Answer:
The correct answer is option <em>B. AA</em>
<em></em>
Step-by-step explanation:
Given two triangle:
and 
.
The dimensions given in are:
We know that the sum of three angles in a triangle is equal to 
.
The dimensions given in are:
We know that the sum of three angles in a triangle is equal to .
Now, if we compare the angles of the two triangles:
So, by AA postulate (i.e. Angle - Angle) postulate, the two triangles are similar.
by <em>AA theorem.</em>
<em>So, correct answer is option B. AA </em>
Answer:
M<1 80 by the corresponding angles postulate
Step-by-step explanation:
Answer:
The statement that is true about dot plot is:
A dot plot shows the frequency of the individual values of any given data set
Step-by-step explanation:
A dot plot also known as a dot chart or a strip plot is just a display of the data depending upon the frequency of the values.
The dot plot is somewhat like the histogram but the difference is:
A histogram shows the frequency of an interval of values of any given data set.
for example:
we may make a histogram for the weight of students of a class.
since we may divide the weight of the students into some interval.
whereas the dot plot gives the frequency of the individual data points or discrete data points.
for example:
we may plot a dot plot for rolling a number cube 20 times.
Hence, the correct statement is:
A dot plot shows the frequency of the individual values or of any given data set.
Given the function, y = x/( x^2 – 1)
Add x and subtract x from (x^2 – 1) to make it a complete
square
y = x/(x^2 + x – x – 1)
y = x/[x(x + 1) – 1(x + 1)]
y = x/[(x – 1)(x + 1)]
In order to find the y -intercept, we set x = 0
When x = 0
y = 0/[(0 – 1)(0 + 1)]
y = 0.
Therefore, the y-intercept is zero.
In order to find the x -intercept, we set y = 0
When y = 0
0 = x/[(x – 1)(x + 1)]
The only way the product of a division will be zero is if
the numerator is zero
So, if x/[(x – 1)(x + 1)] = 0
x = 0
Therefore, the x-intercept is also zero.
Since both x- intercept and y- intercept equal zero,
Then, the given function has an x-intercept that is equal to
its y-intercept
Answer:
f(x) = 8x⁴-8x²+1
Step-by-step explanation:
I will assume that f(cos θ) = cos(4θ). Otherwise, f would not be a polynomial. lets divide cos(4θ) in an expression depending on cos(θ). We use this properties
- cos(2a) = cos²(a) - sin²(b)
- sin(2a) = 2sin(a)cos(a)
- sin²(a) = 1-cos²(a)
cos(4θ) = cos(2 * (2θ) ) = cos²(2θ) - sin²(2θ) = [ cos²(θ)-sin²(θ) ]² - [2cos(θ)sin(θ)]² = [cos²(θ) - ( 1 - cos²(θ) ) ]² - 4cos²(θ)sin²(θ) = [2cos²(θ)-1]² - 4cos²(θ) (1 - cos²(θ) ) = 4 cos⁴(θ) - 4 cos²(θ) + 1 - 4 cos²(θ) + 4 cos⁴(θ) = 8cos⁴(θ) - 8 cos²(θ) + 1
Thus f(cos(θ)) = 8 cos⁴(θ) - 8 cos²(θ) + 1, and, as a result
f(x) = 8x⁴-8x²+1.
