Answer:
Step-by-step explanation:
Okay, so attached is a diagram of the triangle we are solving. Because buildings are almost always perpendicular (90 degrees) to the ground, it is a right triangle.
You can now use the pythagorean theorem with the sides to fill in the other side:
a^2+ b^2= c^2
5^2 + b^2= 22^2
25+b^2=484
b^2= 459
b=21.42
Okay, so for slope you need 2 points- think of the wall as your y axis, and the ground as your x axis. The ladder is the line.
Your first point is (-5,0) because the bottom of the ladder is touching the ground (no y movement) and the bottom of the ladder is 5 feet from the base of the wall and ground (origin).
The second point is going to be (0, 21.42) because that is the height of the wall where the ladder is touching (x is at origin). The 21.42 is positive, because you can't have negative height.
Okay so far? :)
(-5,0) and (0, 21.42)
(x1, y1) and (x2, y2)
slope= (y2-y1)/(x2-x1)
slope= (21.42-0)/ (0-(-5)) ---- becomes positive
slope= 4.284
(Note: slope could also be negative if you put the ladder on the other side of the wall- 5 would become positive... google "positive vs negative slopes" for more info)
Hopefully that answers your question!
Answer:
Explanation:
1. By driving 6 miles each, the cars will be 6 miles + 6 miles = 12 miles appart.
2. When one car stops and the other car makes a 90° left-hand turn and drive 8 miles, you can model the situation with a right triangle, where one leg is 12 miles, the other leg is 8 miles, and the hypotenuse is the distance that separates the cars.
Hence, you must use Pythagoras to find that distance.
3. Pythagoras
- hypotenuse² = leg₁² + leg₂²
- hypotenuse = (12 mile)² + (8 mile)² = 144 mile² + 64 mile² = 208 mile²
, which is rounded to the neartest tenth of a mile.
Answer:
x = -5, 5
Step-by-step explanation:
-x^2-8=-33
Add 8 to each side
-x^2-8+8=-33+8
-x^2 = -25
Divide each side by -1
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Answer:
a) 150 plates
b) 30 plates
c) 180 plates
Step-by-step explanation:
Given that:
She bought twelve (12) packages of plates for the party in which each package contains 15 plates.
Out of the 12 packages;
10packages are small plates & 2 packages are large plates.
a) The number of small plates she bought = 10 × 15 = 150 plates
b) The number of large plates she bought = 2 × 15 = 30 plates
c) The total number of plates she bought all together is:
= number of small plates bought + = number of large plates bought
= (150 +30) plates
The total number of plates she bought all together = 180 plates
