To divide these complex numbers you have to multiply by the conjugate of the denominator. That will look like this:
. Multiply straight across the top and straight across the bottom to get
. In the denominator, the 12i and -12i cancel each other out, which is nice. Now, in both the numerator and the denominator we have an i-squared. i-squared is equal to -1, so we will make that substitution in our solution:
. Doing the math on that we have
. We can simplify that as well as write it in standard form:
. Now we will get it into legit standard form, separating the real part of the complex number from the imaginary part.
. That can be reduced to its final answer of
. There you go!
Answer:
m<Q = 133°
Step-by-step explanation:
From the question given above, the following data were obtained:
m<P = (x + 13)°
m<Q = (10x + 13)°
m<R = (2x – 2)°
m<Q =?
Next, we shall determine the value of x. This can be obtained as follow:
m<P + m<Q + m<R = 180 (sum of angles in a triangle)
(x + 13)° + (10x + 13)° + (2x – 2)° = 180
x + 13 + 10x + 13 + 2x – 2 = 180
x + 10x + 2x + 13 + 13 – 2 = 180
13x + 24 = 180
Collect like terms
13x = 180 – 24
13x = 156
Divide both side by 13
x = 156 / 13
x = 12
Finally, we shall determine m<Q. This can be obtained as follow:
m<Q = (10x + 13)°
x = 12
m<Q = 10(12) + 13
m<Q = 120 + 13
m<Q = 133°
Answer:
z =
Step-by-step explanation:
Small triangle:
<em>s</em>hort leg = 2
<em>l</em>ong leg = z
Large triangle
<em>s</em>hort leg = z
<em>l</em>ong leg = 5
-------------------------
The triangles are similar therefor
S<em>short </em>/ L<em>short</em> = S<em>long </em>/ L<em>long</em>
2/z = z/5
multiply both sides by z
2 = /5
multiply both sides by 5
10 =
Take the square root of both sides
z =
Answer: about 78 mL
Step-by-step explanation:
When you see the liquid in a curved shape, you want to look at the very bottom of the curve. The bottom shows that our answer will be in the 70 mL, but close to 80. If you look at the lines in between, we can see that there are 5 lines, meaning each line represents 2 mL. Now, we count up and reach 78 mL.
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