Answer:
Step-by-step explanation:
There is a relationship between lines that are perpendicular. Their slopes are negative reciprocals of each other. Example: if one line has a slope of 4/3 then a line with the slope of -3/4 is perpendicular to it (they intersect at right angles).
So to find the slope of a line perpendicular to y = -2/3x + 4 we must know the slope of it. The slope, when the line is in the slope-intercept form (aka y = mx + b), is the multiplier in front of the "x" so in this case it is -2/3. So a line perpendicular to it has a slope of 3/2.
Now that we know the slope (m = 3/2) we can find the equation of the line that has a slope of 3/2 but goes through the point (-2, -2) in a couple of ways.
1) Use the slope-intercept form of a line and plug in the values of x = -2 and y = -2 (from the point (-2, -2) like this:
y = mx + b
y = 3/2x + b
-2 = 3/2(-2) + b
-2 = -3 + b
1 = b
So y = 3/2x + 1
2) We can use the point-slope equation y - y1 = m(x - x1) which works great if you know the value of m (we do, m = 3/2) and some point (x1, y1) on the line (and we do, (-2, -2); so x1 = -2 and y1 = -2):
y - y1 = m(x - x1)
y - y1 = 3/2(x - x1)
y - (-2) = 3/2(x - (-2))
y + 2 = 3/2(x + 2)
Although it looks different than the other equation, it is really the same. Just distribute and combine like-terms and you'll see it's the same. So either is an acceptable answer for this quest
Answer:
No, it can not be applied.
Step-by-step explanation:
f(x) = 1/x²
f(x) is a polynomial that is not continuous
As,
f(x) = 1/0 is undefines
Secondly, it is not differentiable (i.e. the derivative does not exists on the interval given)
Derivative of this function
f'(x) = (1)x^-2
= -2x^(-2-1)
= -2x^(-3)
= -2/x³
= -2/x³
f'(0) = -2/0 is undefined
Thus, mean value theorem can not be applied.
<span>B = 2S
B + 7 = 1.5(S+7)
-----
2S+7 = 1.5S + 10.5
0.5S = 3.5
Samuel is 7
Bro is 14</span>
Answer:
Hans deposits $6000 into an account.
=> Principal P = 6000
Simple interest rate 5% per year.
=> Rate R = 5% = 5/100 = 0.05
The formula to calculate the amount of interest after 4 years:
A = P x R x years = 6000 x (5/100) x 4 = 1200$
Hope this helps!
:)
Answer:
sqrt(170) or approximately 13.038
Step-by-step explanation:
We can use the Pythagorean theorem to find the diagonal since the diagonal makes a right triangle
a^2 + b^2 = c^2
We need to find the leg lengths
ML = 7 and MJ = 11
7^2 + 11^2 = JL^2
49+ 121 = JL ^2
170 = JL ^2
Take the square root of each side
sqrt(170) = JL
13.038 = JL