Estimate how many times larger 4 x 10^15 is than 8 x 10^9 in the form of a single digit times an integer power of 10. estimate how many times larger 2 x 10^-5 is than 4 x 10^-12 in the form of a single digit times an integer power of 10.

Problem A

When you use the term larger, you mean that (if the power is positive) the bigger number is in the numerator. 4*10^15 > 8 * 10^9 So 8 * 10^9  is in the denominator

Solution

Note:The tricky part is recognizing what to do with the 0.5 * 10^6. You can always break apart a power into it's parts. Since 6 = 5 + 1, the power can be broken down into 10^1*10^5. The 10^1 is used to get the 0.5 to a number that is a single digit.

Problem 2

I'm just going to give you the answer to this. Please use Problem A as a guide.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b

the answer is 40.

proof: