Answer:
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Answer:
the third side must be greater than 6 but less than 16
Step-by-step explanation:
use triangle inequality theorem - 3 scenarios (one of which is discounted because it produces a negative and a side of a triangle cannot be negative)
5 + 11 > 3rd side (n) n < 16
5 + n > 11 n > 6
11 + n > 5; n > -6 discounted
Answer:
7
Step-by-step explanation:
The order of operations tells you to start any evaluation by looking at the innermost set of parentheses first.
Here, that means your first step is to find the value of h(-3). You do that by finding the input (x) value -3 in the table for h(x), and locating the corresponding output, h(x), which is 2.
Now, the problem becomes evaluating g(2).
You do the same thing for that function: locate the input x=2 in the table for g(x) and find the corresponding output: 7.
Now, you know ...
g(h(-3)) = g(2) = 7
Answer:

Step-by-step explanation:
The given expression: ![4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}](https://tex.z-dn.net/?f=4%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%20%5Ccdot%20y%5E%7B4%7D%20%5Ccdot%20%5Csqrt%7Bx%7D%20%5Ccdot%20%5Csqrt%5B3%5D%7By%5E%7B5%7D%7D)
Step 1: Change radical to fractional exponent.
Formula for fractional exponent: ![\sqrt[n]{a}=a^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
The power to which the base is raised becomes the numerator and the root becomes the denominator.
Step 2: Apply law of exponent for a product
Multiply powers with same base.
Take LCM for the fractions in the power.

Hence the simplified form of
.
Answer:
x = 
y = 2
Step-by-step explanation:
By applying tangent rule in the given triangle,
tan(45°) = 
1 = 
x = √2
By applying sine rule in the given triangle,
sin(45°) = 

y = 
y = 2