The answer is z = 3 + i
z = a + bi
conj(z) = a - bi
conj(7 + 3i) = 7 - 3i
<span>(conj)z + 2z = 2 + 4i + conj(7 + 3i)
</span>a - bi + 2(a + bi) =<span> 2 + 4i + 7 - 3i
</span>a - bi + 2a + 2bi =<span> 2 + 4i + 7 - 3i
</span>3a + bi = 9 + i
From here:
3a = 9 and bi = i
a = 9/3 b = i/i
a = 3 b = 1
z = a + bi
z = 3 + 1 * i
z = 3 + i
Answer:
40 and 10
Step-by-step explanation:
1. if the length is 'l' and height is 'h', then according to the condition 1/4*l=h.
2. if the given area is 400, it means, h*l=400;
3. if to substitute h=1/4*l into the formula of the area, then
l*l*1/4=400; ⇔ 1/4*l²=400;
4. if to calculate the value of the 'l', then l=40 (the required length).
5. if to substitute l=40 into 1/4*l=h, then h=10 (the required height).
<h2>
Explanation:</h2><h2>
</h2>
Here we need to set a system of two linear equations in two variables. So:
- <em>The sum of digits in a two digit number formed by two digits from 1 to 9 is 8:</em>
Let
be those digits, then:

- <em>If 9 is added to a number then both the digits become equal. find the number:</em>
<em />
<em />
<em />
<em />
But from eq 1:

Substituting y into the expression 1:

The x-value will be found by hit and trial, so:

We have to reject this solution because digits are different.

We have to reject this solution because digits are different.

<em>Then this is a two digit number formed by two equal digits. </em>
Finally, the number is:
44
The equation of the circumference of a circle in terms of
is
or
.
The circumference for a circle with diameter 10 is
.
The circumference for a circle with diameter 19 is
.
The circumference for a circle with diameter 30 is
.
The circumference for a circle with diameter 16 is
.
Relatively easy, right?
The equation of the area of a circle in terms of
is
.
The area of a circle with radius 5 is
.
The area of a circle with radius 9.5 is
.
The area of a circle with radius 15 is
.
The area of a circle with radius 8 is
.
Hope this helped!
(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)
Answer:
slope = - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 2 ← is in slope- intercept form
with slope m = - 3