Answer: <em>-4</em>
Step-by-step explanation:
<em>gj-h^2</em>
<em>(4)(8)-6^2</em>
<em>32-6^2</em>
<em>32-36</em>
<em>-4</em>
Domain: Anything at all. All numbers and sub-divisions of a number line. - ∞ < x < ∞
The range is much harder. You could complete the square to get the range, which I will do after we get the answer. The simplest way to get the smallest part of the range is to graph the quadratic. The lowest point is at (-2, -25) so the range is
Range: -25 ≤ y < ∞
Completing the square.
y = x^2 + 4x - 21
y = (x^2 + 4x) - 21
y = (x^2 + 4x + (4/2)^2 ) - 21 - (4/2)^2
y = (x^2 + 4x + 4) - 21 - 4
y = (x + 2)^2 - 25
The minimum point is (- 2,-25) just as the graph predicted.
Answer:
x = log(33)/(3·log(2))
Step-by-step explanation:
The relevant logarithm relation is ...
log(a^b) = b·log(a)
__
Taking the logarithm of both sides of your equation gives ...
2^(3x) = 33
log(2^(3x)) = log(33)
(3x)·log(2) = log(33)
The coefficient of x is 3·log(2). Dividing by that gives the value of x:
x = log(33)/(3·log(2))
x ≈ 1.51851/(3·0.301030) ≈ 1.6814647
Answer:
a) d = 3 b) a(n) = 3n – 13 c) a(27) = 68
Step-by-step explanation:
solutions are (x, y) = (29,13) and (9349, 4181), which lead to (a, b) = (15,5) and (4895 ... corresponding to integer values of x give the quadruples. (x, y, z ... Since no number congruent to 3, modulo 4, can be written as the sum of two squares ... k is odd, the equation x2 - (k2 - 4)y2 = 4 has smallest solution in positive integers .
