The angle measure of a straight line is 180°, and so if the you know that one angle off of it is (5x)°, then you know that the other section is (180 - 5x)°.
Because it's an isosceles triangle, there are two identical angles, which happen to be the angles with the measure of (5x - 30)° and (180 - 5x)°.
Since they have the same measure, 5x - 30 = 180 - 5x. Solve:
Thus,
x = 21°.
Answer: 17 nickels, 8 dimes
Step-by-step explanation:
Since we are given system of equations, we can use elimination method to find n or d. First, let's eliminate n. To do so, we need to make sure they are equal to each other. Then, we would have to multilpy the second equaiton by 0.05.
0.05N+0.1D=1.65
0.05N+0.05D=1.25
Now, we can subtract the 2 equations.
0.05D=0.4
D=8
Now that we know the number of dimes, we can plug it into any of the equations to find nickels.
N+8=25
N=17
There are 17 nickels and 8 dimes.
Answer:
71.6 degrees
Step-by-step explanation:
Given the vectors
u= <8,4> v = <9.-9> (5 points)
u*v = (8, 4)*(9, -9)
u*v = 8(9)+(4)(-9)
u*v = 72 - 36
u*v = 36
|u| = √8²+4²
|u| = √64+16
|u| = √80
|v| = √9²+9²
|v| = √81+81
|v| = √162
Using the formula
u*v = ||u||v| cos theta
36 = √80(√162)cos theta
36 = √12960 cos theta
cos theta = 36/√12960
cos theta = 36/113.8
cos theta = 0.3162
theta = arccos(0.3162)
theta = 71.56 degrees
Hence the angle between the given vectors to the nearest tenth of a
degree is 71.6 degrees
Answer:
0.666666667
Step-by-step explanation:
The surface area would be all those areas combined. The shape has been split up into 6 smaller quadrilaterals, so we can easily solve from there. The leftmost one would be 3*4 = 12. The two rectangles beside it can be combined: 4*7 = 28, the one beside it would be: 3*4 = 12, and the last column would be 4*7 = 28. The last thing you need to do is add them together: 12+28+12+28 = 80.
The surface area of the rectangular prism is 80
