All Questions ⁺⁰233683 Questions

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+721

Geometry

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

bingboy Jun 10, 2024

0

3

1

+721

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

bingboy Jun 10, 2024

0

4

1

+436

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

siIviajendeukie Jun 10, 2024

0

5

1

+436

Algebra

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

siIviajendeukie Jun 10, 2024

0

1

1

+436

Algebra

My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team read more ..

siIviajendeukie Jun 10, 2024

-4

4

1

+153

Algebra

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

BRAlNBOLT Jun 10, 2024

-3

4

1

+153

Algebra

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
$$f(x) = 2x^2-8x+1.$$
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

BRAlNBOLT Jun 10, 2024

-4

3

1

+153

Algebra

For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

BRAlNBOLT Jun 10, 2024

-4

3

1

+153

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

BRAlNBOLT Jun 10, 2024

0

4

1

+436

Algebra

The product $(3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})$ can be expressed in the form $a+b\sqrt{5}$, where $a$ and $b$ are integers. Find $a+b$.

siIviajendeukie Jun 10, 2024

0

4

1

+436

Algebra

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 600 pounds more than each of her trucks, but no more than 1/2 of the total load her four trucks combined can carry. Based on these read more ..

siIviajendeukie Jun 10, 2024

0

2

1

+436

help algebra

Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.

siIviajendeukie Jun 10, 2024

0

2

1

+436

help algebra

Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

siIviajendeukie Jun 10, 2024

0

8

0

+887

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

learnmgcat Jun 10, 2024

0

5

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+887

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

learnmgcat Jun 10, 2024

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+118

Help Geometry

I have found that angle C is 75 degrees, but I don't know what to do next.

SilviaJendeukie Jun 10, 2024

-1

4

1

+1444

Geometry

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.

NotThatSmart ●

ABJeIIy Jun 10, 2024

0

5

1

+118

Help Geometry

The lengths of the legs of the triangle are 1 and 3, find the area of the square.

SilviaJendeukie Jun 10, 2024

Jun 9, 2024

-1

3

1

+153

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

NotThatSmart ●

BRAlNBOLT Jun 9, 2024

0

3

1

+2115

Geometry

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.

LiIIiam0216 Jun 9, 2024

0

5

1

+2115

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.

LiIIiam0216 Jun 9, 2024

-2

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+153

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 $ABD$.

BRAlNBOLT Jun 9, 2024

-2

6

0

+153

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 $BX$?

BRAlNBOLT Jun 9, 2024

0

6

1

+2115

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

LiIIiam0216 Jun 9, 2024

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