Answer:
False. Correct ratio is 
Step-by-step explanation:
the ratio of sine is opposite over hypotenuse
(opposite is the side across from the angle and hypotenuse it the slant line in the triangle)
Answer:
The restricted value is x=0
Step-by-step explanation:
We have been given the expression 
This is a rational function. We know that the rational expression is undefined if denominator is zero.
Here, we will use this fact to find the restricted value (s) of .
Restricted values means the values for which the function is not defined.
The given function is not defined if the denominator is zero.
12x =0
x =0
Hence, the restricted value is x=0
The third one correctly eliminates the y-value from the equation.
Answer:
10 ÷ 0.2=50
Step-by-step explanation:
10 lbs in total. Each batch uses 0.2 lbs.
We can find how many batches can be made by dividing 10 by 0.2.
10 ÷ 0.2=50
Juan is incorrect because if they could only make 5 batches then they would have only had 1 pound of red dye available.
They have 10 pounds of red dye available to make marbles, and if each batch takes only 0.2 lbs of it, then they can make 50 batches of marbles.
Answer:
1. x⁴³/³⁵
2. 1/x⁶
3. x⁴/2
Step-by-step explanation:
1. ⁷√x³. ⁵√x⁴
The above expression can be simplified as follow:
Recall:
ᵐ√aⁿ = aⁿ/ᵐ
⁷√x³ × ⁵√x⁴ = x³/⁷ × x⁴/⁵
Recall:
aⁿ × aᵐ = aⁿ⁺ᵐ
x³/⁷ × x⁴/⁵ = x⁽³/⁷ ⁺ ⁴/⁵⁾ = x⁴³/³⁵
Therefore,
⁷√x³. ⁵√x⁴ = x⁴³/³⁵
2. x¯³ / x⁵x¯²
The above expression can be simplified as follow:
Recall:
aⁿ × aᵐ = aⁿ⁺ᵐ
x⁵x¯² = x⁵ ⁺ ⁽¯²⁾ = x⁵ ¯ ² = x³
Thus,
x¯³ / x⁵x¯² = x¯³ / x³
Recall:
aⁿ / aᵐ = aⁿ ¯ ᵐ
x¯³ / x³ = x¯³ ¯ ³ = x¯⁶
Recall
a¯ⁿ = 1/aⁿ
x¯⁶ = 1/x⁶
Therefore,
x¯³ / x⁵x¯² = 1/x⁶
3. 5(x⁴)³ / 10x⁸
The above expression can be simplified as follow:
Recall:
(aⁿ)ᵐ = aⁿ×ᵐ
5(x⁴)³ / 10x⁸ = 5x¹² / 10x⁸
Recall:
aⁿ / aᵐ = aⁿ ¯ ᵐ
5x¹² / 10x⁸ = (5/10)x¹² ¯ ⁸ = 1/2 x⁴ = x⁴/2
Therefore,
5(x⁴)³ / 10x⁸ = x⁴/2
