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Vikentia [17]
3 years ago
11

James types 25 words per minute. He spends 15 minutes typing his homework. What is the domain of this situation?

Mathematics
1 answer:
Law Incorporation [45]3 years ago
7 0

Answer:

1. All numbers between, including 0 and 15.

Step-by-step explanation:

The domain is the independent variable (x), so in this case, it's be the amount of time James spent typing. James types for 15 minutes, so of course 0 and 15 have to be included, as it'll give a complete graph of what he's done so far.

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What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following
skelet666 [1.2K]

For this case we have the following expression:

x ^ 2-4x + 10 = 4x + 10

We follow the steps below:

We subtract 4x on both sides of the equation:

x ^ 2-4x + 10-4x = 4x + 10-4x\\x ^ 2-8x + 10 = 10

We subtract 10 from both sides of the equation:

x ^ 2-8x + 10-10 = 10-10\\x ^ 2-8x = 0

Now, we must complete squares.

When we have an equation of the form:

ax ^ 2 + bx + c = 0, if we want to complete squares we must subtract c on both sides of the equation obtaining:

ax ^ 2 + bx + c-c = -c\\ax ^ 2 + bx = -c

The square is completed by adding to both sides of the equation: (\frac{b}{2})^{2}

So, we have left:

ax^2+bx + (\frac {b} {2})^{2} = - c + (\frac {b} {2}) ^ {2}

In the given expression we have:

a = 1\\b = -8\\c = 0

And to complete the square we have:

(\frac {b} {2}) ^ {2} = (\frac {-8} {2}) ^ {2} = 16

Rewriting we have:

x ^ 2-8x + 16 = 16

We factor the left side of the equation, that is, we look for two numbers that when added together result in -8 and when multiplied as a result 16. We have:

-4-4 = -8\\-4 * -4 = 16

So, we have:

(x-4) (x-4) = 16\\(x-4) ^ 2 = 16

Answer:

The intermediate step is to complete squares

(x-4) ^ 2 = 16


7 0
3 years ago
Are rectangles abcd and wxyz congruent? why or why not? yes, all right angles were preserved. yes, both rectangles have an area
Alexxx [7]
The correct answer is D. 
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One could observe this strong negative correlation and claim that hotter climate has solved the pirate issue. Of course this is a joke, but it explains why you shouldn't confuse correlation with causation.

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2 years ago
Suppose x is a real number and epsilon > 0. Prove that (x - epsilon, x epsilon) is a neighborhood of each of its members; in
kaheart [24]

Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let y\in (x-\epsilon,x+\epsilon). then we have that x-\epsilon. Hence, it makes sense to define the positive number delta as \delta=\min\{x+\epsilon-y,y-(x-\epsilon)\} (the inequality guarantees that these numbers are positive).

Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that (y-\delta,y+\delta)\subseteq  (x-\epsilon,x+\epsilon), and if we prove this, we are done. To prove it, let z\in (y-\delta,y+\delta), then y-\delta. First, \delta \leq y-(x-\epsilon) then -\delta \geq -y+x-\epsilon hence z>y-\delta \geq x-\epsilon

On the other hand, \delta \leq x+\epsilon-y then z hence z. Combining the inequalities, we have that  x-\epsilon, therefore (y-\delta,y+\delta)\subseteq  (x-\epsilon,x+\epsilon) as required.  

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