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Arada [10]
4 years ago
10

7. What is the value of x?

Mathematics
2 answers:
bekas [8.4K]4 years ago
5 0
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

=====================================================

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

=====================================================

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

=====================================================

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

=====================================================

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

=====================================================

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.
Dmitriy789 [7]4 years ago
4 0

Answer:

For problem 11 the answer is

9 miles

Step-by-step explanation:

This is the question that was on my test so it is the only answer I can confirm to be correct. If you need an explanation, the other answer on here has GREAT answers! Good luck everyone! :D

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Because the x-axis is labeled time (in minutes) and the y-axis is labeled distance (in kilometers).

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In this situatuon, m = \frac{9-0}{5-0} = \frac{9}{5}

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Answer:  The speed of the motorboat is 70 miles per hour

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so now for each of those coordinates you would subtract four from each X and add 3 to each Y. For example:
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<A (1,1)                                       <A' (-3,4)
<B (3,4)                                       <B' (-1,6)
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