1.evaluate
8
e -(n-5)
n=2
sigma notation

The sigma means that you add up all the values you get after you plug in the designated range of n. 

so, what that means in simplest terms: 

plug in the value for n on the bottom first, which is 2. then plug in everything up to the number on top of the sigma 

so you'd plug in, 2 for n, then, 3, then 4, then 5, then 6, then 7, and finally 8 into the expression -(n-5) 

doing this we'd end up with: 

-(2-5) = 3 
-(3-5) = 2 
-(4-5) = 1 
-(5-5) = 0 
-(6-5) = -1 
-(7-5) = -2 
-(8-5) = -3 

so then, after we do all that, we add up all the values we found, in this case they all cancel each other out and go to zero: 

3 + 2 + 1 + 0 + (-1) + (-2) + (-3) = 0 

Ithink it is 7. 16

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.