Cos 52 = 0.6157
sin 42 = cos 48 = 2/3 (because 42 + 38 = 90 - complementary angles)
if tan 20,5 = 3/8 then tan 69.5 wil = 1 / 3/8 = 8/3
Step-by-step explanation:
4x + y = 6 => 8x + 2y = 12.
8x + 2y = 12
+ (-5x - 2y = -3)
=> 3x = 9, x = 3.
Therefore 4(3) + y = 6, 12 + y = 6, y = -6.
The solutions are x = 3 and y = -6.
Step-by-step explanation:
I think I did the right process but the answer didn't match.
<span>This would be a bell curve with a z-score of greater than +2.00, since 3 minutes is exactly two standard deviations greater than the mean of 2.00. Looking at a z-score table for the proportion of the curve that lies in the 1-tailed area greater than 2.00, we find that the value is .0228. This would be the probability that the conversation is over three minutes: 0.0228 or 2.28%.</span>
The width of the rug is 3 inches
Step-by-step explanation:
A knitter wants to make a rug for a dollhouse
- The length of the rug will be 2 inches more than it’s width
- The total area of the rug ( in square inches) based on the width w of the rug (in inches ) is given by A(w) = w (2 + w)
- The desired area of the rug is 15 square inches
We need to find the width of the rug
∵ The area of the rug is A(w) = w(2 + w)
- Simplify the right hand side
∴ A(w) = 2w + w²
∵ The desired area of the rug is 15 square inches
- Equate A(w) by 15
∴ 2w + w² = 15
- Subtract 15 from both sides
∴ 2w + w² - 15 = 0
- Its a quadratic equation arrange its terms from the greatest power of x
∴ w² + 2w - 15 = 0
Factorize it into two binomial factors
∵ w² = w × w
∵ 15 = 3 × 5
∵ 5w - 3w = 2w
∴ w² + 2w - 15 = (w -3)(w + 5)
∴ (w - 3)(w + 5) = 0
- Equate each factor by 0
∴ w - 3 = 0 OR w + 5 = 0
∵ w - 3 = 0
- Add 3 to both sides
∴ w = 3
∵ w + 5 = 0
- Subtract 5 from both sides
∴ w = -5 ⇒ rejected because no dimension with -ve value
∴ w = 3 only
The width of the rug is 3 inches
Learn more:
You can learn more about the quadratic equation in brainly.com/question/9328925
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