Answer:
x = -6
Step-by-step explanation:
3x-6+4=-20
Combine like terms
3x -2 = -20
Add 2 to each side
3x-2+2 = -20 +2
3x = -18
Divide each side by 3
3x/3 = -18/3
x = -6
In every case, you're finding the surface area of a rectangular prism. That area is the sum of the areas of the 6 rectangular faces. Since opposite faces have the same area, the formula can be written
... S = 2(LW +WH +HL)
The number of multiplications can be reduced if you rearrange the formula to
... S = 2(LW +H(L +W))
where L, W, and H are the length, width, and height of the prism. (It does not matter which dimension gets what name, as long as you use the same number for the same variable in the formula.)
When you're evaluating this formula over and over for diffferent sets of numbers, it is convenient to let a calculator or spreadsheet program do it for you.
1. S = 2((5 cm)(5 cm) +(5 cm)(5 cm +5 cm)) = 2(25 cm² +(5 cm)(10 cm))
... = 2(25 cm² + 50 cm²) = 150 cm²
2. S = 2(12·6 + 2(12+6)) mm² = 2(72 +36) mm² = 216 mm²
3. S = 2(11·6 + 4(11 +6)) ft² = 2·134 ft² = 264 ft²
4. S = 2(10·4 +3(10 +4)) in² = 164 in²
The polar coordinate of any point can be written as:
(r, θ) = (r, θ + 2nπ) when positive
(r, θ) = [ - r, θ + (2n + 1)π ] when negative
The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).
When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)
When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.
Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].
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Answer:
p = 4.0
q = 2.0
angle <P = 64 degrees
Step-by-step explanation:
We can use the definition of cosine to find the value of side p (the adjacent side to the 26 degree angle, via the formula:
![cos(26^o)= \frac{adjacent}{hypotenuse} \\cos(26^o)= \frac{p}{4.5}\\p= 4.5 *cos(26^o)\\p=4.0445](https://tex.z-dn.net/?f=cos%2826%5Eo%29%3D%20%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D%20%5C%5Ccos%2826%5Eo%29%3D%20%5Cfrac%7Bp%7D%7B4.5%7D%5C%5Cp%3D%204.5%20%2Acos%2826%5Eo%29%5C%5Cp%3D4.0445)
which rounded to the nearest tenth gives : p = 4.0
Now we use the sine function to help us determine side q:
![sin(26^o)= \frac{opposite}{hypotenuse} \\sin(26^o)= \frac{q}{4.5}\\q= 4.5 *sin(26^o)\\q=1.9726](https://tex.z-dn.net/?f=sin%2826%5Eo%29%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%20%5C%5Csin%2826%5Eo%29%3D%20%5Cfrac%7Bq%7D%7B4.5%7D%5C%5Cq%3D%204.5%20%2Asin%2826%5Eo%29%5C%5Cq%3D1.9726)
which rounded to the nearest tenth gives:
q = 2.0
Finally, we determine the measure of angle P using the fact that the addition of all internal angles of a triangle must add to 180 degrees:
< P + < Q + < R = 180
< P + 26 + 90 = 180
< P = 180 - 26 - 90
< P = 64 degrees