Step-by-step explanation:
slope = (y2 - y1)/(x2 - x1)
-4/3 = (6 - y)/[4-(-2)]
-4/3 = (6-y)/6
(-4/3)×6 = 6-y
-8 = 6-y
y = 6 + 8
= 14
1. First, let us define the width of the rectangle as w and the length as l.
2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:
l = w + 6
3. The formula for the perimeter of a rectangle is P = 2w + 2l. We know that the perimeter of the rectangle in the problem is 24 in. so we can rewrite this as:
24 = 2w + 2l
4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:
24 = 2w + 2l
if l = w + 6, then: 24 = 2w + 2(w + 6)
24 = 2w + 2w + 12 (Expand 2(w + 6) )
24 = 4w + 12
12 = 4w (Subtract 12 from each side)
w = 12/4 (Divide each side by 4)
w = 3 in.
5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :
l = w + 6
l = 3 + 6
l = 9 in.
6. Therefor the rectangle has a width of 3 in. and a length of 9 in.
1. a²+b²=c²
a=6²=36
b=x²
c=15²=225
x=√189 feet deep (the square root of 189)
2. a²+b²=c²
a=3²=9
b=x²
c=5²=25
x=√16=4
Hope that helped
;)
Answer:
a
The null hypothesis is 
The alternative hypothesis 
b
The 95% confidence interval is 
Step-by-step explanation:
From the question the we are told that
The population mean is 
The sample size is n = 30
The sample mean is 
The standard deviation is 
Given that the confidence level is
then the level of significance is mathematically represented as


=> 
Next we obtain the critical value of
from the normal distribution table
The value is 
Generally the margin of error is mathematically represented as

substituting values


The 95% confidence interval confidence interval is mathematically represented as

substituting values


Answer:
The answer to your question is:
a) sin Ф = -3/√10
b) cos Ф = 1/√10
c) tan Ф = -3
Step-by-step explanation:
See the picture below
just remember
sin Ф = opposite / hypotenuse
cos Ф = adjacent / hypotenuse
tan Ф = opposite / hypotenuse