All Questions ⁺⁰235731 Questions

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26

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+1439

triangle

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle BAC = 42^\circ$. Find $\angle PBC$ in degrees.

kittykat Mar 9, 2024

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22

1

+1439

Circle

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

kittykat Mar 9, 2024

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16

2

+1439

Sector

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

kittykat Mar 9, 2024

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43

2

+2669

Algebra

Find all solutions of the equation
|x^2 - 30x - 1| + |x^2 - 30x + 29| = 30

LiIIiam0216 Mar 9, 2024

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18

1

+2669

help algebra

(1) Let a_1, a_2, a_3 be real numbers such that
|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.
What is the largest possible value of |a_1 - a_2|?

(2) Let a_1, a_2, a_3, \dots, a_{10} be real numbers such that read more ..

LiIIiam0216 Mar 9, 2024

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40

1

+2669

need help with sum

Let
f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.)

LiIIiam0216 Mar 9, 2024

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17

2

+355

algebra

Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 120 meters per hour when walking across flat ground, and 150 meters per hour when walking downhill. One day, Carissa walks across Boston read more ..

Lilliam0216 Mar 9, 2024

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16

2

+40

percent square puzzle

In the percent square below, you must fill in every empty square (including shaded squares) so that:
• Each square contains a positive digit (1-9). Digits may be reused.
• The percent next to a row gives the percent of the row sum contained read more ..

onyulee Mar 9, 2024

Mar 8, 2024

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25

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+4

HOW DO I SOLVE THIS!! RESPOND QUICK PLEASE QUICK QUICK QUICK

A new road that connects Uniontown to Springville is 4 1/3 miles long. What is the change in distance when using the new road instead of the dirt roads? Write your answer as a mixed number.

BrooklynSBadger Mar 8, 2024

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26

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+52

Please help!!

A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates.
The height of the water at point B located between two read more ..

xXValeXx Mar 8, 2024

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23

1

+52

The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months

The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.)

A read more ..

xXValeXx Mar 8, 2024

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24

1

+85

Algebra

Can anyone solve this?

Akhaim1 Mar 8, 2024

-1

14

1

+1911

System problem

For a certain value of $k$, the system
x + y + 8z = 10,
x + 5y + 3z = 7 + 7z - 4y,
kx + 2z = 3 - 4y
has no solutions. What is this value of $k$?

tomtom Mar 8, 2024

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13

2

+85

Geometry Questions

Please solve these!
1.

2.

Akhaim1 Mar 8, 2024

-1

26

1

+1911

System question

For certain values of k and m, the system
3a + 2b = 12 - 5a + 7b
8a + 6b = k - a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

tomtom Mar 8, 2024

-1

19

1

+1911

System

The system of equations
\frac{xy}{x + y} = 0, \quad \frac{xz}{x + z} = 0, \quad \frac{yz}{y + z} = 1
has exactly one solution. What is $z$ in this solution?

tomtom Mar 8, 2024

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26

1

+1768

Roots

Let $a$ and $b$ be the roots of the quadratic equation $2x^2 - 7x + 2 = -x^2 + 4x + 9.$ Find $\frac{1}{a+7}+\frac{1}{b+7}.$

bader Mar 8, 2024

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25

1

+1768

Quadratic

Let $a$ and $b$ be the roots of the quadratic equation $x^2-25x+80=-28x+75$. Compute $\frac{a^2}{b} + \frac{b^2}{a}$.

bader Mar 8, 2024

-1

17

1

+1911

Algebra

Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water. She thinks the solution is a little strong, so she drains 150 mL from the beaker, adds 150 mL of water, and stirs the solution. Ruth thinks the solution is still too strong, read more ..

tomtom Mar 8, 2024

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22

1

+1768

Geometry

Semicircles are constructed on AB, AC, and BC. Find the radius of the circle.

AB read more ..

bader Mar 8, 2024

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