Answer:
PQ= <em><u>1</u></em><em><u>0</u></em>
Step-by-step explanation:
To find intersection of the line ,put y=0 in the equation,cuz points on x axis have ordinate equals to '0'
you have, y=2x+8 ; put y =0,to find it's intersection to x-axis
i.e, 0=2x+8
i.e, 2x= -8
i.e, x= -8/2
i.e, x= -4
Point P is (-4,0)
again, you have y=2x-12, put y=0
i.e,0= 2x-12
i.e, 2x=12
i.e, x=6
Point Q is (6,0)
now distance PQ is
√(6-(-4))^2 +(0-0)^2
i.e, √(10)^2
i.e, 10
distance btwn PQ is 10 unit!
✌️:)
Answer: Angle 2
The 7.5 cm side is opposite angle 2, so opposite = 7.5
The 18 cm side is adjacent to angle 2, so adjacent = 18
Therefore, tan(angle 2) = opposite/adjacent = 7.5/18
Replace "angle 2" with "A" and we have tan(A) = 7.5/18
Answer:
90
Step-by-step explanation:
- change mixed number to improper fraction 22 1/2 = 22*2+1/2 = <u>45/2</u>
- now flip numbers on the second fraction 1/4 = 4/1
- now you can multiply across 45*4 and 18*2 = 180/2
- and simply so its 90
They had 20:2 point problems. They also had 20:5 point problems.
<h3>
Answer: A. 18*sqrt(3)</h3>
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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
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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.