The correct answer is: [B]: " ∠C ≅ ∠F " .
______________________________________________________
Note: We are given that:
"I<span>n △ABC, m∠A=38° and m∠B=67 " .
Since a triangle has three (3) angles (by definition) ; and since all 3 angles in any triangle must add up to 180</span>°<span> (by definition); we can solve for:
m</span>∠C ;
m∠C = 180 − (38 + 67) = 180 <span>− 105 = 75 .
</span>m∠C = 75° ;
________________________________________________________
Likewise, given △DEF, m∠D=38° and m∠E=67 ; we find m∠F as follows:
m∠F = 180 - (38 + 67) = 180 − 105 = 75 .
m∠F = 75° .
__________________________________________________
So, let us consider the answer choices given:
__________________________________________________
Choice [A]: "m∠F = 67° " ; is incorrect. We know that "<span>m∠F = 75° " .
__________________________________________________
Choice [B]: " </span>∠C ≅ ∠F " is correct. We know that ΔABC ≅ ΔDEF ; and that;
m∠A = m∠D = 38° ; and that: m∠B = m∠E = 67° ; and that:
m∠C = m∠F = 75° ; and as such:
∠A ≅ D ; and ∠B ≅ ∠E ; and ∠C ≅ ∠F .
___________________________________________________
Choice [C]: "<span>m∠C = 75° only" ; is incorrect. While it is correct that:
"m</span><span>∠C = 75° " ; this answer choice is INCORRECT; since this answer choice is not the ONLY answer choice provided that holds true. In fact, we have already determined that answer choice: [B] (see above) is a correct statement.
___________________________________________________
Choice [D]: "</span><span>∠C is not necessarily congruent to ∠F. " ; This answer choice is INCORRECT; as explained in Answer choice: [B]: (see above).
___________________________________________________
Choice [E]: "</span>It is not possible to determine m∠F." ; This answer choice is INCORRECT. We know that " m∠F = 75° " .
___________________________________________________
Choice [F]: " <span>It is not possible to determine m∠C." ; This answer choice is
INCORRECT. We know that " m</span>∠C = 75° " .
___________________________________________________
The correct answer is: [B]: " <span>∠C ≅ ∠F " .
___________________________________________________</span>
It would be equal to (6x6) x (2x6) x (2x6) x (2x6) x (2x6). Look that up.
Answer:
y=1/2x-2
Step-by-step explanation:
Hope this helps!
Let's start by solving this problem when there are only two positive numbers involved, and then see whether we can apply the same technique when there are three positive integers.
Let the two positive integers be x and y.
Then x + y = 100, and xy = the product.
Let's eliminate x. Solve x + y = 100 for x: x = 100 - y. Now subst. this last result into P = xy: P = product = (100 - y)(y) = 100y - y^2
Differentiating, dP/dy = 100 - 2y. Set this = to 0 and solve for y: -2y = -100, and y = 50. Since x + y = 100, x is thus also = to 50.
Solution set: (50,50).
Now suppose that three positive integers add up to 100, and that we want to maximize their product.
Then x + y + z = 100. Let's maximize f(x,y,z) = xyz (the product of x, y and z).
Since x + y + z = 100, we can eliminate z by solving x + y + z = 100 for z and subst. the result back into f(x,y,z) = xyz:
We get f(x,y) =xy(100-x-y), a function of two variables instead of three.
I won't go through the entire procedure of maximizing a function in three variables, but will get you started:
Find the 'partial of f with respect to x' and then the 'partial of f with respect to y'. Set each of these partial derivatives = to 0:
f = 0 = (partial of xy(100-x-y) with respect to x
x
= xy(partial of 100-x-y with respect to x) + (100-x-y)(partial of xy with respect to x)
= xy(-1) + (100-x-y)(y)
We must set this partial = to 0: -xy+100y-xy-y^2 = 0
-2xy + 100y - y^2 = 0
or y(-2x + 100 - y) = 0
of which y=0 is one solution and in which -2x + 100 - y = 0
You must now go through the same procedure with respect to the partials with respect to y.
If you'd like to continue this discussion, please respond with questions and comments.
I just want the points
tysm!
:)