Question

WILL GIVE THANKS, BRAINIEST, AND 5 STARS! PLEASE HELP!

Answer 1

Answer:

a = $\frac{1}{2}$ , b = 5, and  $\frac{2b}{a}$ = 20

Step-by-step explanation:

f(x) = - x² + b, x ≤ 0     You would use this equation for f(-2). Since -2 is less than 0.

f(x) = - x² + b, x ≤ 0   ← You can ignore the x ≤ 0 part.

f(-2) = - (-2)² + b         Input the value -2 as x. The question states that f(-2) =1.

1 = - (-2)² + b              So switch f(-2) with 1 on the left side only.

1 = - (4) + b                Simplify. Do the exponents first, so (-2)² = 4.

1 = - 4 + b

+4  +4                      Do inverse operations

5 = b

Next,

f(x) = 2ax +3, x > 0      You would use his equation for f(2). Since 2 is greater than 0.

f(x) = 2ax +3, x > 0   ← You can ignore the x > 0 part.

f(2) = 2a(2) + 3             Input the value 2 as x.

f(2) = 4a +3           Simplify. The equation states f(2) = 5. So switch f(2) with 5

5 = 4a +3              on the left side only.

-3        - 3                     Do inverse operations

2 = 4a                          

$\frac{2}{4}$ = $\frac{4a}{4}$                           Divide 4 on both sides to isolate the variable a

$\frac{2}{4}$ = a                            Simplify

$\frac{1}{2}$ = a

Then,

The second part says to find $\frac{2b}{a}$

$\frac{2b}{a}$

$\frac{2(5)}{(\frac{1}{2}) }$                  Input both the values of a and b

$\frac{10}{\frac{1}{2} }$                    Simplify

20.

The answer for a is $\frac{1}{2}$, the answer for b is 5, and the answer for $\frac{2b}{a}$ is 20.