All Questions ⁺⁰236343 Questions

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Circle

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

Akhain1 Mar 15, 2024

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help parabola

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

Akhain1 Mar 15, 2024

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Parabola

Find the vertex of the graph of the equation $x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14$.

Akhain1 Mar 15, 2024

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44

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Parabola

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

Akhain1 Mar 15, 2024

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35

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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.

Akhain1 Mar 15, 2024

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Graphs

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

ABJeIIy Mar 15, 2024

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42

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Graphing question

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 ..

ABJeIIy Mar 15, 2024

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30

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Coordinates

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

ABJeIIy Mar 15, 2024

Mar 14, 2024

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Parallelogram

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 $\overline{FH}$ read more ..

Akhain1 Mar 14, 2024

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35

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Trapezoid

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.

Akhain1 Mar 14, 2024

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25

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Trapezoid

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.

Akhain1 Mar 14, 2024

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25

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Polygon

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

Akhain1 Mar 14, 2024

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30

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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 $f$?

Akhain1 Mar 14, 2024

+1

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Help

A cone is generated by rotating right triangle around side (Length of is 3). The right triangle's side lengths are 3, 4, and 5. What is the cone's total surface area?
I know the height is 3 and the radius read more ..

CPhill ●●●

jilin73 Mar 14, 2024

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+2653

geometry

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 ..

LiIIiam0216 Mar 14, 2024

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45

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Angles

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 ..

LiIIiam0216 Mar 14, 2024

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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 ..

LiIIiam0216 Mar 14, 2024

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29

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Altitudes

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

LiIIiam0216 Mar 14, 2024

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algebra

Let for all x and y such that . Find all values of a such that . Write your answer as a list separated by commas.

Akhain1 Mar 14, 2024

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28

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Function

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

Akhain1 Mar 14, 2024

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38

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Function

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

Akhain1 Mar 14, 2024

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42

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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 $x$.

Akhain1 Mar 14, 2024

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