All Questions ⁺⁰235714 Questions

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+838

Function problem

Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.

magenta Feb 20, 2024

Feb 19, 2024

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28

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+838

help with functions

Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.

magenta Feb 19, 2024

0

40

1

+838

Function

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.

magenta Feb 19, 2024

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27

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+838

Domain

Find the domain of the function \[f(x)=\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}}.\]

magenta Feb 19, 2024

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30

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+0

help with lines

Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common divisor $1$.) read more ..

Vxrtate Feb 19, 2024

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23

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+0

Coordinates

A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (1,7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive. read more ..

Vxrtate Feb 19, 2024

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38

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+0

Analytic Geometry

Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 2x - 4y$.

Vxrtate Feb 19, 2024

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31

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+1768

Coordinates

A line passes through the points $A,$ $B,$ and $C.$ If $A = (-2,5),$ $B = (-3,1),$ and $C = (4,y),$ then find $y.$

bader Feb 19, 2024

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2

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+1768

Equation of line

A line has a slope of $m,$ and its $y$-intercept is $(0,b)$. If $m = 2$ and $b = 2,$ then what is the $x$-intercept of the line?

bader Feb 19, 2024

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31

0

+1439

System question

Find the ordered pair (s, t) that satisfies the system
(s/2) + 5t =3 - 7t + 8s
3t - 6s = 9 - 2t

kittykat Feb 19, 2024

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22

4

+0

Analytic Geometry

Help please!!
1
2.

3.<#> <#> read more ..

Akhaim1 Feb 19, 2024

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24

1

+0

A rectangle contains a strip of width 1 as shown below. Find the area of the strip.

A rectangle contains a strip of width 1 as shown below. Find the area of the strip.

Matmad Feb 19, 2024

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17

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+700

Fraction

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.

booboo44 Feb 19, 2024

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24

3

+0

HELP ASAPPPP!

1. What is the imaginary part of the center of the circle with the equation
2. Find the value of if the Mobius transformation is its own inverse.
3. The function represents read more ..

jibirshna Feb 19, 2024

+1

37

2

+0

Tough Question

What is 1+1? Please help! So hard!

YourDarkFriend Feb 19, 2024

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40

1

+700

help Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6 + 2ab,$ then what is $a^3 + b^3?$

booboo44 Feb 19, 2024

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37

1

+700

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 = 22
3a + 4b + 5c = -17 read more ..

booboo44 Feb 19, 2024

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11

1

+1678

Counting

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

wiseowl Feb 19, 2024

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31

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+1678

help how to count

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if everything mathematician must be between two scientists? (Two seatings are considered read more ..

wiseowl Feb 19, 2024

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32

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+1678

Counting question

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

wiseowl Feb 19, 2024

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30

0

+1678

help counting

Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c read more ..

wiseowl Feb 19, 2024

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31

1

+0

Linear equation

I need help solving the problem below.
For certain values of k and m, the system a + 2b = -3, 4a + 2b = k - a - mb has infinitely many solutions (a,b). What are k and m?

Lilliam0216 Feb 19, 2024

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37

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+1439

Circles

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 Feb 19, 2024

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32

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+400

Probability question

A function $f$ randomly assigns values to $f(1), f(2), f(3),$ and $f(4)$ from the set $\{1,2,3,4\}$ with replacement. What is the probability that $f(x) = x$ for each $x$ in the set $\{1,2,3,4\}\,?$ Express your answer as a common fraction.

omgitsrne Feb 19, 2024

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