–12 ÷ 3 • [–8 + (–4)² ∧ 6] + 2
According to PEMDAS, (Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction) we need to solve the exponent in the parenthesis first.
-12 ÷ 3 • [-8 + 16 - 6] + 2
-12 ÷ 3 • [-8 + 10 ] +2
-12 ÷ 3 • 2 + 2
-4 • 6 + 2
-24 + 2 = - 22
Hope this helps!
Using the distance formula I got 10.81665383 : 10.82
The correct answer is x>-2. The graph is attached.
To solve this:
-x/2 + 3/2 < 5/2
Subtract 3/2 from both sides:
-x/2 + 3/2 - 3/2 < 5/2 - 3/2
-x/2 < 2/2
-x/2 < 1
Multiply both sides by 2:
(-x/2)*2 < 1*2
-x < 2
Divide both sides by -1:
-x/-1 < 2/-1
Remember to flip the the symbol since you divide both sides by a negative:
x > -2
To graph the inequality, we draw a number line, making sure we have -2 on it. We circle -2 and leave it open, since it is strictly greater than. Then we shade the line to the left.
The definite integral from x=2 to x=k of (6x-5) is
x^2
6*------- - 5x, [2,k] or 3[ k^2 -5k] - 3 [ 2^2 - 5(2) ]
2 or
3[k^2 - 5k] - 3[4-10] = 10 (as given)
3k^2 -15k + 18 = 10, or
3k^2 - 15k + 8 = 0
This is a quadratic equation; solve it using the quadratic formula:
-(-15) plus or minus sqrt( [-15]^2 - 4(3)(8) )
k = ------------------------------------------------------------
6
15 plus or minus 26.36
= ------------------------------------
6