Answer:
The expression of (5)(x+3)(y+3) is a binomial
The amount of pounds of vegetable needed in fractions to make the stew exactly 10 pounds is 3 3 / 8 pounds
<h3>How to solve fractions?</h3>
The amount of pounds of vegetable needed to make the stew exactly 10 pounds can be calculated as follows:
potatoes weight = 2 7 / 8 pounds = 23 / 8 pounds
green beans weight = 1 1 / 4 = 5 / 4 pounds
pepper weight = 2 1 / 2 = 5 / 2 pounds
Therefore,
weight needed = 10 - 23 / 8 - 5 / 4 - 5 / 2
weight needed = 80 - 23 - 10 - 20 / 8
weight needed = 80 - 53 / 8
weight needed = 27 / 8
weight needed in fractions to make the stew exactly 10 pounds = 3 3 / 8 pounds
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Answer:
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If you learned about the 45-45-90 triangle (which is isosceles), then the faster way is to know that the hypotenuse (side opposite of right angle) is √2 times either one of the sides.
3√2 = (√2)x
x = 3
But if you didn't learn the 45-45-90 triangle yet, that's ok.
Recall the trigonometric ratios for right triangles: sine (sin), cosine (cos), tangent (tan).
If your angle is x, then
sin(x) = opposite side / hypotenuse
cos(x) = adjacent side / hypotenuse
tan(x) = opposite side / adjacent side
Remember the hypotenuse is the side opposite and across from the right angle (3√2 in this case).
An acronym to remember this is SohCahToa.
In this problem, the angle given is 45°, and you need to find the length of the adjacent side x. The hypotenuse is also given as 3√2.
Because we have the adjacent side and the hypotenuse, we use cosine to relate those two sides
cos(45°) = x / (3√2)
x = (3√2)cos45°
If you plug this into your calculator (in degree mode), then
x = 3
