Answer: 5
Step-by-step explanation:
32
32 can be written in index form as 2x2x2x2x2 , which could be written as .
32 the becomes
Which could be written as
5 2
From law of logarithms; 2 = 1
Therefore : 5 2 = 5 x 1 = 5
Answer:
Step-by-step explanation:
For (a), you will use that 2 points that are closest to lying on the line which are the points located at (1, 14) and (7, 7).
For (b), you will use those 2 points to find the slope of the line using the slope formula:
For (c), you will use point-slope form to write the equation. Point-slope form is
where x and y stay x and y in the equation and x1 and y1 are replaced with one of the coordinates. Let's use (7, 7). Keep in mind that IT DOESN'T MATTER WHICH POINT YOU PICK...YOU WILL GET THE SAME EQUATION WITH EITHER ONE! And this is because both those points lie on the same line...the line for which we will write the equation.
We have m = -1.167, y = 7 and x = 7:
y - 7 = -1.167(x - 7)
That's the point-slope form of the line, but rarely is it ever left in that form. I've only seen it left in point-slope form in calculus. Most of the time, from point-slope form, you are asked to put it into slope-intercept form, and here is no exception. Putting the equation into slope-intercept form is the same thing as solving it for y. So let's get y all by itself on one side of the equals sign and everything else over on the other side. We also of course need to distribute into the parenthesis:
y - 7 = -1.167x + 8.169 and
y = -1.167 + 8.169 + 7 so
y = -1.167 + 15.169
That's your equation in slope-intercept form, so you're done!
Sam's money will double faster.
The formula for compound interest is
A=p(1+r)ˣ, where A is the total amount in the account, p is the principal you invest, r is the interest rate as a decimal, and x is the amount of time.
If we want to represent the money being doubled, we would use 2p for A:
2p=p(1+0.09)ˣ
2p=p(1.09)ˣ
Divide both sides by p:
2p/p = p(1.09)ˣ/p
2 = 1.09ˣ
Using logarithms to solve this,
The formula for simple interest is
I = prt
If we want to find the amount of time to double the principal, this means the amount of interest would be equal to the principal invested:
p = p(0.09)t
Dividing both sides by p,
p/p = p(0.09)t/p
1 = 0.09t
Dividing both sides by 0.09,
1/0.09 = t
11.11 = t
Answer: 13.3
Step-by-step explanation:
9.1-(-4.2)
answer:
yes, it is a right triangle
step-by-step explanation:
- remember: a triangle can only be a right triangle if it works with the pythagorean theorem
- therefore, we can plug in the numbers we have in the formula
- know the formula: a^2 + b^2 = c^2
- now, plug in
a^2 + b^2 = c^2
6^2 + 8^2 = 10^2
- the largest side is always the hypotenuse
- we have to see if both sides equal to the same value
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
- yes they are equal, therefore it is a right triangle