6y+x=8 I need help with this problem
1 answer:
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Explanation:
There are two different formulas that are useful with the given information:
Area = (1/2)ab·sin(C)
Area = √(s(s-a)(s-b)(s-c)) . . . where s=(a+b+c)/2
It does not matter which sides are designated a, b, and c. Angle C will be opposite side c.
The third angle can be computed based on the fact that the sum of angles in a triangle is 180°. It will be 180° -32° -28° = 120°. The least-to-greatest order of the angles is the same as the least-to-greatest order of the length of the opposite side. So, we might have ...
- a = 7, A = 28°
- b = 8, B = 32°
- c = 13, C = 120°
Utilizing the first formula, the area is ...
Area = (1/2)(7)(8)sin(120°) = 14√3 ≈ 24.249 . . . square units
Utilizing the second formula, the area is ...
s = (7+8+13)/2 = 14
Area = √(14(14-7)(14-8)(14-13)) = 14√3 ≈ 24.249 . . . square units
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For the answer to be complete, it should be noted that using either of the other two angles will give different results for the area. That is because those angles are not exact values, but are rounded to the nearest degree. Using the first formula with the different angles, we get ...
- area = (1/2)(8)(13)sin(28°) ≈ 24.413 . . . square units
- area = (1/2)(7)(13)sin(32°) ≈ 24.111 . . . square units
The first of these answers is a little high because 28° is a little more than the actual value of the angle. Likewise, the second of these answers is a little low because 32° is slightly smaller than the actual angle.
In short, the most accurate information available should be used if the answer is to be the most accurate possible. If the angles are exact, then their values should be used. If the side measures are exact, then their values should be used. In general, it will be easier to make accurate measurements of the side lengths than to make accurate angle measurements.
3 RIGHT TRIANGLES
1 big right triangle is divided into 2 smaller ones. Medium and small.
<span> a.How far is the spot on the beach from the parking lot? </span>Medium triangle: long leg = 32 m ; short leg = x
Small triangle: long leg = x ; short leg = 18m
32/x = x/18
32*18 = x*x
576 = x²
√576 = √x²
24 = x
Parking lot to the beach is 24 meters.
<span>b. How far will he have to walk from the parking lot to get to the refreshment stand?</span>Use Pythagorean theorem:
Medium triangle: long leg = 32 m ; short leg = 24 m ; hypotenuse = ?
32²+ 24² = c²
1024 + 576 = c²
1600 = c²
√1600 = √c²
40 m = c
Parking lot to refreshment stand is 40 meters.
Answer:
5. Inequality form: n ≥ 3
Interval notation: [3, ∞)
6. Inequality form: x < 4
Interval notation: (- ∞, 4)
11. Inequality form: x > 50
Interval notation: (50, ∞)
12. Inequality form: y 8
Interval notation: [8, ∞)
15. Inequality form: z < 8
Interval notation: (- ∞, 8)
16. Inequality form: y 4
Interval notation: [4, ∞)
Step-by-step explanation:
I tried to graph them as best as I could, I hope this helps!
