Answer:
The polynomial function 
To determine the multiplicity of 0, -2, -4, 5.
The multiplicity of a root is the number of times the root appears.
First find the root of the equation, set the function equals to zero.
therefore, the root of this function are, x=0,-2, -4, 5
To find the multiplicity of the roots:
A factor of x would have a root at x=0 with multiplicity of 1
similarly, x=-2 with multiplicity of 3
x=-4 with multiplicity of 2
x=5 with multiplicity of 4.
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
1) Write the number in exponential form with a base of 10:
3√1000 = 3√10^3
2) Reduce the index of radical and exponent with 3:
3√10^3=10
If you would like to write each rate as a unit rate, you can do this using the following steps:
$2 ... 5 cans of a soup
$1 ... x cans of a soup = ?
2 * x = 5 * 1
2 * x = 5
x = 5 / 2
x = 2.5 cans of a soup per $1
$2 ... 5 cans of a soup
$x = ? ... 1 can of a soup
2 * 1 = 5 * x
2 = 5 * x
x = 2 / 5
x = $0.4 per 1 can of a soup
Answer:
1/12
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that you have 3 tops: green, white, and yellow, the probability of you wearing a green shirt p(g)
= 1/3
since you have 2 pairs of pants: blue and black, the probability of you wearing a blue pant p(b)
= 1/2
And you have 2 pairs of shoes: boots and sandals, the probability of you wearing a pair of boots p(bo)
= 1/2
Hence the probability that you will wear a green shirt with blue pants and boots
= 1/3 * 1/2 * 1/2
= 1/12
