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3 years ago

What is the y intercept of the given graph?

Mathematics

1 answer:

Genrish500 [490]3 years ago

6 0

Answer:

The answer would be -2.

Step-by-step explanation:You have to look at where the line is hitting.It has to be perfectly on the corners of the square. The bottom of the y-intercept is always negative and the top is always positive but for the x-intercept the right side is positive and the left side is negative. I hope that helped you!!

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How do I determine z ∈ C:

saw5 [17]

Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}$

So, the equation is simplified to

$-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5$

Let's combine the fractions on the right side:

$\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22$

$\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}$

Then

$-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}$

reduces to

$-(17+11i) z = 5-4i$

Multiply both sides by -1/(17 + 11i) :

$\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}$

$z = -\dfrac{5-4i}{17+11i}$

Finally, simplify the right side:

$-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}$

So, the solution to the equation is

$z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}$

4 0

3 years ago

The longest worm is blank times as long as the shortest worm

Allisa [31]

The answer is 2 times

6 0

3 years ago

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nevsk [136]

Answer:

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3 years ago

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Marrrta [24]

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3 0

3 years ago

A vector is used to express a car's change in position, or displacement, by tracking its motion over a large area defined by a c

kirill [66]

Answer:

C(8,14)

Step-by-step explanation:

initial point (-3,-5) and terminal point (5,9)

vector form=(change in x, change in y)

V=(Xf-Xi,Yf-Yi)

V=[5-(-3), 9-(-5)]

V=(8,14)

8 0

3 years ago

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