Answer:
P'(-9, 3)
Step-by-step explanation:
The transformation for rotation counterclockwise about the origin by some angle α will be ...
(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))
When the angle is α = 90°, this reduces to ...
(x, y) ⇒ (-y, x)
You have (x, y) = (3, 9), so the image point is P'(-9, 3).
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<em>Additional comment</em>
The "work" is applying the right sign and choosing the right coordinate to fill in the values (-y, x). I find it easier to look up the transformations for ±90° and 180°, rather than try to derive them from first principles every time. Your text may have a list:
- 90° CCW or 270° CW: (x, y) ⇒ (-y, x)
- 90° CW or 270° CCW: (x, y) ⇒ (y, -x)
- 180°: (x, y) ⇒ (-x, -y)
Answer:
first one is 42
second one is 3/8
Step-by-step explanation:
Answer:
The fan = x = 400
The heater = y = 3600
Step-by-step explanation:
Let the cost price of
The fan = x
The heater = y
Aaya bought a fan and a heater for Rs 4,000.
x + y = 4000
x = 4000 - y
He sold the fan at a profit of 25%
25% × x = 0.25x
And the heater at a loss of 5%.
5% × x = 0.05y
If he gained 7% on his total outlay, at
Hence:
0.25x + 0.05y = 7% × 4,000
0.25x + 0.05y = 280
Note:
x = 4000 - y
Hence:
0.25(4000 - y) + 0.05y = 280
1000 - 0.25y + 0.05y = 280
Collect like terms
-0.25y + 0.05y = 280 - 1000
-0.20y = -720
y = -720/0.20
y = 3600
x = 4000 - y
x = 4000 - 3600
x = 400
Hence, the price that he bought each item is given as:
The fan = x = 400
The heater = y = 3600
Well -5 is the whole number, and .36 is the fractional part which is equal to 36/100 so:
-5 and 36/100 with four being the greatest common factor of the fraction....
-5 8/25
3b + 2y = 5g
20g ÷ 5g = 4
4 x 2 = 8
8 oz of yellow paint
