Answer:
Step-by-step explanation:
In order to make d the subject of the formula, you need to isolate it.
- You started with d-7 = 4d + 3/e
- Move 4d to the left side by subtracting 4d from both sides to cancel it from the right so you have...
d - 7 = 4d + 3/e This will leave you left with -3d - 7 = 3/e
-4d -4d
- Then move over the -7 by adding 7 to both sides...
-3d - 7 = 3/e This will leave you left with -3d = 3/e + 7
+7 +7
- Finally to get d by itself divide both sides of the equation by -3 and you'll be left with...
- You can cancel out the 3 in the -3/3e and make it -1/e so your final answer will be
Answer:
22.5 degrees
Step-by-step explanation:
Complementary angles add up to be 90 degrees. You can model the simple equation 
where is x is the small angle and 3x is the large angle.
the smaller angle is 22.5 degrees
Answer: a) 15, b) 1.
Step-by-step explanation:
A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?
(a) 10% of all adult Americans support the changes
Here, 
And , 
So, consider the equality, to find the value of 'n'.
So, there are 
more adult Americans needed.
(b) 15% of all adult Americans supports the changes
Here, 
So, again we get that
So, there are 
more adult Americans needed.
Hence, a) 15, b) 1.
A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.
Let's look at the four equations, with each solved as needed, into y = mx + b form.
A: 2x + y = 5
y = 5 - 2x
y = -2x + 5
Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.
B: y = 2x + 5
Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.
C: 2x - 4y = 10
-4y = 10 - 2x
-4y = -2x + 10
y = 2/4x -10/4
Here the slopes are different, so, like A this is not a good choice.
D: 2y - 4x = -10
2y = =10 + 4x
2y = 4x - 10
y = 2x - 5
Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.
Thus, D is the best choice.
The value of 
is 31
Explanation:
The given expression is 
We need to determine the value of
The value of can be determined by substituting 
in the expression
Thus, we have,
Adding the terms, we have,
Thus, the value is 31.
Therefore, the simplified value of the expression by substituting in the expression is 31.
