Answer:
Equations of straight lines are in the form y = mx + c (m and c are numbers). m is the gradient of the line and c is the y-intercept (where the graph crosses the y-axis).
Answer:
Step-by-step explanation:
You need to use parentheses around the numerator and denominator.
(x-3)(3-x) = -1
Answer:
(3) and
(4)
Step-by-step explanation:
Question 3
Required
Solve for x and y
We have:
--- angle on a straight line
Collect like terms
Solve for x
Also:
---- opposite angles
So, we have:
Divide by 2
Question 4:
Required
Solve for x
We have:
---- angle at right-angled
Collect like terms
Divide by 16
Answer: 40.13% of the soda bottles will have a volume less than 32 oz.
First, we need to find the z-score. That is the number of standard deviations below the mean.
(32 - 32.3) / 1.2 = -0.25
A bottle of 32 oz is -0.25 standard deviations below the mean. Use a standard normal distribution probability table and you will find the 40.13% of the scores are below a z-score of -0.25.
V (Volume) = s^2 * h = 48 ------> h = 48s^-2
C (Cost) = (4sh)(2) + (2s^2)(1) = 2s^2 + 8sh = 2s^2 + 8s(48s^-2) = 2s^2 + 384s^-1
dC/ds = 4s - 384s^-2 = 0 ------> 4s(1 - 96s^-3) = 0
Since s can't be 0, the only possible solution is:
1 - 96s^-3 = 0
s^3 - 96 = 0
s = cube root(96) = 2 cube root(12) ~ 4.579 cm
s^2 = 4 + 2 cube root(18) = 2[2 + cube root(18)]
h = 48/s^2 = 24/[2 + cube root(18)] ~ 5.194 cm