Answer:
(9x²)²
Step-by-step explanation:
Given the expression 81x⁴, to write the expression as a square of a monomial, first we will assign a variable to the expression.
y = 81x⁴
Then we take the square root of both sides of the expression
√y = √81x⁴
y^½ = √81 × √x⁴
y^½ = 9x²
Squaring both sides of the resulting equation to get y back
(y^½)² = (9x²)²
y = (9x²)²
The expression as a square of a monomial is (9x²)²
Answer:
D) 5
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes.
The line: 
has a slope of 
as it is in y=mx+b form, where m is the slope, and b is the y-intercept.
Since the slope is , we see that the negative reciprocal slope is 
, as 
is the reciprocal (flip the numerator and denominator).
From here, we can use point slope form: 
, where 
is the point. In this case, (3, 1) is the point.
Thus, we have: 
as our final equation.
Simplifying: 
And: 
, which gives us the y-intercept to be 5.
Let me know if this helps!
Square root of (5-9)^2+(1+6)^2
9514 1404 393
Answer:
∠N = 10°
Step-by-step explanation:
Assuming the marked point on segment LN is supposed to be the center of the circle, arc NML is 180°, so arc ML is 180° -160° = 20°.
Arc ML is intercepted by inscribed angle LNM, so the measure of that angle is half the arc measure:
∠N = (1/2)(20°) = 10°
First of all, let's consider the line, since it's simpler to graph: we draw the endpoints and connect them:
So, you just need to draw the points
As for the trigonometric function, we have to start from the parent function 
and derive the graph of its child function via transformations:
- When we multiply the whole function by 2, we stretch the graph vertically. So, the function has still period
, but now it ranges from -2 to 2 instead of from -1 to 1 (amplitude 2) - When we multiply the argument by 2, we compress the function horizontally. So, the new period becomes
, and the function makes two complete oscillations from 0 to
You can see the two functions in the image below. You can also see that the two graphs cross 4 times, meaning that the equation
has four solutions.
