All Questions ⁺⁰237734 Questions

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+850

Algebra

What is the equation of the line of symmetry of the parabola $y = f(x)$.
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

cooIcooIcooI17 Feb 18, 2025

0

4

31

0

+850

Algebra

For parts (a) through (d), let f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
What is the vertex of the parabola y = f(x)?
Enter your answer as a coordinate pair, that is, as $(x,y)$ where $x$ and $y$ are replaced by read more ..

cooIcooIcooI17 Feb 18, 2025

0

2

22

0

+850

Algebra

Complete the square: 3x^2 + 8x + 9 - 4x^2 + 25x + 19

cooIcooIcooI17 Feb 18, 2025

0

2

25

1

+850

Algebra

Complete the square: x^2 - 10x + 21 + 3x^2 - 2x + 8.

cooIcooIcooI17 Feb 18, 2025

0

1

25

0

+850

Algebra

Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.

cooIcooIcooI17 Feb 18, 2025

0

2

31

0

+850

Algebra

What is the area of the region of the complex plane defined by |z| < 3 + 2|z - 1|?

cooIcooIcooI17 Feb 18, 2025

0

2

34

0

+850

Algebra

Find all complex solutions to the equation z^3 = 8i - (15 + 2i)z^2 + (7 - 4i)z.

cooIcooIcooI17 Feb 18, 2025

0

1

24

0

+850

Algebra

Find all complex solutions to the equation z^2 = -55 - 48i + 40 + 63i.

cooIcooIcooI17 Feb 18, 2025

0

2

17

1

+850

Algebra

Simplify (i + 1)(100) - (i - 1)(100).

cooIcooIcooI17 Feb 18, 2025

0

4

28

0

+850

Algebra

Compute (-5 + 4i) + (-5 - 4i).
Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.

cooIcooIcooI17 Feb 18, 2025

0

44

0

+850

Algebra

Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that
z^2 + 2z = -53 + 8i.

cooIcooIcooI17 Feb 18, 2025

0

36

0

+850

Algebra

Find all complex numbers z satisfying the equation
\frac{z + 1}{z - 1} = 2 + i + \frac{-7 + 3z}{z}.

cooIcooIcooI17 Feb 18, 2025

0

40

0

+850

Algebra

Find all complex numbers $z$ satisfying the equation
\frac{z + 1}{z - 1} = 1 + i + \frac{5 + 2i}{z}.

cooIcooIcooI17 Feb 18, 2025

0

35

0

+850

Algebra

Express
\cfrac{1}{1 - \cfrac{1}{2 + \cfrac{1}{i}}}
in the form a+bi, where a and b are real numbers.

cooIcooIcooI17 Feb 18, 2025

0

33

0

+850

Algebra

Express (2 + i)(3 + i) in the form a + bi, where a and b a real numbers.

cooIcooIcooI17 Feb 18, 2025

0

43

0

+850

Algebra

Compute 1 + i + i^2 + i^3 + i^4 + \dots + i^{2000} + \dots + i^{2025}.

cooIcooIcooI17 Feb 18, 2025

0

25

1

+850

Algebra

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

cooIcooIcooI17 Feb 18, 2025

0

37

0

+850

Algebra

Compute (-5 + 3i) + (-5 - 3i).
Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.

cooIcooIcooI17 Feb 18, 2025

0

46

0

+850

Algebra

Compute (2i-6) + (5+i), where i^2 = -1.

cooIcooIcooI17 Feb 18, 2025

0

42

0

+1741

Algebra

The function
f(x) = \frac{cx}{x - 1}
satisfies f(f(x)) = x for all real numbers x \neq 1. Find the value of c.

parmen Feb 18, 2025

0

40

0

+1741

Algebra

Functions that aren't invertible can be made invertible by restricting their domains. For example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. In that case, the inverse function is read more ..

parmen Feb 18, 2025

0

42

0

+1741

Algebra

Suppose f(x) = \frac{1}{\sqrt{x}} + x^2 for x > 0. Does f have an inverse? If so, find f^{-1}(2). If not, enter "undef".

parmen Feb 18, 2025

0

43

0

+1741

Algebra

Suppose f(x) = -3x^2 + 6x - 17 + 3x^2 + 2x - 14. Does f have an inverse function? If so, find f^{-1}(-41). If not, enter "undef".

parmen Feb 18, 2025

0

44

0

+1741

Algebra

Suppose f(x) = \frac{9}{5} x - 4 + x^2. Does f have an inverse? If so, find f^{-1}(0). If not, enter "undef".

parmen Feb 18, 2025

0

43

0

+1741

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(sqrt(x)/sqrt(-x)).
What is the domain of g?

parmen Feb 18, 2025

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