All Questions ⁺⁰234654 Questions

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need help

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-12)$ and $O(2,8)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

kittykat Jan 15, 2024

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33

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+1341

Coordinates

In the diagram, the four points have coordinates $A(0,1)$, $B(1,3)$, $C(5,2)$, and $D(4.5,0)$. What is the area of quadrilateral $ABCD$?

ElectricPavlov ●

kittykat Jan 15, 2024

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22

1

+1341

Geometry

Two quarter-circles are drawn inside a unit square, as shown. A circle is drawn that is tangent to the quarter-circles, and a side of the square. Find the radius of the circle.

kittykat Jan 15, 2024

0

36

0

+467

Inequality

Find all $x$ that satisfy the inequality $(2x+10)(x+3)<(3x+1)(x+6)$. Express your answer in interval notation.

ChiIIBill Jan 15, 2024

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21

0

+467

Quadratic

Let $p(x) = x^2 + ax + b,$ where $a$ and $b$ are real numbers. Find the number of ordered pairs $(a,b)$ such that $p(a) = p(b) = 1.$

ChiIIBill Jan 15, 2024

0

14

1

+467

Complex numbers

Solve for $z$ in the following equation: $2-3iz = 3 + 2z$.

ChiIIBill Jan 15, 2024

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24

1

+1678

Palindromes

A palindrome is a number that is the same when read forwards and backwards, such as 43234. Find the number of 4-digit palindromes that are divisible by 8.

wiseowl Jan 15, 2024

0

15

1

+1678

help counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 19 skaters, including 2 Americans and 5 Canadians, in how many ways can the medals be awarded to three of the 19 skaters read more ..

wiseowl Jan 15, 2024

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20

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+19

Function problems :)

the function f(x) = (cx)/(4x - 5) satisfies f(f(x))=x for all real numbers x not equal 5/4. find c.
If you have any idea how to do this, please answer! I appreciate it :)

breadysetgo Jan 15, 2024

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21

1

+290

Problem

I have a beaker with a mixture of 5 parts water and 1 part salt. If I have 500 ml water and I drain 250 ml of the mixture assuming that the mixture is evenly dissolved and then add 200 ml of water and 10 grams of salt, what is the ratio of read more ..

DS2011 Jan 15, 2024

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19

1

+1341

Equilateral triangle

The vertices of triangle $ABC$ lie on the sides of equilateral triangle $DEF$, as shown. If $CD = 5$, $CE = BD = 3$, and $\angle ACB = 90^\circ$, then find $AE$.

kittykat Jan 15, 2024

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41

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+1341

Rectangle

In the diagram, right-angled triangles $AED$ and $BFC$ are constructed inside rectangle $ABCD$ so that $F$ lies on $DE$. If $AE = 7$, $ED = 24$, and $BF = 15$, what is the length of $AB$?

kittykat Jan 15, 2024

0

29

1

+1475

Expected value

Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have an 8 on them.
a) What is the expected value of the number shown when we draw a single slip of paper?
b) What is read more ..

parmen Jan 15, 2024

0

32

1

+1348

Circles

For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?

ElectricPavlov ●

sandwich Jan 15, 2024

0

36

1

+1348

coordinates

What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?

sandwich Jan 15, 2024

Jan 14, 2024

+1

22

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+17

Number theory

How many positive integers are not less than the sum of their divisors?

ruiruima Jan 14, 2024

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27

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+1348

Quadratic

The quadratic equation $x^2+4mx+m = 2x - 6$ has exactly one real root. Find the positive value of $m$.

sandwich Jan 14, 2024

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