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3 years ago

Function or non function !!

Mathematics

1 answer:

Phoenix [80]3 years ago

5 0

Answer:

not a fucton

Step-by-step explanation: because i got it right

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Point P is the center of the circle in the figure above. What is the value of x?

LenaWriter [7]

Answer:

x = 80°

Step-by-step explanation:

To find x, we need to create an equation.

Recall that the sum of all the 4 interior angles of a quadrilateral = 360°.

Therefore:

m<B + m<A + m<C + m<P = 360°

m<B = 20° (given)

m<C = 20° (given)

m<A = ½*x = x/2 (inscribed angle theorem)

m<P = (360 - x)°

Plug in the values and solve for x

$20 + \frac{x}{2} + 20 + (360 - x) = 360$

$20 + \frac{x}{2} + 20 + 360 - x = 360$

Collect like terms

$20 + 20 + 360 + \frac{x}{2} - x = 360$

$400 + \frac{x}{2} - x = 360$

Subtract 400 from each side 

$400 + \frac{x}{2} - x - 400 = 360 - 400$

$\frac{x}{2} - x = -40$

$\frac{x - 2x}{2} = -40$

$\frac{-x}{2} = -40$

Multiply both sides by 2

$\frac{-x}{2} \times 2 = -40 \times 2$

$-x = -80$

Divide both sides by -1

$\frac{-x}{-1} = \frac{-80}{-1}$

$x = 80$

3 0

3 years ago

If y=40 when x=16, find y when x=10.

andrew-mc [135]

Answer:

Step-by-step explanation:

Y/10 = 40/16

Y=25

4 0

3 years ago

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

What is the height, in inches, of a parallelogram that has a base of 3 feet and an area of 324 square inches?

AlekseyPX

The area of a parallelogram is just:

A=bh, we are given b=3ft, so b=36in and A=324in^2 so

324=36h dividing both sides by 36

h=9

So the height is 9 inches.

7 0

3 years ago

Read 2 more answers

Kelsey has $100 in an account. The intrest rate is %11 compounded annually. To the nearest cent, how much will she have in 2 yea

postnew [5]

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$100\\ r=rate\to 11\%\to \frac{11}{100}\dotfill &0.11\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=100\left(1+\frac{0.11}{1}\right)^{1\cdot 2}\implies A=100(1.11)^2\implies A=123.21$

6 0

3 years ago