A=43°
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
.08 , .6, 4, 20
.08 has a hundredth value, while .6 has a tenth value. You could also look at .6 as .60 which might help.
Discussion
The discriminate is b^2 - 4*a*c
The general equation for a quadratic is ax^2 + bx + c
In this equation's case
a = 1
b= -5
c = - 3
Solve
(-5)^2 - 4*(1)*(-3)
25 - (-12)
25 + 12
37
Note
Since the discriminate is > 0, the roots are real and different. The roots do exist and there are 2 of them.
The ordered pair which is a solution to the given inequality is: C. (2, 1).
<h3>What is an inequality?</h3>
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
- Less than (<).
- Greater than (>).
- Less than or equal to (≤).
- Greater than or equal to (≥).
Next, we would test the ordered pair with the given inequality to determine a solution as follows:
For ordered pair (4, 4), we have:
3x + 2y < 15
3(4) + 2(4) < 15
12 + 8 < 15
20 < 15 (False).
For ordered pair (3, 3), we have:
3x + 2y < 15
3(3) + 2(3) < 15
9 + 6 < 15
15 < 15 (False).
7x - 4y > 9
7(3) - 4(3) > 9
21 - 12 > 9
9 > 9 (False)
For ordered pair (2, 1), we have:
3x + 2y < 15
3(2) + 2(1) < 15
6 + 2 < 15
8 < 15 (True).
7x - 4y > 9
7(2) - 4(1) > 9
14 - 4 > 9
10 > 9 (True)
For ordered pair (1, 0), we have:
3x + 2y < 15
3(1) + 2(0) < 15
3 + 0 < 15
3 < 15 (True).
7x - 4y > 9
7(1) - 4(0) > 9
7 - 4 > 9
3 > 9 (False)
Read more on inequality here: brainly.com/question/27166555
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1/2 cubed= 1/2 times 1/2 times 1/2
1/2 time 1/2 = 1/4
1/4 times 1/2 = 1/8
A: 1/2 cubed equals 1/8
