Response:
b + d = 180°, a = d, and a = c
Detailed explanation:
In the diagram, we observe that the only condition for the lines to be parallel is that the angles correspond with their counterparts, for instance, a must equal d. The equation a = c indicates that all angles must be equal for lines m and n to remain parallel. Finally, the equation b + d = 180° confirms that this holds true only if lines m and n are parallel.
We can formulate the trajectory of the parabola using the vertex form equation: y = a (x – h)^2 + k. The coordinates for the vertex are at h and k, representing the peak height, thus h = 250 and k = 120. Consequently, the equation becomes y = a (x – 250)^2 + 120. At the starting point where x = 0 and y = 0, we find a: 0 = a (0 – 250)^2 + 120, which simplifies to 0 = a (62,500) + 120, leading to a = -0.00192. The complete equation is y = -0.00192 (x – 250)^2 + 120. To determine y when x = 400, we substitute: y = -0.00192 (400 - 250)^2 + 120, yielding y = 76.8 ft. Hence, the ball clears the tree by 76.8 ft – 60 ft = 16.8 ft.
Answer:
1. x=±4
2. t=±9
3. r=±10
4. x=±12
5. s=±5
Step-by-step explanation:
1. x^2 = 16
By extracting the square root on both sides
x=±4
2. t^2=81
Again, take the square root of each side
t=±9
3. r^2-100=0
r=±10
4. x²-144=0
We rewrite as x²=144
Applying square roots
x=±12
5. 2s²=50
s=±5 ..
Response:
14 feet
Detailed explanation:
<pThere are 3 feet for each yard, resulting in a total of 36 feet in 12 yards. The leftover ribbon will equal the initial amount minus what has been utilized.
36 - 22 = 14.... feet left
Jerome's share of the total profit amounts to one-third. To determine the overall profit of the company, multiply his profit by 3.
If he earned $150,000, the calculation would be:
150,000 × 3 = $450,000
So, the total profit is $450,000.
The dot simply represents multiplication.
