Multiply both sides by 6
(b-4)/6*6= b-4
b/2*6= 3b

Rewrite the equation
b-4= 3b

Subtract b from both sides
-4=2b

Divide both sides by 2
-2=b

Final answer: b=-2

5 0

2 years ago

What is lim x→-3 sqrt x^2-8

vitfil [10]

If the -8 is under the square root, then...

$\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1\\\\$

If the -8 is not under the square root, then...

$\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5$

Either way, we replace x with -3 and simplify.

For more information, refer to the direct substitution rule for limits.

4 0

1 year ago

The graph of f(x)=x^2 is sketched in red and the graph of g(x) is sketched in blue. Use the translation rule and f(x)=x^2 to ide

Yuki888 [10]

We can use the vertex form of a quadratic, $y = a(x-h)^{2} + k$ , to find that $g(x) = a x^{2} - 7$ . Plugging $(x,y)$ ordered pairs into g(x), we see that a = 1. For example, for $(3, 2)$ , $2 = a * 3^{2} - 7$ . Solving for a gives 1.

3 0

2 years ago