Answer:
5-46i
Step-by-step explanation:
1. Multiply (10-4i) and (4-5i), I recomnd using foil:
40-50i-16+20i^2 + (-15+20i)
2. Remove the parenthesis around -15+20i
*we can do this since there is a "+":
40-50i-16+20i^2 + (-15)+20
3. Simplify i^2
* i^2 is -1 by textbook defination:
40-50i-16+20(-1) + (-15)+20
4. Simplify
40-50i-16-20 + (-15)+20
6. Combine like terms:
-5-50i-16i+20i
5-46i
And the problem is done
Answer:
y = x + 11
Explanation:
The general form of an equation is:
y = mx+c
where:
m is the slope
c is the y-intercept
1- getting the slope:
We are given that the line is parallel to GH. This means that:
slope of the line = slope of GH
We have G as (-2,2) and H as (2,6)
slope of GH = (y2-y1) / (x2-x2)
slope of GH = (6-2) / (2--2) = 1
slope of line = slope of GH =1
Therefore, the equation on the line now becomes:
y = x + c
2- getting the y-intercept:
We are given that point (-5,6) passes through the line. This means that this point satisfies the equation of the line. So, we will substitute with this point in the equation and solve for c as follows:
y = x + c
6 = -5 + c
c = 6_5
c = 11
Based on the above, the equation of the line is:
y = x + 11
Hope this helps :)
Answer:
The volume of the solid is 420m³
Step-by-step explanation:
The area of any pyramid is "1/3 · B · h", where B is the area of the base, and h is the height.
Knowing this we just need to solve for a couple of things.
First, and the easiest is the height of the triangle which (thankfully) is given to us. The height is 15m, which plus one number into our equation.
1/3 · B · 15
Second, we need to find the area of the base of the pyramid. That's done easily by finding the area of a triangle ( 
→ 
→ 
→ 
) giving us 84 units. This puts another number into our equation.
1/3 · 84 · 15
Now that we have all of the parts to our equation, we can solve it.
1/3 · 84 · 15
1/3 · 1260
420
The volume of the solid is 420m³
That would be called the solution
