2x + 3y = 15 x + y = 6 Work out the values of x and y.

Giveing 15 points.Use the rectangle to find the measure of the following angles measure ane BAC=25

Vinil7 [7]

1) All angles of a rectangle are right angles, so the measure of angle CBA is 90 degrees.

2) Since all angles of a rectangle are right angles, angle BAD measures 90 degrees. Subtracting the 25 degrees of angle BAW from this, we get that angle CAD has a measure of 65 degrees.

3) Opposite sides of a rectangle are parallel, so by the alternate interior angles theorem, the measure of angle ACD is 25 degrees.

4) Because diagonals of a rectangle are congruent and bisect each other, this means BW=WA. So, since angles opposite equal sides in a triangle (in this case triangle ABW) are equal, the measure of angle ABW is 25 degrees. This means that the measure of angle CBD is 90-25=65 degrees.

5) In triangle AWB, since angles in a triangle add to 180 degrees, angle BWA measures 130 degrees.

6) Once again, since diagonals of a rectangle are congruent and bisect each other, AW=WD. So, the measures of angles WAD and ADW are each 65 degrees. Thus, because angles in a triangle (in this case triangle AWD) add to 180 degrees, the measure of angle AWD is 50 degrees.

4 0

2 years ago

1. A movie theater designs two bags to hold 96 cubic inches of popcorn. a. Find the height of each bag b. Which bag should the t

MrRissso [65]

I have attached a screenshot with the images of the two popcorn bags used by the theater.

Part (a):
Bag A:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 3 in
width = 4 in
Therefore:
96 = 3 * 4 * height
96 = 12 * height
height of bag A = 8 in
Bag B:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 4 in
width = 4 in
Therefore:
96 = 4 * 4 * height
96 = 16 * height
height of bag B = 6 in

Part (b):
To determine the amount of paper needed, we will need to calculate the surface of each bag. Excluding the top base, each bag will have 5 faces. Four side faces (each two opposite are equal) and the base.
Bag A:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (3*4) + 2(8*4) + 2(8*3)
Surface area = 12 + 64 + 48
Surface area of bag A = 124 in²
Bag B:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (4*4) + 2(6*4) + 2(6*4)
Surface area = 16 + 48 + 48
Surface area of bag B = 112 in²
From the above calculations, we can deduce that the theater should choose bag B in order to reduce the amount of paper needed.

Hope this helps :)