Rational number, because the Square root of 400 is 20, since 20 x itself is 400. Hope this helps!
I believe the answer is A "If a triangle is equilateral, then it has three congruent angles". Hope this helps!
Answer:
The domain and range remain the same.
Step-by-step explanation:
Hi there!
First, we must determine what increasing <em>a</em> by 2 really does to the exponential function.
In f(x)=ab^x, <em>a</em> represents the initial value (y-intercept) of the function while <em>b</em> represents the common ratio for each consecutive value of f(x).
Increasing <em>a</em> by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).
The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.
The range remains the same as well; for the original function, it would have been 
. Because increasing <em>a</em> by 2 does not move the entire function up or down, the range remains the same.
I hope this helps!
Answer:
x = 33
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180 for x
x = 180 - (90 + 57) = 180 - 147 = 33
<span> Direct-substituting x = -2 gives 0/0, so we know that by the factor theorem, both the numerator and denominator have a factor of x + 2. From there, we can cancel out the conflicting factors and apply the limit.
We can factor the numerator and denominator to get:
x^3 - x^2 - x + 10 = (x + 2)(x^2 - 3x + 5)
x^2 + 3x + 2 = (x + 2)(x + 1).
So we have:
lim (x-->-2) (x^3 - x^2 - x + 10)/(x^2 + 3x + 2)
= lim (x-->-2) [(x + 2)(x^2 - 3x + 5)]/[(x + 2)(x + 1)]
= lim (x-->-2) (x^2 - 3x + 5)/(x + 1), by canceling out x + 2
= [2^2 - 3(-2) + 5]/(-2 + 1)
= (4 + 6 + 5)/(-1)
= -15.
I hope this helps! </span>
