Please help! ive been stuck on this for three weeks Use your calculator to find the smallest solution ot -5e^(-4x+2)+3=1/2log(x^(2)+1) and describe the steps you used. Round your answer to three decimals.

Step-by-step explanation:

Solution to Question 1

y = Log(x) if and only if

x = 10y

Interchange x and y

y = 10x

Hence

f -1(x) = 10x

Solution to Question 2

Use the change of base formula to write

Log4 65 = ln(65) / ln(4)

Then use a calculator

= 3.01 (rounded to 2 decimal places)

Solution to Question 3

Rewrite equation using 16 = 24

2 3x - 1 = 24

The two bases of the exponential expressions in the above equation are equal to 2. Hence their exponents has also to be equal

3x - 1 = 4

Solve for x

x = 5/3

Solution to Question 4

Logx 9 = 2 if and only if

x 2 = 9

x 2 = 32

For the above exponential expressions to be equal, their bases must be equal. Hence

x = 3

Solution to Question 5

Expand the polynomials on the right side

x 2 + kx - 6 = x 2 + x - 6

For two polynomials to be equal, all their corresponding coefficients must be equal. Hence

k = 1

Solution to Question 6

Write y in vertex form by completing the square

y = 2x 2 + 8x - 3 = 2(x 2 + 4x + 4 - 4) - 3

= 2(x 2 + 4x + 4) - 8 - 3

= 2(x + 2)2 - 11 which is of the form a(x - h)2 + k

vertex at (-2 , -11)

Solution to Question 7

Checking the given roots by substituting in equations A., B., C. and D. shows that D. is the equation with roots 3 and 5.

Solution to Question 8

We first note that

(x + 2)(x - 4) = x 2 - 2x - 8

We now multiply all terms of the given equation by (x + 2)(x - 4) and simplify to get

x (x - 4) + 3 (x + 2)= (4x + 2)

answer: true

step-by-step explanation:

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: