Answer:
1/5 + 2/5 i sqrt(6) = .2 + .98i
1/5 - 2/5 i sqrt(6) = .2 - .98i
Step-by-step explanation:
5z^2−9z=−7z−5
We need to get all the terms on one side (set the right side equal to zero)
Add 7z to each side
5z^2−9z+7z=−7z+7z−5
5z^2−2z=−5
Add 5 to each side
5z^2−2z+5=−5 +5
5z^2−2z+5=0
This is in the form
az^2 +bz+c = 0 so we can use the quadratic formula
where a = 5 b = -2 and c = 5
-b± sqrt(b^2-4ac)
-------------------------
2a
-(-2)± sqrt((-2)^2-4(5)5)
-------------------------
2(5)
2± sqrt(4-100)
-------------------------
10
2± sqrt(-96)
-------------------------
10
2± sqrt(16)sqrt(-1) sqrt(6)
-------------------------
10
2± 4i sqrt(6)
-------------------------
10
1/5 ± 2/5 i sqrt(6)
Splitting the ±
1/5 + 2/5 i sqrt(6) = .2 + .98i
1/5 - 2/5 i sqrt(6) = .2 - .98i
Step-by-step explanation:
Given
as equation 1.
I used q-p as the difference as logically the woman will be older than her son.
Also given,
as equation 2.
Using equation 2,
substitute this equation into equation 1.
Substitute P into equation 2.
Therefore the woman is 45 years old while her son is 15 years old.
Using proportions, it is found that the coordinates of point B are given as follows:
A. (1.6, 0).
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Point B is 3/4 of the way from AB to AC, hence:
The points are:
Then, to find the x-coordinate:
x + 2 = 3.6.
x = 1.6.
For the y-coordinate:
y + 3 = 3
y = 0.
Hence option A is correct.
More can be learned about proportions at brainly.com/question/24372153
#SPJ1
Answer:
54y² +255y +300
Step-by-step explanation:
Such an expression is simplified by eliminating parentheses and combining like terms.
<h3>Eliminate parentheses</h3>
Taking the given expression at face value, we have ...
{2(3y+6)-3(-4-y)}2(3y+6)−3(−4−y)
= {6y +12 +12 +3y}(6y +12) +12 +3y
= (9y +24)(6y +12) +12 +3y
= (9y)(6y +12) +24(6y +12) +12 +3y
= 54y² +108y +144y +288 +12 +3y
<h3>Combine like terms</h3>
= 54y² +(108 +144 +3)y +(288 +12)
= 54y² +255y +300
