All Questions ⁺⁰237360 Questions

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help plz

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

sandwich Nov 23, 2023

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77

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triangle

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

sandwich Nov 23, 2023

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69

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rectangle

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

sandwich Nov 23, 2023

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66

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rectangle

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

sandwich Nov 23, 2023

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55

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circle

A circle has a radius of $15.$ Let $\overline{AB}$ be a chord of the circle, such that $AB = 40$. What is the distance between the chord and the center of the circle?

sandwich Nov 23, 2023

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48

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triangle

Triangle $ABC$ is isosceles with $AB = BC.$ If $AC = 20$ and $[ABC] = 100*\sqrt{3},$ then find the perimeter of triangle $ABC.$

sandwich Nov 23, 2023

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54

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Function question

The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).
Explain why the functions f and h are not the same function.

blackpanther Nov 23, 2023

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71

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Function

Let $f(a,b) = 2a - 3b^2 + 7 - 5a^2 + b^3$. If $f(k,-3) = -10$, then what is $k$?

blackpanther Nov 23, 2023

-1

75

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constant

Find the real number $k$ such that $f(x) = f(k - x)$ for all real numbers $x$, where
\[f(x) = 2x^2 + 7x + x^3 - 5x + 18x.\]

blackpanther Nov 23, 2023

-1

69

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+1786

Function

Let $f$ be a function such that
\[f(x+y) = x + f(y) + x^2 - f(x + f(y))\]
for any two real numbers $x$ and $y$. If $f(0) = -5$, then what is $f(17)?$

blackpanther Nov 23, 2023

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90

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+1786

Equation

Find the value of $a$ for which there is exactly one real value of $x$ such that $f(x) = a,$ where
\[f(x) = x^3 + 4x - 31 + 2x + 18.\]

blackpanther Nov 23, 2023

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64

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+1786

Algebra

Let
\[f(x) = \frac{4x - 1}{5x + 2} + \frac{6x + 3}{x^2 - 7}.\]
For what value of $a$ is $f(a) = 3$?

blackpanther Nov 23, 2023

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67

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+1786

Range

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

blackpanther Nov 23, 2023

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Domain

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

blackpanther Nov 23, 2023

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72

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Function

The function $f$ satisfies
\[f(\sqrt{2x - 1} + x^2) = \frac{1}{x}\]
for all $x \ge \frac{1}{2}.$ Find $f(x)$.

blackpanther Nov 23, 2023

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75

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+1786

Function

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

blackpanther Nov 23, 2023

+1

56

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+67

algebra

If is a function f(x)whose domain is[-8,8] , and g(x)=f(x/2) , then the domain of g(x) is an interval of what width?

USERSPPB Nov 23, 2023

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73

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+1348

right triangle

In triangle $ABC,$ $\angle ACB = 90^\circ.$ Let $H$ be the foot of the altitude from $C$ to side $\overline{AB}.$
Prove that
\[(x + h)^2 (y + h)^2 = (a + b)^4.\]

sandwich Nov 23, 2023

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55

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+1348

triangle

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 $ABC.$

sandwich Nov 23, 2023

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78

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+1348

square in triangle

A square is inscribed in a right triangle, as shown below. Find the area of the square.

sandwich Nov 23, 2023

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81

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+1348

similar triangles

In the diagram below, $\angle PQR = \angle PRQ = \angle STR = \angle TSR$, $RQ = 8$, and $SQ = 3$. Find $PQ$.

sandwich Nov 23, 2023

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59

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similar triangles

In the diagram below, $SR = PQ = 20$ and $RT:TS = 2:3$. Find $UV$.

sandwich Nov 23, 2023

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64

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+1348

altitudes

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

sandwich Nov 23, 2023

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58

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+1348

triangle

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

sandwich Nov 23, 2023

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47

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+1348

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 $BX$?

sandwich Nov 23, 2023

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