Answer:
7 movies
Step-by-step explanation:
You pay $45 each month for satellite Tv
$1.75 for every movie you purchase
Total bill is $57.25
They're asking for the number of movies that purchased during the month.
So, the equation is 1.75x+45=57.25
Answer: Either 25.0 or 25 depending on how your teacher wants you to format the answer
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Explanation:
To start off, it probably helps to translate what the question wants.
It states "For the pilot of airplane B, calculate the angle between the lines of sight to the airplane at C and Jenny's airplane [at point A]".
This fairly long, and possibly complex, sentence boils down to "find angle B"
To find angle B, we need to find the length of side 'a' first
Let,
a = x
b = 4.2
c = 5.7
Note how the lowercase letters (a,b,c) are opposite their uppercase counterparts (A,B,C). This is often the conventional way to label triangles. The lowercase letters are usually for the side lengths while the upper case is for the angles.
We have angle A = 120 degrees
Plug these values into the law of cosines formula below. Then solve for x
a^2 = b^2 + c^2 - 2*b*c*cos(A)
x^2 = 4.2^2 + 5.7^2 - 2*4.2*5.7*cos(120)
x^2 = 17.64 + 32.49 - 47.88*cos(120)
x^2 = 17.64 + 32.49 - 47.88*(-0.5)
x^2 = 17.64 + 32.49 + 23.94
x^2 = 74.07
x = sqrt(74.07)
x = 8.60639297266863
x = 8.6064
So side 'a' is roughly 8.6064 kilometers when we round to four decimal places
Now we'll use this to find angle B
Use the law of cosines again, but this time, the formula is slightly altered so that angle B is the focus instead of angle A
Plug in the side lengths (a,b,c). Solve for angle B
b^2 = a^2 + c^2 - 2*a*c*cos(B)
(4.2)^2 = (8.6064)^2 + (5.7)^2 - 2*(8.6064)*(5.7)*cos(B)
17.64 = 74.07012096 + 32.49 - 98.11296*cos(B)
17.64 = 106.56012096 - 98.11296*cos(B)
17.64 - 106.56012096 = 106.56012096 - 98.11296*cos(B)-106.56012096
-88.92012096 = -98.11296*cos(B)
(-88.92012096)/(-98.11296) = (-98.11296*cos(B))/(-98.11296)
0.906303519535034 = cos(B)
cos(B) = 0.906303519535034
arccos(cos(B)) = arccos(0.906303519535034)
B = 25.0005785532867
It's a bit messier this time around, but we get the approximate angle
B = 25.0005785532867
which rounds to
B = 25.0 degrees
when we round to the nearest tenth. We can write "25.0" as simply "25"
Answer:
it is true
Step-by-step explanation:
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
So we have to find out what x is before we can solve for either angle
because vertical angles are always congruent we can set the two equations to equal each other and solve for x
so
-3x + 58 = x - 2
we need to get all the x terms on one side before we can solve for x so let's add 2 to both sides to get x alone on the right side
now we have
-3x + 60 = x
now we add 3x to both sides
60 = 4x
we isolated the terms and now we can solve for x by dividing both sides by 4
15 = x
so if x = 15 we need to plug that in to both equations to check our work
C = -3(15) + 58
C = 13
D = 15 - 2
D = 13
x does in fact equal 15 because both equations got the same answer and we found out that angle D = 13
Answer:
$554.58
Step-by-step explanation:
The interest on the loan can be computed by first determining the future value of the loan in three years as follows:
FV=PV*(1+r)^n
PV is the amount of the loan which is $2,000
r is the interest rate which is 8.5%
n is the number of years which is 3 years
FV=$2000*(1+8.5%)^3=$ 2,554.58
Since the value of the loan in three years is $ 2,554.58 ,the interest on the loan is the difference between the future value and the present value
interest=$ 2,554.58-$2,000.00=$554.58
