Part A
Use the FOIL rule to expand out the expression below
(2x+7)(5x+9)
2x*5x + 2x*9 + 7*5x + 7*9
10x^2 + 18x + 35x + 63
10x^2 + 53x + 63 is the final answer for part A
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Part B
The degree is 2. This is a quadratic trinomial.
The degree is simply the largest exponent after expanding everything out. The degree directly determines the type of polynomial. Since the degree is 2, we have a quadratic. The polynomial is a trinomial because it has 3 terms.
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Part C
Imagine we had a machine in which we deposit 2 coins into it. One would happen on either side. After the coins are deposited, a third coin pops out. The 2 coins going in and the third coin coming out are the same currency. This represents an example of closure.
In mathematics, the idea of closure is taking any two objects of the same type, applying an operation on them, and getting the same type of object as the input.
For example, we could take two whole numbers and multiply them together. The result is always a whole number. The set of whole numbers is closed under multiplication because you can't leave the set (hence the gate is closed not letting anything out).
Similarly, taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this in action because (2x+7), (5x+9) and 10x^2 + 53x + 63 are all polynomials.
<span>12(X+20)=372
12X+240=372
Subtract the 240
</span>12X=372-240 ----> 12X=132
Divide by 12
12X/12=132/12 ---> x = 11
Since we are given the mean μ = .80, and standard deviation σ = 5, we compute first the corresponding z scores of x₁ = .70 and x₂ = .80.
The formula for z score is z = (x-μ)/σ.
z₁ = (.70-.80)/5 = -0.02
z₂ = (.80-.80)/5 = 0
Then, using a z table, we find the probability of the corresponding z scores.
For z₁, it is 0.4920 and for z₂ it is 0.5000. (If you notice, x=μ, its probability will always be 0.5000).
We then find the difference between the two probabilities in order to find the percentage of students that earned <span>a score between 70% and 80%
0.5000 - 0.4920 = 0.008 = 0.8%
Only 0.8% of students earned a score between 70% and 80%.</span>
Answer: yes they are equivalent
Step-by-step explanation:
No matter how the number is placed in the equation if it is the same numbers they are equivalent
32
31.832142857 is what you got, look at your tenths digit. if it's greater or equal to 5, it will always round to the higher number. if its less than or equal to 4, it will be the lower number.
for example, 10.4 will be 10, as it is lower than 5
or 10.6 will be 11 cause it is higher than 5