The correct answer is the third one (x,y) - (-x, -y)
Answer: 6.82
Step-by-step explanation:
So we know the Law of Sines which is that Sin A/a = Sin B/b = Sin C/c. The Sin on top of the fraction is the angle, and the letter on the bottom is the side opposite from that angle.
Our first step is going to be finding the last angle. We have 2 angles already, but one that's missing. We know that all triangles' angles add up to 180, so we can add 68+40=108. Then do 180-108 to get 72. Now we know the third and final angle.
Ok so back to Law of Sines. Now we can plug into that equation. We only need Sin A/a = Sin B/b (It doesn't matter what order you put them in). And remember the lowercase letter at the bottom represents the OPPOSITE side from one of the angles. Since the problem wants the side opposite Sin 68, let's set up a proportion.

Set up we have what we know. We know one side, and opposite that is the angle we already solved for. Now we can cross multiply and end up with:

Since we want to isolate x, we can divide each side by Sin 72.
x= 7(Sin 68)/Sin 72
So now let's put it into the calculator:
7(Sin 68)=6.2853
Now let's divide 6.2853/Sin 72
And you should be left with 6.82 if you round it!
Ant's mass: 4 x 10 - 3
Elephant's mass: 8 x 106
First, we should evaluate these expressions by using PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. From P to S is the order that we must follow these steps.
So first for the ant's mass, we have to multiply first since the M comes before the S, resulting in 40 - 3 grams.
Next we have to subtract, leading us to getting 37.
For the elephant since there is only one operation, all we have to do is multiply, which equals 848.
In order to see how many times larger the elephant is than the ant, we have to divide the elephant's mass by the ant's.
848/37 = 22.9
Since you only want an approximate answer, you can put down 23 or even go a bit more vague and put down 20.
Answer:
The angle complies with the state regulations.
Step-by-step explanation:
The angle of elevation is the angle
in the figure, and from trigonometry we find that

taking the inverse sine of both sides we get

which gives

which is less than 5°, and therefore is well within the state regulations.
Answer: Equation:
or
x is the cost of each shrub x = $10
Step-by-step explanation: Total bill = $62.50.
Subtract the cost of potting soil for $12.50 to find the cost of just the shrubs. 5x equals that amount
5x = 62.50 - 12.50
5x = 50 divide both sides by 5
5x/5 = 50/5
x = 10