calculating each of the products
noting that i² = (√- 1 )² = - 1
(1 + 2i)(8i) ( distribute by 8i )
= 8i + 16i² = - 16 + 8i ← complex number
(1 + 2i)(2 - 5i) ( expand using FOIL )
= 2 - 5i + 4i - 10i²
= 2 - i + 10 = 12 - i ← complex number
(1 + 2i)(1 - 2i) ( expand using FOIL )
= 1 - 2i + 2i - 4i²
= 1 + 4 = 5 ← real number
(1 + 2i)(4i) ( distribute by 4i )
= 4i +8i² = - 8 + 4i ← complex number
(1 + 2i)(1 - 2i) is the only product which results in a real number
Answer:
7-5n
Step-by-step explanation:
first you multiply both sides and get the equation 2n+2-7n+7 then you rearange the numbers to 2n-7n +2+7 and get -5n+7. you can change that to 7-5n.
Setting up the proportion ,you get that x=92.
Answer:
The data set with the greater range is the Girls
The greater median is the Girls at 110
Step-by-step explanation:
The range is the difference between the largest and smallest values.
As the largest value for the boys is 120 and the smallest is 60, the range would be 60
As the largest value for the girls is 150 and the smallest is 70, the range would be 80.
This means that the Girls have the greater range
The median is the number in the middle when the data is in ascending order.
As we have an even number, we will have to find the middle value between 5 and 6. To do this, we can add them together and divide them by 2.
The 5th boy in ascending order is 90 and the 6th boy is 90.
The 5th 5irl is 100 and the 6th girl is 120
This means that the median is greater for the Girls.
Answer:
4 3/8 cups of baking soda
Step-by-step explanation:
1 3/4 cups of baking soda are needed to make 1 batch of a homemade cleaning product,
Cups of baking soda : batches of homemade cleaning
1 3/4 cups : 1 batch
How many total cups of baking soda I needed to make 2 1/2 batches of the cleaning product?
Let x = total cups of baking soda needed
Cups of baking soda : batches of homemade cleaning
x cups : 2 1/2 batches
Equate the ratios
1 3/4 cups : 1 batch = x cups : 2 1/2 batches
7/4 ÷ 1 = x ÷ 5/2
7/4 × 1/1 = x * 2/5
7/4 = 2/5x
Divide both sides by 2/5
x = 7/4 ÷ 2/5
= 7/4 × 5/2
Cross product
x = 35/8
= 4 3/8 cups of baking soda
