<span>A radical is a mathematical symbol used to represent the root of a number. Here’s a quick example: the phrase “the square root of 81” is represented by the radical expression . (In the case of square roots, this expression is commonly shortened to —notice the absence of the small “2.”) When we find we are finding the non-negative number r such that , which is 9.</span>
<span>While square roots are probably the most common radical, we can also find the third root, the fifth root, the 10th root, or really any other nth root of a number. The nth root of a number can be represented by the radical expression.</span>
Radicals and exponents are inverse operations. For example, we know that 92 = 81 and = 9. This property can be generalized to all radicals and exponents as well: for any number, x, raised to an exponent n to produce the number y, the nth root of y is x.
We can represent this property like this: . A warning though: it is always true if x ≥ 0, and it is always true if n is odd. But it is not true when x < 0 and n is even.
Why is this the case? It is because raising any number, positive or negative, to an even power has the effect of making the new number positive. This is not the case for odd exponents. For example, think about inserting x = -3 and n = 2 into the formula above.
<span>The radical would be written as , which works out to, or 3. But our initial x value was -3, so we are left with the statement 3 = -3. </span>
Area of a Lawn = 14*16 + 1/2*8*14
A = 224 + 56
A = 280 Ft²
In short, Your Answer would be: Option C
Hope this helps!
true transformation is a dilation
<span>First convert liters to milliliters by
multiplying by 1000 mL/L . Then convert hours to seconds
by
dividing by 3600 seconds/hr.
</span>
Answer: 490 grams of the first alloy should be used.
30 grams of the second alloy should be used.
Step-by-step explanation:
Let x represent the weight of the first alloy in grams that should be used.
Let y represent the weight of the second alloy in grams that should be used.
A chemist has two alloys, one of which is 15% gold and 20% lead. This means that the amount of gold and lead in the first alloy is
0.15x and 0.2x
The second alloy contains 30% gold and 50% lead. This means that the amount of gold and lead in the second alloy is
0.3y and 0.5y
If the alloy to be made contains 82.5 g of gold, it means that
0.15x + 0.3y = 82.5 - - - - - - - - - - - -1
The second alloy would also contain 113 g of lead. This means that
0.2x + 0.5y = 113 - - - - - - - - - - - - -2
Multiplying equation 1 by 0.2 and equation 2 by 0.15, it becomes
0.03x + 0.06y = 16.5
0.03x + 0.075y = 16.95
Subtracting, it becomes
- 0.015y = - 0.45
y = - 0.45/- 0.015
y = 30
Substituting y = 30 into equation 1, it becomes
0.15x + 0.3 × 30 = 82.5
0.15x + 9 = 82.5
0.15x = 82.5 - 9 = 73.5
x = 73.5/0.15
x = 490
