Answer:
y = (3/2)x - (1/2)
Step-by-step explanation:
The general structure of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of "m" (3/2). To find the value of "b", you should plug "m" into the equation in addition to the "x" and "y" values from the given point (1,1)
(1,1) ----> x = 1, y = 1
m = 3/2
y = mx + b <----- Slope-intercept form
y = (3/2)x + b <----- Plug (3/2) into "m"
1 = (3/2)(1) + b <----- Plug values into "x" and "y" from point
1 = (3/2) + b <----- Multiply (3/2) and 1
(2/2) = (3/2) + b <----- Change 1 into common denominator
(-1/2) = b <----- Subtract (3/2) from both sides
Because you now have values for both variables, you can construct your final equation.
y = (3/2)x - (1/2)
The answer is 8.25 years
The exponential function can be expressed as:
A = P * e^(kt)
A - the final amount
P - the current amount
k - the rate
t - time in years
If the final amount is the half of its current amount, then:
A = P/2
So,
A = P * e^(kt)
P/2 = P * e^(kt)
Divide P from both sides:
1/2 = e^(kt)
Logarithm both sides with natural logarithm:
ln(1/2) = ln(e^(kt))
ln(0.5) = kt * ln(e)
k = -0.084
-0.693 = -0.084 * t * 1
-0.693 = -0.084t
t = -0.693 / -0.084
t = 8.25 years
Answer:
See explanation
Step-by-step explanation:
4x = 12x + 32
Subtract 12x from both sides
-8x = 32
Divide each side by -8.
x = -4
Answer:
P = 16 inches
Step-by-step explanation:
The perimeter is given by
P = 2(l+w)
= 2(2in+6in)
= 2 ( 8in)
= 16 in
