Is it true that the set of integers is a subset of the set of whole numbers

Two ships leave the same port at the same time. Two hours later ship A has traveled 12 miles and ship B has traveled 8 miles.

sashaice [31]

Answer:

the angle between their paths is 100.8°

Step-by-step explanation:

From the given information, you can construct a triangle, just like the one in the figure.

We will use the Cosine Rule which is:

c² = b² + a² - 2 b c cos(θ)

where

c = 16 miles
b = 8 miles
a = 12 miles

Therefore,

2 b c cos(θ) = b² + a² - c²

cos(θ) = (b² + a² - c²) / 2 b c

θ = cos⁻¹( (b² + a² - c²) / (2 b c) )

θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )

θ = 100.8°

Therefore, the angle between their paths is 100.8°

4 0

3 years ago

Each month cameron budgets $1040 for fixed expenses $980 for living expenses and $120 for annual expenses his annual net income

sineoko [7]

Let us first find how much he is spending every year, to do this let's find his monthly expense and multiply it by 12.

Every month Cameron spends 1040 + 980 + 120 = 2140

To find out how much he spends yearly, multiply the monthly value by 12,
2140 x 12 = 25680

This value is more than his net income so he clearly has a surplus, but to check we can subtract 129 from every month to get:

(1040 + 980 + 120 - 129) = 2011

2011 x 12 = 24132, which shows that his budget is saving 129 surplus every month. Choice B is correct.

5 0

3 years ago

Read 2 more answers

Is the following statement correct? Explain.

Maksim231197 [3]

Answer: The answer is NO.

Step-by-step explanation: The given statement is -

If the graph of two equations are coincident lines, then that system of equations will have no solution.

We are to check whether the above statement is correct or not.

Any two equations having graphs as coincident lines are of the form -

$ax+by=c,\\\\dax+dby=dc,\\\\\textup{where}~~d\neq 1.$

If we take d = 1, then both the equations will be same.

Now, subtracting the second equation from first, we have

$a(1-d)x+b(1-d)y=c(1-d)\\\\\Rightarrow ax+by=c,~\textup{since}~d\neq 1,~\textup{so}~1-d\neq 0.$

Again, we will get the first equation, which is linear in two unknown variables. So, the system will have infinite number of solutions, which consists of the points lying on the line.

For example, see the attached figure, the graphs of following two equations is drawn and they are coincident. Also, the result is again the same straight line which has infinite number of points on it. These points makes the solution for the following system.

$2x+5y=10,\\\\6x+15y=30.$