The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend? Sydney is cutting the crust from the edges of her sandwich. The dimensions, in centimeters, of the sandwich is shown.

A rectangle labeled sandwich. The right side is labeled 2 x squared + 9. The bottom side is labeled 2 x squared + 8.
Which expression represents the total perimeter of her sandwich, and if x = 1.2, what is the approximate length of the crust?

8x2 + 34; 43.6 centimeters
8x2 + 34; 45.52 centimeters
4x2 + 17; 21.8 centimeters
4x2 + 17; 22.76 centimeters
6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 4c3d2 + 3c2d3 – 4cd4 + 8
6d5 – 4c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 2c3d2 – 3c2d3 – 4cd4 + 8

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.