<h3>
Answer: A. 18*sqrt(3)</h3>
=============================================
Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
----------------------
An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
The probability that a biscuit picked at random contains chocolate
chips. = 1/5 , The Venn Diagram is attached with the answer.
<h3>What is Probability ?</h3>
Probability is defined as the study of likeliness of an event to happen.
It is given that
There are 30 biscuits in a tin
8 of the biscuits are iced, of which 6 contain chocolate chips
4 biscuits are neither iced nor contain chocolate chips.
the probability that a biscuit picked at random contains chocolate
chips.
There are total 6 biscuits which have chocolate chips
The probability that a biscuit picked at random contains chocolate
chips. = 6/8 *8/30 = 6/30 = 1/5
The probability that a biscuit picked at random contains chocolate
chips. = 1/5
The Venn Diagram is attached with the answer.
To know more about Probability
brainly.com/question/11234923
#SPJ1
Answer:
6
Step-by-step explanation:
(-12)^2-4*1*36=0
144-144=0
x= -(-12)/2*1=
12/2=
6
x=6
The slope-intercept form:
m - slope
b - y-intercept
The formula of a slope:
We have the points (-3, 1) and (2, -4). Substitute:
Therefore we have the equation of a line
Put the coordinates of the point (-3, 1) to the equation:
<em>subtract 3 from both sides</em>
<h3>Answer: y = -x - 2</h3>
