Find the difference. 35 - (-8)
2 answers:
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Answer:
km
Step-by-step explanation:
The submarine's path from its base forms a right triangle when its final position is "connected" to the base. We know that the right triangle has legs of km and
km, and we need to find the length of its hypotenuse. To do so, we can use the Pythagorean Theorem, which states that in a right triangle,
, where
and
are the lengths of the triangle's legs and
is the length of the triangle's hypotenuse. In this case, we know what
and
are, and we need to solve for c, so after substituting the given values of
and
into
to solve for c, we get:
(Substitute
and
into the equation)
(Evaluate the squares on the LHS)
(Simplify the LHS)
(Symmetric Property of Equality)
(Take the square root of both sides of the equation)
(Simplify)
is an extraneous solution because you can't have negative distance, if that makes sense, so therefore, the submarine is approximately
km away from its base. Hope this helps!
You only flip the inequality sign when you multiply or divide both sides by a negative number.
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Problem 1
The inequality sign flip happens because we divided both sides by -8.
The graph will have a closed circle at 4 with shading to the left.
Three solutions are x = 0, x = 1, x = 2. You can pick any three numbers you want as long as they are 4 or smaller.
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Problem 2
The graph will have an open circle at 13/3 = 4&1/3 = 4.333 approx. The shading is to the left. No inequality sign flip happens because we divided both sides by a positive number.
Your choice of three solutions is correct. You can pick anything smaller than 4.3333
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Problem 3
The solution set is any value 3 or larger. Three solutions are x = 5, x = 6 and x = 7.
The graph has a closed circle at 3 on the number line. The shading is to the right.