5 more because Mary had double and it was 5
The meaning of circumference is to find the distance around a circle or in other words the perimeter of the circle. The circumference of a circle can be calculate by using the formula
C=2πr or
C=πd, where r refers to the radius.
In this exercise is given a circle, which radius is 1 yard and it is asked to find its circumference and use 3.14 as the value of pi. In order to do that, you should substitute the given value of the radius and pi into the formula C=2πr.
The circumference of the circle is 6.28 yards.
7 x -4 = -28
-28 = 33x
33/28 = 1.18
1.18 = x
Problem 7
This is a 30-60-90 triangle. The short leg is half of the hypotenuse so 12/2 = 6 units long
The long leg, x, is equal to sqrt(3) times the short leg
long leg = (short leg)*sqrt(3)
long leg = (6)*sqrt(3)
long leg = 6*sqrt(3)
Answer: Choice B
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Problem 8
This is a 45-45-90 triangle. The two legs are congruent. In this case, they are both 7*sqrt(2) units long.
Hypotenuse = (leg)*sqrt(2)
Hypotenuse = (7*sqrt(2))*sqrt(2)
Hypotenuse = 7*(sqrt(2)*sqrt(2))
Hypotenuse = 7*sqrt(2*2)
Hypotenuse = 7*sqrt(4)
Hypotenuse = 7*2
Hypotenuse = 14
So the value of x is 14
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Problem 9
Use the SAS area of a triangle rule
Area of triangle = 0.5*(side1)*(side2)*sin(included angle)
A = 0.5*(8)*(12)*sin(65)
A = 48*sin(65)
A = 43.5027737777591
A = 43.5
Answer: 43.5
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Problem 10
Angle C is the included angle (aka the angle between the given sides). Like with problem 9, we use the SAS area rule
Area = 0.5*(side1)*(side2)*sin(included angle)
Area = 0.5*12*1.5*sin(63)
Area = 9*sin(63)
Area = 8.01905871769531
Area = 8.02
Answer: 8.02
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Problem 11
G = Grocery Store
B = Bank
P = Pedro's house
Given: GP = 11
What we want to find: Distance from G to B (ie find the length of GB). Call this distance x for now
a
Law of Sines:
sin(B)/GP = sin(P)/GB
sin(75)/11 = sin(54)/x
x*sin(75) = 11*sin(54)
x = 11*sin(54)/sin(75)
x = 9.21311626205676
Rounding to the nearest mile, x is roughly 9 miles
Answer: 9 miles
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Problem 12
D = Dino
G = Garret
M = Marco
Given Info:
DM = 17 yards
GM = 15 yards
angle M = 81 degrees
What we want to find:
distance from D to G, aka the length of DG
Call this value x for now
Use the law of cosines to find x
(DG)^2 = (DM)^2 + (GM)^2 - 2*(DM)*(GM)*cos(M)
x^2 = 17^2 + 15^2 - 2*17*15*cos(81)
x^2 = 289 + 225 - 510*cos(81)
x^2 = 514 - 510*cos(81)
x^2 = 514 - 79.7815771705178
x^2 = 434.218422829482
sqrt(x^2) = sqrt(434.218422829482)
x = 20.8379083122439
Rounded to the nearest yard, the distance from Garret to Dino is roughly 21 yards.