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Post New Question
All Questions
+0
234503 Questions
0
18
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+1348
help plz
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
sandwich
Nov 23, 2023
0
48
0
+1348
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
0
40
0
+1348
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
0
33
0
+1348
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
0
23
1
+1348
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?
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sandwich
Nov 23, 2023
0
24
0
+1348
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
-1
31
0
+1307
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
-1
43
0
+1307
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
46
0
+1307
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
35
0
+1307
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
0
50
0
+1307
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
0
37
0
+1307
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
0
29
0
+1307
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
0
26
0
+1307
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
0
37
0
+1307
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
0
38
0
+1307
Function
Let $A(t) = 3 - 5t^3 \cdot 4 \cdot 2^t$. Find $A(2) - A(1)$.
blackpanther
Nov 23, 2023
+1
34
1
+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
0
36
0
+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
0
26
0
+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
0
44
0
+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
0
39
0
+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
0
36
1
+1348
similar triangles
In the diagram below, $SR = PQ = 20$ and $RT:TS = 2:3$. Find $UV$.
●
sandwich
Nov 23, 2023
0
33
0
+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
0
28
0
+1348
triangle
Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 30^\circ$.
sandwich
Nov 23, 2023
0
20
0
+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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