

0

+868

Math

A particle moves so that it is at (2t, t^2) at time t. Find the speed of the particle, measured in unit of distance per unit of time.

eramsby1O1O May 15, 2024

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22

0

+868

Counting

Two numbers are independently selected from the set of positive integers less than or equal to 3. What is the probability that the sum of the two numbers is greater than their product? Express your answer as a common fraction.

eramsby1O1O May 15, 2024

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19

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+868

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

eramsby1O1O May 15, 2024

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34

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+868

Math problem

If x and y are positive integers for which 3x + 2y + xy = 18 + 7x + 5y, then what is x + y?

eramsby1O1O May 15, 2024

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30

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+868

Help with math

A mathematician works for t hours per day and solves p problems per hour, where and are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve p + 8 problems per hour. In fact, he only read more ..

eramsby1O1O May 15, 2024

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24

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+868

Polar graph

Consider the graph of r = theta for theta > 0 given in radians, also known as the Archimedean spiral. Prove that the intersections of this graph with the graph r = -theta are equidistant from each other. What is that distance?
Here's the picture read more ..

eramsby1O1O May 15, 2024

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22

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+868

Trig question

Let a be a real number such that 0 < a < \frac{\pi}{2}. Show that \left(\sin(a)\right)^7 + \left(\cos ( a)\right)^7< 2 sin(a)^4 cos(a)^4.

eramsby1O1O May 15, 2024

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17

2

+5

Alcumus help

What is the sum of all integer values of such that is true?

MEXICO May 15, 2024

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20

1

+868

Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

eramsby1O1O May 15, 2024

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22

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+868

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

eramsby1O1O May 15, 2024

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25

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+868

Geometry

In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.

eramsby1O1O May 15, 2024

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23

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+868

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

eramsby1O1O May 15, 2024

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13

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+18

this is so confusing...

a-> =<−3,−5> and b-> =<1,4⟩.
Represent a-> +b-> using the parallelogram method.
Use the Vector tool to draw the vectors, complete the parallelogram method, and draw a-> +b-> .
To read more ..

FireflySky May 15, 2024

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18

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+868

Geometry

In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 1:1, and let N be the point on \overline{EH} such that HN:NE = 1:1. Line segments \overline{FH} and \overline{GM} intersect at P, and line segments \overline{FH} and GN intersect read more ..

eramsby1O1O May 15, 2024

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