, 28.10.2019 14:45 kuanjunjunkuan

# By how much must 5p² - 3p² be diminished to give 2p² + q²? ​

3p² - 4q²

Step-by-step explanation:

5p² - 3q² - (2p² + q²)

5p² - 3q² - 2p² - q²

3p² - 4q²

Checking:

5p² - 3q² - (3p² - 4q²)

5p² - 3q² - 3p² + 4q²)

2p² + q²

xx

step-by-step explanation:

bottom of the ladder is 24 feet from the bottom of the building.

step-by-step explanation:

use pythagorean theorem to solve for the horizontal distance along the ground between the bottoms of ladder and building.

the pythagorean theorem states that the square of the hypotenuse (c) of the right triangle (with a 90-degree angle) is equal to the the sum of the squares of its two other sides a and b.

, c² = a² + b²

to visualize the given problem:

there are three sides that represent the sides of the right trianglethe height of the building is perpendicular to the distance along the ground creating a 90-degree angle of the right trianglethe height and distance along the ground are the two sides the ladder is the hypotenuse.

therefore:

c = 26 fta = 10 ftb =

find   b, the distance from the bottom of the ladder to the bottom of the building:

c² = a² + b²

(26 ft)² = (10 ft)² + b²

b² = (26 ft)² - (10 ft)²

b² = 676 ft² - 100 ft²

b = √(576 ft²)

b = 24 bottom of the ladder is 24 feet from the bottom of the building.

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