The Complex<span> conjugate root </span><span>theorem states that if a-bi is a solution, so is a+bi, and vice versa. Therefore, 1+6i is another solution</span>
For graphing you would have to make sure your number line up with the y axis and the x axis
Answer:
<em>-3/2 and 1</em>
Step-by-step explanation:
Given the arithmetic sequence (y+2) (y+3) and (2y²+1), the common difference is gotten by taking the difference in their terms. For example if we have 3 terms T1, T2, T3... the common difference d = T2-T1 = T3-T2
From the sequence given;
T1 = y+2, T2 = y+3 and T3 = 2y²+1
d = y+3-(y+2) = 2y²+1- (y+3)
open the parenthesis
y+3-y-2 = 2y²+1- y-3
1 = 2y²+1- y-3
1 = 2y²- y-2
2y²- y-2-1 = 0
2y²- y-3 =0
Factorize the resulting expression
2y²- y-3 =0
2y²- 2y+3y-3 =0
2y(y-1)+3(y-1) = 0
(2y+3)(y-1) = 0
2y+3 = 0 and y-1 = 0
2y = -3 and y =1
y = -3/2 and 1
<em>Hence the possible values of y are -3/2 and 1</em>
Answer:
<h2>3500</h2>
Step-by-step explanation:
Given the ratio of the profit, cost of materials and labour in the production of
an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25
If the cost of labour is x, the cost of material will be 840+x (since the cost of materials is Le 840 more than that of labour) .
Let the total cost of producing the article be y.
Cost of labour = 13/25 * y = x
Cost of labour = 13y/25 = x.................... 1
Cost of material = 7/25*y = 840+x
Cost of material = 7y/25 = 840+x ..................... 2
From 1, 13y = 25x
x = 13y/25 ................... 3
Substituting equation 3 into 2:
7y/25 = 840+x
7y/25 = 840+13y/25
collect the like terms:
7y/25 - 13y/25 = 840
-6y/25 = 840
-6y = 25*840
y = 25*840/6
y = 3,500
<em>Hence the total cost of producing the article is 3500</em>
