Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
For the volume of triangular prism, volume = 0.5xaxbxc
=0.5x10x7x6
=210cm^3
The total pounds of shrimp they catch is 9.625 pounds
<h3>Sum of values and decimals</h3>
Decimal number are numbers that has decimal points. Given the following information;
The total shrimp Spencer catch = 2 pounds
The total shrimp Jaclyn catch = 3.25 pounds
The total shrimp Ayden catch = 4.375 pounds
Determine the total pounds of shrimp they catch
Total shrimp = 2 + 3.25 + 4.375
Total shrimp = 9.625 pounds
Hence the total pounds of shrimp they catch is 9.625 pounds
Learn more on sum of decimals here; brainly.com/question/1827193
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Answer:
Kinetic theory explains why the volume of a container must expand when the temperature of the gas inside increases in order for the pressure to remain constant.
Step-by-step explanation:
Charles' law: for a fixed mass of gas at constant pressure the volume is directly proportional to the temperature.
Analysis of a gas when its temperature increases according to kinetic theory:
The temperature has increased therefore the molecules have more kinetic energy, so they move with a greater velocity.¹
If the container's dimensions do not change the molecules will travel across the container between the walls in less time (because they are moving faster and covering the same distance between the container walls). This will increase the rate of collisions, which would increase the pressure.²
But if the dimensions of the container increased then the molecules would cover a larger distance faster thereby maintaining a constant rate of collisions. This would maintain a constant pressure.
So first you’ll have to find the total or the sum of collected.
$90+$60= $150
Because you’re finding the percent of the total collected by girl scouts, divide the amount collected from the girl scouts by the total.
$90/$150= .6
Multiply that by 100 to get %60.
