All Questions ⁺⁰234657 Questions

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+328

Algebra

Find the largest value of x for which
x^2 + y^2 = 4x + 5y
has a solution, if x and y are real.

onyuIee Aug 19, 2024

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+484

Algebra

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $4$ days earlier. If the job needs to be completed $20$ days earlier, how many additional workers should be hired?

gnistory Aug 19, 2024

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+484

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

gnistory Aug 19, 2024

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+1706

Algebra

For a certain value of $k$, the system
x + y + 3z &= 10, \\
6x + 4y + z &= 18 - 5y - x, \\
kx + 7z &= 8 - 14y
has no solutions. What is this value of $k$?

ABJeIIy Aug 19, 2024

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+1706

Algebra

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a+2b+3c+4d+5e=47
2a+3b+4c+5d=15
3a+4b+5c=34 read more ..

ABJeIIy Aug 19, 2024

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+1706

Algebra

Let x and y be real numbers. If x and y satisfy x^2+y^2=4x+16y+15, then find the largest possible value of x. Give your answer in exact form using radicals, simplified as far as possible.

ABJeIIy Aug 19, 2024

Aug 18, 2024

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+116

Algebra

Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$

MEMEG0D Aug 18, 2024

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+116

Algebra

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

MEMEG0D Aug 18, 2024

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+96

Algebra

Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

bIueb3rry Aug 18, 2024

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+96

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?

bIueb3rry Aug 18, 2024

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+523

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.

siIviajendeukie Aug 18, 2024

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+523

Algebra

Compute (1 + i)/(2 - i)(3 + i).

siIviajendeukie Aug 18, 2024

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+296

Algebra

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

Stanry Aug 18, 2024

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+296

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 ..

Stanry Aug 18, 2024

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+1887

help counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

tomtom Aug 18, 2024

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+673

Counting

A coin is tossed $12$ times. How many different sequences of tosses could there have been, if the number of heads was at least $5?$

magenta Aug 18, 2024

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+673

Counting

In how many ways can we distribute 13 pieces of identical candy to 3 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?

magenta Aug 18, 2024

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+779

Geometry

A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.

eramsby1O1O Aug 18, 2024

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+779

Geometry

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

eramsby1O1O Aug 18, 2024

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+2651

Geometry

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 $BX$?

LiIIiam0216 Aug 18, 2024

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+38

Number theory help please!

1. Find all integers, such that n is its own inverse modulo 163
2. The inverse of a modulo 44 is b. What is the inverse of 9a modulo 44 in terms of b?
3. Let read more ..

AUnVerifiedTaxPayer Aug 18, 2024

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+92

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.

jaekg Aug 18, 2024

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+92

Geometry

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 $ABC.$

jaekg Aug 18, 2024

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+96

Geometry

In the diagram, $ABCD$ is a square. Find $PR.$
The side length of the square is 10. L, M, N, O are midpoints.

bIueb3rry Aug 18, 2024

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