All Questions ⁺⁰237460 Questions

0

40

1

+1729

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
\[a_n = a_{n - 1} + a_{n - 2}\]
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

parmen Aug 14, 2024

0

34

1

+608

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

onyuIee Aug 14, 2024

0

44

1

+1520

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

learnmgcat Aug 14, 2024

0

40

2

+1520

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

learnmgcat Aug 14, 2024

0

30

1

+466

Algebra

Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b \cdot g(x), where f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5 and g(x) = x^6 - 17x^5 + 2x^4 + 6x^3 + 11x^2 - 8x + 1.

bIueb3rry Aug 14, 2024

0

42

1

+1271

Need help

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

Akhain1 Aug 14, 2024

0

47

2

+1271

Need help

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

Akhain1 Aug 14, 2024

0

25

2

+32

Help w/ altitudes

Triangle ABC has altitudes AD, BE, and CF. If AD=14, BE=16, and CF is a positive integer, then find the largest possible value of CF.
Ive tried drawing things out but don't know how to figure it out. If anyone can read more ..

surfz Aug 14, 2024

0

25

1

+1855

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

ABJeIIy Aug 14, 2024

0

48

0

+1855

Geometry

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.
If angle CAD = 67 degrees, then what is angle read more ..

ABJeIIy Aug 14, 2024

-1

50

0

+400

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

Stanry Aug 14, 2024

-1

26

1

+400

Algebra

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

Stanry Aug 14, 2024

0

51

1

+466

need help

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

bIueb3rry Aug 14, 2024

0

42

1

+466

help geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

bIueb3rry Aug 14, 2024

0

43

1

+12

Geometry Helpp

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 ADT if [ABC] = 14.
<read more ..

blueb3rry Aug 14, 2024

0

43

2

+12

Geometry Help

Points M, N, and O, are the midpoints of sides KL, LJ, and JK, respectively, of triangle JKL. Points P, Q, and R are the midpoints of NO, OM, and MN, respectively. If the area of triangle PQR is 12, then what is the area of triangle read more ..

blueb3rry Aug 14, 2024

0

40

1

+608

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

onyuIee Aug 14, 2024

0

32

0

+279

Geometry

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

fjeihqoO Aug 14, 2024

0

54

0

+1556

Algebra

Find all $w$ so that neither $-2(6+2w)\le -16 + 7w$ nor $-3w\ge 18 - 5w + 3$.

kittykat Aug 14, 2024

0

30

0

+1556

Algebra

Find all $z$ such that neither $2+z-5z$ nor $2-z+8z$ is in the interval $(-7,13]$. Express your answer as an interval or as a union of intervals.

kittykat Aug 14, 2024

0

53

0

+1520

Algebra

Find all $x$ such that $1-3x < x + 8 \le 7-x$. Give your answer in interval notation.

learnmgcat Aug 14, 2024

0

52

0

+1520

Algebra

Find all $x$ such that both $2x$ and $3x-7$ are in the interval $(-1,12)$.

learnmgcat Aug 14, 2024

0

26

1

+12

geometry problem with triangles

In triangle STU, let M be the midpoint of ST and let N be on TU such that SN is an altitude of triangle STU. If ST and SU are both 13, TU is 8, and SN and UM intersect at X, then what is SX? Thank you. read more ..

blueb3rry Aug 14, 2024

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