Answer:
the angle between u=(8, -2) and v=(9,3) is 32.5°
Step-by-step explanation:
u=(8,-2)=(u1,u2)→u1=8, u2=-2
v=(9,3)=(v1,v2)→v1=9, v2=3
We can find the angle between two vectors using the formula of dot product:
u . v =║u║║v║cos α (1)
And the dot product is:
u . v = u1 v1 + u2 v2
u . v = (8)(9)+(-2)(3)
u . v = 72-6
u . v = 66
║u║=√(u1²+u2²)
║u║=√((8)²+(-2)²)
║u║=√(64+4)
║u║=√(68)
║u║=√((4)(17))
║u║=√(4)√(17)
║u║=2√(17)
║v║=√(v1²+v2²)
║v║=√((9)²+(3)²)
║v║=√(81+9)
║v║=√(90)
║v║=√((9)(10))
║v║=√(9)√(10)
║v║=3√(10)
Replacing the known values in the formula of dot product (1):
u . v =║u║║v║cos α
66 = 2√(17) 3√(10) cos α
Multiplying:
66 = 6√((17)(10)) cos α
66 = 6√(170) cos α
Solving first for cos α: Dividing both sides of the equation by 6√(170):
Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:
(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170
cosα=11/13.03840481→cosα=0.84366149
19.607...% of her gross pay is being taken out in taxes.
<u><em>Explanation</em></u>
Susie paid $579 in taxes on gross income of $2953
For finding the percentage of tax, first we need to <u>divide the amount of tax paid by the total gross income and then multiply the result by 100%</u>
So, percentage of tax 
% = 19.607....%
Problem 10
<h3>Answer: 80 degrees</h3>
Work Shown: 80-0 = 80
You subtract the values on the protractor where the two angle arms line up.
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Problem 11
<h3>Answer: 45 degrees</h3>
Work Shown: 45-0 = 45
Same idea as problem 10
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Problem 12
<h3>Answer: 83 degrees</h3>
Work Shown: 128-45 = 83
Same idea as the others. The arm TS isn't fully on 130 degrees, and it's a bit short of it. It looks to be about 128 degrees or so.
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Problem 13
<h3>Answer: 35 degrees</h3>
Explanation: Luis forgot to subtract the value of each arm of the angle. So he should have done 80-45 = 35. The answer would be 80 degrees if arm TQ was at 0 degrees (so 80-0 = 80), but instead TQ is at 45 degrees.
Answer:
12/20
Step-by-step explanation:
Answer:
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