We know that
the law of sines establish
a/sin A=b/sin B
problem N 1
50/sin K=53/sin 76-------> 50*sin 76=53*sin K-----> sin K=50*sin 76/53
sin K=0.9154
K=arc sin (0.9154)--------> K=66.25°------> K=66°
the answer problem N 1 is the option
<span>c.) 66°
</span>
Problem N 2
30/sin R=35/sin 69------> sin R=30*sin 69/35-----> sin R=0.8002
R=arc sin(0.8002)-------> R=53.15°-----> R=53°
the answer problem N 2 is the option
<span>b.) 53°</span>
The best angle relationship that describes angles BAC and EAF is supplementary angles
The sum of angle on a straight line is supplementary i.e. they sum up to 180 degrees.
If Angles BAE and FAC are straight angles, it means they are linear pairs and their sum is 180 degrees. Mathematically;
m<BAE + m<FAC = 180degrees
Hence we can conclude that the best angle relationship that describes angles BAC and EAF is supplementary angles
Learn more here: brainly.com/question/22309882
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Define adult and student tickets
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Let the number of adult tickets be x
Adult tickets = x
Student tickets = x + 69
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Form equation and solve for x
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x + x + 69 = 569
2x + 69 = 569 ← Combine like terms
2x = 569 - 69 ← Subtract 69 from both sides
2x = 500
x = 250 ← Divide by 2 to find x
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Find the number of adult tickets and student tickets
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Adult tickets = x = 250
Student tickets = x + 69 = 319
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Answer: Adult tickets = 250 ; Student tickets = 319
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The first solution involves the volume of a pyramid. With the parameters, the volume is given as: 51cm³
<h3>What is the Volume of a Pyramid?</h3>
The volume of a pyramid is given as:
V = (lwh)/3
Where:
- L = base length
- w = base width
- h = pyramid height.
Hence, the volume of the pyramid is given as:
(6 x 5.2 x 4.9)/3
= 152.88/3
= 50.96
≈ 51 cm³
<h3>
What is the volume of the juice container?</h3>
Assuming that it is a cuboid, the volume for the shape of a cuboid is given as:
L x B x H
Where:
L = Length = 2cm
B (Width) = 34cm
H = Height = 12.2
Hence the Volume =
2 x 34 x 12.2
= 829.6
≈ 830 cm³
<h3>
What is the volume of the pit?</h3>
We are not given it's geometric description so we assume that it is a Cuboid.
Recall that the Volume of a Cuboid = L x B x H
Hence the Volume of the pit is:
7 x 5 x 8
<h3>
= 280 cm³
How much space can a box that measures 50cm on each edge hold?
</h3>
From the question, we can infer that we are dealing with a Cube.
The volume of a cube is given as L³.
Recall that L = 50cm
Hence, the volume is = 50³
= 125,000 cm³
<h3>
What is the volume of a rectangular prism?
</h3>
The formula for the volume of a rectangular prism is:
L x W x H; where
L (Length) = 130cm
W (Width) = 70cm
H (Height) = 110cm
→ 130 x 70 x 110
= 1,001,000 cm³
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Answer: it will take 5 months for both gyms to cost the same.
Step-by-step explanation:
Let x represent the number of months for which the total cost of gyms are the same.
Gym A charges a new member fee of $65 and $20 per month. This means that the cost of using gym A for x months would be
20x + 65
Gym B charges a new member fee of $25 and $35 per month but you get a discount of 20% monthly.
20% of 35 is 20/100 × 35 = 7
The monthly charge would be
35 - 7 = 28
This means that the cost of using gym A for x months would be
28x + 25
The number of months that it will take for the cost of both gyms to be the same would be
20x + 65 = 28x + 25
28x - 20x = 65 - 25
8x = 40
x = 40/8 = 5