Answer: Todd used 27 black tiles.
Step-by-step explanation:
Let x represent the number of black tiles that Todd used.
Todd uses 21 white tiles & some black tiles to make a mosaic. This means that the total number of white and black tiles that Todd used is 21 + x
Each tile has an area of 3 square centimeters. This means that the total area covered by the white tiles is
21 × 3 = 63 square centimeters
Also, the total area covered by the black tiles is
3 × x = 3x square centimeters
The mosaic has a total area of 144 square centimeters. This means that
3x + 63 = 144
3x = 144 - 63
3x = 81
x = 81/3 = 27
9514 1404 393
Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
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<em>Additional comments</em>
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
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At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
Add 4/5 and 1/5 to make 5/5 or 1 mile the subtract 1 from 2 1/2 to equal 1 1/2 miles
the answer is 16 because .80 times 20 is 16
Answer:
(-7,4)
Step-by-step explanation:
goal: (y-k)^2=4p(x-h)
y^2-8y=4x+12 Rearranged and added 4x and 12 on both sides
y^2-8y+(-8/2)^2=4x+12+(-8/2)^2 complete square time (add same thing on both sides)
y^2-8y+(-4)^2=4x+12+(-4)^2 (simplify inside the squares)
(y-4)^2=4x+12+16 (now write the left hand side as a square)
(y-4)^2=4x+28
(y-4)^2=4(x+7) factored...
vertex is (-7,4)
