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 ![4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}](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%20%5Ctext%20%7B%20is%20%7D%204%20x%5E%7B%5Cfrac%7B11%7D%7B10%7D%7D%20%5Ccdot%20y%5E%7B%5Cfrac%7B17%7D%7B3%7D%7D)
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Answer:
x = 8
Step-by-step explanation:
Hello!
The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.
This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.
The side lengths opposite these two angles are congruent.
We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.
The value of x is 8.
Answer:
7n + 5 − 9n = 8 − 2n − 3 = true
-2 n + 5 = 5 - 2 n = true
Step-by-step explanation:
Left-hand side:
Simplify the following:
7 n - 9 n + 5
Grouping like terms, 7 n - 9 n + 5 = 5 + (7 n - 9 n):
5 + (7 n - 9 n)
7 n - 9 n = -2 n:
Answer: -2 n + 5
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Right-hand side:
Simplify the following:
-2 n - 3 + 8
Grouping like terms, -2 n - 3 + 8 = (8 - 3) - 2 n:
(8 - 3) - 2 n
8 - 3 = 5:
Answer: 5 - 2 n
Answer:
Set up trig ratio using tangent.
Tan theta = opp/adj
Tan theta = 500/800
Tan^-1 (500/800) = 32 degrees
