<h3>2
Answers: Choice B and Choice D</h3>
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Explanation:
Standard form will always have the largest exponents listed first on the left side. Then as you move to the right, the exponents will decrease. Choice B shows this with the exponents counting down (3,2). Choice D is a similar story with the exponents counting down (9,2,1,0). Think of -6x as -6x^1, and also think of the 10 as 10x^0.
Something like choice A is a non-answer because the term with the largest exponent 3 is buried in the middle, and not at the left side. The exponents are not in decreasing order. Choice C can be ruled out for similar reasons.
Side note: the largest exponent is the degree of the polynomial. This only applies to single variable polynomials.
<h3>
Answer:</h3>
6 hours
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Step-by-step explanation:</h3>
The two hoses together take 1/3 the time (4/12 = 1/3), so the two hoses together are equivalent to 3 of the first hose.
That is, the second hose is equivalent to 2 of the first hose. Two of the first hose could fill the vat in half the time one of them can, so 6 hours.
The second hose alone can fill the vat in 6 hours.
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The first hose's rate of doing work is ...
... (1 vat)/(12 hours) = (1/12) vat/hour
If h is the second hose's rate of doing work, then working together their rate is ...
... (1/12 vat/hour) + h = (1/4 vat/hour)
... h = (1/4 - 1/12) vat/hour = (3/12 -1/12) vat/hour = 2/12 vat/hour
... h = 1/6 vat/hour
so will take 6 hours to fill 1 vat.
Y-intercept: (0,-3)
x-intercept: (0,5)
Yes, we can obtain a diagonal matrix by multiplying two non diagonal matrix.
Consider the matrix multiplication below
For the product to be a diagonal matrix,
a f + b h = 0 ⇒ a f = -b h
and c e + d g = 0 ⇒ c e = -d g
Consider the following sets of values
The the matrix product becomes:
Thus, as can be seen we can obtain a diagonal matrix that is a product of non diagonal matrices.