The basis to respond this question are:
1) Perpedicular lines form a 90° angle between them.
2) The product of the slopes of two any perpendicular lines is - 1.
So, from that basic knowledge you can analyze each option:
<span>a.Lines s and t have slopes that are opposite reciprocals.
TRUE. Tha comes the number 2 basic condition for the perpendicular lines.
slope_1 * slope_2 = - 1 => slope_1 = - 1 / slope_2, which is what opposite reciprocals means.
b.Lines s and t have the same slope.
FALSE. We have already stated the the slopes are opposite reciprocals.
c.The product of the slopes of s and t is equal to -1
TRUE: that is one of the basic statements that you need to know and handle.
d.The lines have the same steepness.
FALSE: the slope is a measure of steepness, so they have different steepness.
e.The lines have different y intercepts.
FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.
f.The lines never intersect.
FALSE: perpendicular lines always intersept (in a 90° angle).
g.The intersection of s and t forms right angle.
TRUE: right angle = 90°.
h.If the slope of s is 6, the slope of t is -6
FALSE. - 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is - 1/6.
So, the right choices are a, c and g.
</span>
We know that
point A(1,1) C(3,5)
point D(-2,-4) F(0,0)
step 1
find the slope FD
m=(y2-y1)/(x2-x1)------> m=(0+4)/(0+2)----> m=4/2----> m=2
step 2
find the slope AC
m=(y2-y1)/(x2-x1)------> m=(5-1)/(3-1)----> m=4/2-----> m=2
mAC=mFD
the answer is
the slope FD is 2
Let's analyse the function
The amplitude is A, so we want A=1.5
Now, we start at x=0, and we have 
After one second, i.e. x=1, we want this sine function to make 330 cycles, i.e. the argument must be 
So, we have
so, the function is
notice the picture of the graph added here
low and behold, x = -17, y is 0, and x= 15, y is 0
the graph is touching the x-axis, an x-intercept
or so-called, a "solution"
Answer: Option A and Option C.
Step-by-step explanation:
For this exercise it is important to know the definition of "Vertical Angles".
When two lines intersect or cross, there are a pair of angles that share the same vertex and they are opposite each other. This pair of angles are known as "Vertical angles".
By definition, Vertical angles are congruent, which means that the have the equal measure.
In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.
You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below:
and 
and 
