All Questions ⁺⁰233683 Questions

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help functions

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

tomtom Nov 27, 2023

Nov 26, 2023

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20

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+1859

function question

Let
\[f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.\]
Find the inverse $f^{-1}(x)$.

tomtom Nov 26, 2023

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28

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need help

Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$

tomtom Nov 26, 2023

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20

1

+1859

help with algebra

Let $x \mathbin{\spadesuit} y = \frac{x^2}{y}$ for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.

tomtom Nov 26, 2023

+1

15

3

+150

Counting Problem

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 3
- The sum of the digits is 12
Please help ASAP, thanks! read more ..

BlackjackEd Nov 26, 2023

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29

2

+46

Probability Question

A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is times the probability that a freshman is elected. Everyone on the junior varsity read more ..

NotLatePY Nov 26, 2023

-1

37

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+1348

triangle

Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. What is the area of triangle $ABC$?

sandwich Nov 26, 2023

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31

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+1348

hard geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

sandwich Nov 26, 2023

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21

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+1348

help 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 Nov 26, 2023

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24

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+1348

triangle question

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

sandwich Nov 26, 2023

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need help

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 Nov 26, 2023

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35

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+1348

triangle

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

sandwich Nov 26, 2023

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29

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+1348

help with triangle

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

sandwich Nov 26, 2023

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19

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+1859

coordinates

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

tomtom Nov 26, 2023

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31

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+1859

graphing

The graph of $y = f(x)$ is shown below.
For each point $(a,b)$ that is on the graph of $y = f(x),$ the point $(3a- 7, -b + 3)$ is plotted, forming the graph of another function $y = g(x).$ As an example, the point $(-2,7)$ lies read more ..

tomtom Nov 26, 2023

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help with graph

Assume that $f(3) = 4$. Name a point that must be on the graph of $y= 1/5*f(5x + 5) - 5$.

tomtom Nov 26, 2023

-1

21

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+1678

geometry problem

In triangle $ABC$, point $X$ is on side $\overline{BC}$ such that $AX = 5,$ $BX = 5,$ and the circumcircles of triangles $ABX$ and $ACX$ have the same radius. Find the area of triangle $ABC$.

wiseowl Nov 26, 2023

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25

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+1678

geometry problem

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

wiseowl Nov 26, 2023

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31

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+1678

equilateral triangle

Triangle $DEF$ is equilateral. Find $AE.$

wiseowl Nov 26, 2023

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25

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+1678

trig question

In the diagram, $ABCD$ is a square. Find $\sin \angle PAQ.$

wiseowl Nov 26, 2023

Nov 25, 2023

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17

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+1859

Functions

(a) Let f : (-inf,0) U (0,inf) -> R be defined by f(x) = x + 1/x. Show that f has no inverse function.
(b) Let g : (0,inf) -> R be defined by g(x) = 1/x. Show that g has an inverse function.

tomtom Nov 25, 2023

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27

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+1859

graphing question

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a + b + c$. (The grid lines are one unit apart.)

tomtom Nov 25, 2023

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