I'm pretty sure the simplified answer of (4x^3y^-5)^4 would be 256x^12/y^20 (this is a fraction)
Hope this helps :)
Answer:
5. TS ≅ ML
6. ∠N≅∠U
9. m∠P = 80°
10. QR = 3
Step-by-step explanation:
The congruent symbol ≅ indicates that the two shapes have the same angle and side lengths.
5. TS are the third and second letter in RSTUV. The third and second letters in KLMNO are ML. TS ≅ ML
6. N is the fourth letter in KLMNO. The fourth letter is RSTUV is U. ∠N≅∠U
9. ∠P is congruent to ∠W. Notice they are both on the longer side and the wider angle. Since m∠P ≅ m∠W, and m∠W = 80°, then m∠P = 80°
10. QR is congruent to XY. They are both the shortest sides of the shape. QR ≅ XY and XY = 3, then QR = 3
The composite shape is made up of a cube with a side length of 5 inches and a cylinder with a radius of 2 inches and a height of 4 inches.
The composite solid's surface area is 225.4 square inches.
Step-by-step explanation:
Step 1:
The given composite shape is made up of a cube with a side length of 5 inches and a cylinder with a radius of 2 inches and a height of 4 inches.
The surface area of the composite shape is given by summing the individual surface areas.
The composite shape's surface area = The cube's surface area + the cylinder's surface area.
Step 2:
Any cube's surface area is calculated by multiplying 6 with the square of the side length (
).
The cube's surface area =
=
=
square inches.
Step 3:
Any cylinder's surface area is calculated with the following formula;
The cylinder's surface area =
=
=
square inches
Step 4:
The composite shape's surface area = The cube's surface area + the cylinder's surface area.
The composite shape's surface area = 150 + 75.398 = 225.398 square inches. Rounding this off, we get the area as 225.4 square inches.
The difference between defined and an undefined term in Geometry is that defined terms can be combined with each other or an undefined term, and by doing this, there is another term defined. For example, an angle is a combination of two rays, which is an undefined term. Undefined term on the other hand is used to define other terms.