A because the table doesn’t have a constant rate of change
X^2 + 2x < 8
x^2 + 2x - 8 < 0
(x + 4)(x - 2) < 0 ,,
{x + 4 < 0 and x - 2 > 0} or {x + 4 > 0 ,,and x - 2 < 0} ,,
{x < -4 and x > 2} or {x > -4 and x < 2},,
Discard x < -4 and x > 2 because it has no solutions, leaving just
x > -4 and x < 2 ,,
-4 < x < 2
By using exponent properties we will see that:
1) The expression is equal to 16.
2) The expression is equal to 4^6, so the correct option is B.
<h3>What is the value of the expression?</h3>
Here we want to solve the expression:
(2^0*4^(-2)*2^3*4^3)/2
Remember the exponent property:
a^x*a^y = a^{x + y}
let's rewrite the numerator:
2^0*4^(-2)*2^3*4^3
= (2^0*2^3)*(4^(-2)*4^3)
= 2^(0 + 3)*(4^(-2 + 3))
= 2^3*4 = 2^3*2*2 = 2^(3 + 1 + 1) = 2^5
Then we can rewrite the expression as:
2^5/2 = 2^4 = 16
b)
(1/4^-3)^2
The negative exponent means that we need to take the inverse:
(1/4^-3)^2 = (4^3)^2 = (4^3)*(4^3) = 4^(3 + 3) = 4^6
So the correct option is B.
Learn more about exponents:
brainly.com/question/847241
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<span>(1,625) No
(0,-25) No
(-1,-1) No
Think about what an integer exponent means for an negative base and you'll understand this problem. For instance the powers of -25 would be
-25^1 = -25
-25^2 = (-25) * (-25) = 625
-25^3 = (-25)*(-25)*(-25) = -15625
and so on, giving 390625, -9765625, 244140625, etc.
But that's a different subject. For the ordered pairs given, let's check them out.
(1,625)
-25^1 + 1 = -25 + 1 = -24. And -24 is not equal to 625, so "No".
(0,-25)
-25^0 + 1 = 1 +1 = 2.
Note: Any real number other than 0 raised to the 0th power is 1. And 2 is not equal to -25, so "No".
(-1,-1)
-25^(-1) + 1 = 1/(-25^1) + 1 = 1/-25 + 1 = 24/25.
And 24/25 is not equal to -1, so also "No".</span>