The second one and the fourth one.
Step-by-step explanation:
As the problem states, it takes 166.5 gallons of water in 3 mins. Since it states it is a proportional relationship, we know that 166.5/3 is the number of gallons pumped in 1 minute. We can write this as g(the number of gallons) = 166.5/3 * m(the number of minutes) ! In additon, 166.5/3 is equivalent to 55.5, which gives us the second and the fourth equation correct!
Synthetic division work with the coefficient of the given polynomial expression
We have
-15 -16 84 -17 -9 -15
and the divisor is:
x - ⁸/₅ = 0
x = ⁸/₅
Refer to the diagram below for the steps of synthetic division
Start by multiplying the first coefficient by the divisor, write the answer under the second coefficient, and then add the two values.
Repeat the steps until we use up all the remaining coefficients
The final values are the coefficients of the quotient and the last value is the reminder
The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)
<h3>What is the Closure property under multiplication?</h3>
When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.
Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;
(10x^(0.5) - 8)(5x^(0.5) + 4)
The output will retain the same thing.
Read more about closure property at; brainly.com/question/19340450
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Answer:
(-2.4, 37.014)
Step-by-step explanation:
We are not told how to approach this problem.
One way would be to graph f(x) = x^5 − 10x^3 + 9x on [-3,3] and then to estimate the max and min of this function on this interval visually. A good graph done on a graphing calculator would be sufficient info for this estimation. My graph, on my TI83 calculator, shows that the relative minimum value of f(x) on this interval is between x=2 and x=3 and is approx. -37; the relative maximum value is between x= -3 and x = -2 and is approx. +37.
Thus, we choose Answer A as closest approx. values of the min and max points on [-3,3]. In Answer A, the max is at (-2.4, 37.014) and the min at (2.4, -37.014.
Optional: Another approach would be to use calculus: we'd differentiate f(x) = x^5 − 10x^3 + 9x, set the resulting derivative = to 0 and solve the resulting equation for x. There would be four x-values, which we'd call "critical values."
Answer:
9/4
Step-by-step explanation:
