Answer:
1) a = 51, 2) b = 57, 3) c = 53, 4) e = 49 d = 131, 5) f = 33, 6) g = 79, 7) h = 42 j = 47, 8) m = 59 k = 17 i = 104, 9) n = 55
Step-by-step explanation:
1.
You see that angle HJK has a total degree angle of 115, half of the angle is already stated to be 64 degrees, so you would just have to find the remainder. 115 - 64 = 51
2.
The question follows the same format, when you see the square in the corner it generally means that it is a 90-degree angle. So following the same steps as last time angle b would be 90 - 33 = 57
3.
Whenever there is a flat line given the angle is equal to 180 degrees, think of it as putting two 90 degree angles back to back. So if they equal 180 angle c would equal 180 - 127 = 53
4
This question is just a little different when you see crossing perpendicular lines angles across from each other equal the same amount, so angle d would be 131. Finding angle e is not hard either, back to question 3 for when it was just a straight line the same logic can be applied here. e would equal 180 - 131 = 49
If you have some knowledge of complex numbers: This follows pretty much immediately from Euler's formula and DeMoivre's theorem,
(Euler)
(DeMoivre)
so that is the imaginary part of the expanded left hand side.
If that's unfamiliar to you, you can make use of several identities to expand :
(double angle sine)
(double angle sine and cosine)
(Pythagorean)
Answer:
y = x + 7
Step-by-step explanation:
The equation of a line in slope - intercept form is expressed as y = mx+c
m is the slope
c is the intercept
Get the slope m;
m = tan theta
m = tan 45
m = 1
Get the intercept c;
Substitute m = 1 and (-2, 5) into the equation y = mx+c and get c;
5 = 1(-2)+c
5 = -2+c
c = 5+2
c = 7
Get the required equation;
y = 1(x)+ 7
y = x + 7
Hence the equation of the line is y = x+7
Answer:
Step-by-step explanation:
Percentage increase = increase/original price × 100/1
Increase = final price - initial price
In this case of 2012 - 2013
Initial price = $30, 000
Final price = $31, 200
Increase = $31, 200 - $30, 000
= $1200
% increase = $1200/$30000 × 100/1
= 0.04×100
= 4%
For the year 2013-2014
Initial price = $31, 200
Final price = $32,448
Increase = $32,448-$31, 200
= $1248
% increase = $1248/$31,200 ×100/1
= 0.04×100/1
= 4%
Hence,the percentage increase in tuition year will be at the rate of 4%
Answer:
11%
Step-by-step explanation:
1/3 (twix)
1/3 (snicker)
1/3 x 1/3 = 1/9
1/9 = .11
.11 = 11%