All Questions ⁺⁰235735 Questions

0

28

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+1768

Range

Let
\[f(x) = \frac{2x + 3}{x^2 + 7}.\]
Find the range of $f$. Give your answer using interval notation.

bader Mar 13, 2024

0

17

0

+1768

Function

Let
\[f(x) = \frac{2x + 3}{x^2 + 7}.\]
Find the domain of $f$. Give your answer using interval notation.

bader Mar 13, 2024

0

26

2

+6

halp

There are 6 balls numbered 1 through 6 in a box and I take out two different balls at random. What is the expected value of the product of the two numbers on the balls?

invalidsd Mar 13, 2024

0

28

0

+1768

Function

Function
Let $A(t) = 3 - 5t^3 \cdot 4 \cdot 2^t$. Find $A(2) - A(1)$.

bader Mar 13, 2024

Mar 12, 2024

0

23

0

+479

hard geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

ChiIIBill Mar 12, 2024

-1

16

1

+704

Polygon

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.

booboo44 Mar 12, 2024

0

28

0

+704

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 $IJKLMN$.

booboo44 Mar 12, 2024

0

17

1

+704

Geometry

In triangle $ABC,$ $AC = BC$ and $\angle ACB = 90^\circ.$ Points $P$ and $Q$ are on $\overline{AB}$ such that $P$ is between $A$ and $Q$ and $\angle QCP = 45^\circ.$ If cos ACP = 2/3, then find cos BCQ.

booboo44 Mar 12, 2024

+1

16

1

+280

polynomials

(a) Let b be a constant. What is the smallest possible degree of the polynomial , where and ?
(b) Let f be a cubic polynomial such that f(0) = 5, f(1) = -5, f(2) = 8, and f(3)=13. What is the sum of the coefficients read more ..

ABJelly Mar 12, 2024

+1

17

1

+280

I need help with polynomials

Find if the expansion of the product of and has no term.

ABJelly Mar 12, 2024

0

14

0

+1455

triangle

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 ..

kittykat Mar 12, 2024

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25

0

+1455

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 ..

kittykat Mar 12, 2024

0

29

0

+1455

Triangle

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 ..

kittykat Mar 12, 2024

0

16

1

+1533

Cone

The circular sector below is rolled to form a cone. Find the volume of the cone.

parmen Mar 12, 2024

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31

1

+1533

Cone and Cylinder

Let $A$ be the lateral surface area of the cone below, and let $B$ be the lateral surface area of the cylinder below. Find $\frac{A}{B}.$

The read more ..

parmen Mar 12, 2024

0

11

1

+1533

Cone

The cone below has a lateral surface area of $16 \sqrt{5} \cdot \pi$. Find the volume of the cone.

parmen Mar 12, 2024

-1

18

1

+1443

help geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 45^\circ,$ $\angle ABC = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

blackpanther Mar 12, 2024

-1

26

1

+1443

Altitude

In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.

blackpanther Mar 12, 2024

-1

18

1

+1443

Triangle

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 30^\circ$.

blackpanther Mar 12, 2024

-1

11

1

+1443

Right triangles

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

blackpanther Mar 12, 2024

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