4x + 3y = -26 x-3y =-14
1 answer:
You might be interested in
Question 1.
The Pythagoras Theorem states that the square of the hypotenuse is equal to the sum of the square of the two legs.
From the question, the hypotenuse is h=10 yd and one of the legs is 2yd.
This implies that,
Evaluate the exponents
Subbtract 4 from each side
The correct answer is C
Question 2
We want to solve
using inverse functions.
The inverse of an exponential function is a logarithmic function.
We take natural log of both sides to get;
Recall that
This means
Logarithm of the base is 1
Divide both sides by 4
It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>
</span><span>In notation we write respectively
</span>
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers