All Questions ⁺⁰236027 Questions

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+1911

inequality question

Solve the inequality x^3 + 4x > 5x^2 - 17x - x^4 + 3. Write your answer in interval notation.

tomtom Nov 25, 2023

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23

1

+1911

integers

For an integer $n$, the inequality
\[x^2 + nx + 15 < -21 - x^2 - 150 \]
has no real solutions in $x$. Find the number of different possible values of $n$.

tomtom Nov 25, 2023

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65

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+1911

Algebra

Solve the inequality
\[\frac{3-z}{z+1} \ge 2 + 7z.\]
Write your answer in interval notation.

tomtom Nov 25, 2023

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55

0

+1911

help me

Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

tomtom Nov 25, 2023

0

25

1

+1911

inequality question

Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

tomtom Nov 25, 2023

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62

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+1911

help plz

Solve the inequality $(x - 2)(x + 6) \le x^2 + 14.$ Write your answer in interval notation.

tomtom Nov 25, 2023

0

38

1

+1911

need help

Find the number of integers $n$ that satisfy $n^2 < 64 - 20n - n^2.$

tomtom Nov 25, 2023

0

52

1

+1911

help algebra

Write the values of $x$ that satisfy $-8 \le x + 17 < -3 - 5x$ as an interval.

tomtom Nov 25, 2023

-2

15

4

+28

pls help me im stuck

Six children are each offered a single scoop of any of flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly read more ..

Icebulb2 Nov 25, 2023

Nov 24, 2023

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49

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+1348

bisectors

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 14$, $AY = 14$, and $CY = 8$, find $BZ$.

sandwich Nov 24, 2023

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40

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+1348

bisectors

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 14$, $AY = 14$, and $CY = 8$, find $BC$.

sandwich Nov 24, 2023

0

28

0

+1348

triangle

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ read more ..

sandwich Nov 24, 2023

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61

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+1348

triangle

Find the circumradius of triangle $ABC.$

sandwich Nov 24, 2023

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24

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+1348

triangle

Find the inradius of triangle $ABC.$

sandwich Nov 24, 2023

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37

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+1348

right triangle

For the triangle below, let $x$ be the area of the circumcircle, and let $y$ be the area of the incircle. Compute $x - y.$ read more ..

sandwich Nov 24, 2023

0

39

0

+1678

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 $c$.

wiseowl Nov 24, 2023

0

57

0

+1678

Function

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

wiseowl Nov 24, 2023

0

36

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+1678

function

The function $f(x,y)$ gives an ordered pair as output. It is defined according to the following rules:
* If $x > 4$, $f(x,y) = (x - 4,y)$.
* If $x \le 4$ but $y > 4$, $f(x,y) = (x,y - 4)$.
* Otherwise, $f(x,y) = (x + y + 11, read more ..

wiseowl Nov 24, 2023

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40

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+1678

Algebra

Find all real numbers $x$ such that $f(x) = f(f(x))$, where $f(x) = x^2 - 3x + x^3 - 7x^2 + 5x.$

wiseowl Nov 24, 2023

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48

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+1678

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 $x$.

wiseowl Nov 24, 2023

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55

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+1678

inverse functions

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

wiseowl Nov 24, 2023

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27

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+1678

function

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

wiseowl Nov 24, 2023

0

64

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+1678

equation

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.

wiseowl Nov 24, 2023

0

47

0

+1348

area

Find the area of triangle ABC.

sandwich Nov 24, 2023

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