Ryan is making small meat loaves. Each small meat loaf uses 3/4 pound of meat. How much meat does Ryan need to make 8 small meat
1 answer:
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Answer:
1. Yes.
2. No.
3. Yes.
Step-by-step explanation:
Consider the following subsets of Pn given by
1.Let W1 be the set of all polynomials of the form , where a is in ℝ.
2.Let W2 be the set of all polynomials of the form , where a is in ℝ.
3. Let W3 be the set of all polynomials of the form , where a is in ℝ.
Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:
- The 0 vector of V is in W.
- Given v,w in W then v+w is in W.
- Given v in W and a a real number, then av is in W.
So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.
- First property:
Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.
For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.
- Second property:
W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials
.
We must check that p_1+p_2(t) is in W1.
Note that
Since a+b is another real number, we have that p1(t)+p2(t) is in W1.
W3. Consider two elements in W3. Say . Then
So, again, p1(t)+p2(t) is in W3.
- Third property.
W1. Consider an element in W1 and a real scalar b. Then
.
Since (ba) is another real scalar, we have that bp(t) is in W1.
W3. Consider an element in W3 and a real scalar b. Then
.
Since (ba) is another real scalar, we have that bp(t) is in W3.
After all,
W1 and W3 are subspaces of Pn for n= 2
and W2 is not a subspace of Pn.
The graph shows the solution of your equations is
.. (x, y) = (-6 2/3, -9 2/3)
The closest point to that of the choices offered is (-5, -7.2).
___
The offered "approximations" are not very good approximations.
.. (x, y) = (-6 2/3, -9 2/3)
The closest point to that of the choices offered is (-5, -7.2).
___
The offered "approximations" are not very good approximations.
Answer:
129
Step-by-step explanation:
Let a and b be two numbers.
We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as .
Their least common multiple is twelve times one of the integers. We can represent this information as .
Now, we will use property .
Upon substituting our given values, we will get:
Switch sides:
Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.
The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.
Similarly 96 is also not co-prime with 12 after dividing by 3.
We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.
Let us add 36 and 93 to find the largest possible sum of the required two integers as:
Therefore, the required largest possible sum of the two integers is 129.