Which expression is equivalent to the given expression?

2. Find the number of distinct triangles with c=11,b=7,B=18 a.0 b.1 c.2 d. cannot be determined

jok3333 [9.3K]

Answer: Choice C) 2

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Explanation:

Using the law of sines, we get
sin(B)/b = sin(C)/c
sin(18)/7 = sin(C)/11
0.0441452849107 = sin(C)/11
11*0.0441452849107 = sin(C)
0.4855981340177 = sin(C)
sin(C) = 0.4855981340177
C = arcsin(0.4855981340177) or C = 180-arcsin(0.4855981340177)
C = 29.0516679549861 or C = 150.948332045013
There are two possibilities for angle C because of something like sin(30) = sin(150) = 1/2 = 0.5

Those approximate values of C round to
C = 29.05 and C = 150.95

If C = 29.05, then angle A is
A = 180-B-C
A = 180-18-29.05
A = 132.95
Making this triangle possible since angle A is a positive number

If C = 150.95, then angle A is
A = 180-B-C
A = 180-18-150.95
A = 11.05
making this triangle possible since angle A is a positive number

There are two distinct triangles that can be formed.
One triangle is with the angles: A = 132.95, B = 18, C = 29.05
The other triangle is with the angles: A = 11.05, B = 18, C = 150.95
The decimal values are approximate

7 0

3 years ago

Order these following rational numbers from greatest to least:<br> 25% -0.17 3/5 -1/12 12

Vika [28.1K]

Answer:

12, 3/5, 25%, -1/12, -0.17

Step-by-step explanation:

The simplest way to do this is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

25% is already a percentage

-0.17 = -17%

3/5 = 60%

-1/12 (you can use a calculator to divide and find the percentage here) = -8.33

12 = 1200%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

12, 3/5, 25%, -1/12, -0.17

FINAL ANSWER: 12, 3/5, 25%, -1/12, -0.17

3 0

2 years ago

What is the solution to the equation? (-9x+5)^1/2=(3+4x)1/2

Phoenix [80]

4 0

4 years ago

Solve the system of equations 4x - 2y =8 3x + 4y = 17

igor_vitrenko [27]

Answer:

Solution: x = 3, y = 2, or (3, 2)

Step-by-step explanation:

Given the systems of linear equations with two variables:

$\displaystyle\mathsf{\left \{{Equation\:1:\:4x - 2y =\:8} \atop {Equation\:2:\:3x + 4y = 17}} \right}$

The <u>process of elimination</u> will be used to solve for the solution to the given problem.

First, we must multiply Equation 1 by 2:

(2)[4x - 2y] = 8(2)

8x - 4y = 16

Add the revised Equation 1 (from the previous step) to Equation 2:

$\displaystyle\mathsf{\left \ {{\quad \:\:\:8x\:- 4y = 16} \atop + {\quad\underline {\:\:3x\:+ 4y = 17\:} \underline}} \right.}\\\displaystyle\mathsf{\qquad\:\:11x\qquad\:=33}$