Given that ∠ABC is an inscribed angle, we need to determine the measures of ∠BDA and ∠BCA. To begin, we first calculate the central angle ∠BOA, which corresponds to the intercepted arc measure of BA: ∠BOA = 360° - 250° = 110°. Thus, the intercepted arc AB measures 110°. Applying the relevant formulas: ∠BDA = 55°. Next, we find ∠BCA. In the quadrilateral AOBC, with AC and BD being tangents, we know that ∠CAO = 90° and ∠CBO = 90°. Since the sum of angles in a quadrilateral is 360°, we set up the equation ∠AOB + ∠CAO + ∠CBO + ∠BCA = 360°. Substituting known values, we find ∠BCA = 360° - 290°, yielding ∠BCA = 70°. Thus, the proof is completed.
Answer:
w/2 = 7.5/5
3kg
Here's the detailed explanation:
Remaining question below:
Which proportion could Maddy utilize to solve this issue?
a. w/2 = 7.5/5
b. w/7.5 = 5/2
Solve the proportion to determine the weight of a 2 liter jug.
_____kg
A 5-liter container of sports drink weighs 7.5kg
A 2-liter jug of this drink will weigh x kg
Finding w
Ratio of weight to volume
7.5kg: 5liters translates to 7.5/5
wkg: 2 liters means w/2
Establishing equivalent ratios
7.5 / 5 = w / 2
Cross-multiplying gives
7.5*2=5*w
15=5w
Dividing both sides by 5 results in
w=3
w=3kg
Thus, the weight of the 2-liter sports drink jug is 3kg
Answer:
Nina's speed in MPH: 12.706 miles per hour
Nina is quicker than Sophia.
Step-by-step explanation:
To solve this problem, we will convert feet per second to miles per hour and subsequently compare Nina's speed to that of Sophia's.
Nina rides at 63360 feet in 3400 seconds. To perform this conversion, we know that there are 5280 feet in a mile and 3600 seconds in an hour. Applying these conversions, we can calculate the speed in miles per hour.
(63360 feet / 3400 seconds) * (1 mile / 5280 feet) * (3600 seconds / 1 hour) = 12.706 miles per hour.
Thus, it follows that Nina rides her bike at a rate of 12.706 miles per hour, whereas Sophia rides her bicycle at a rate of 10 miles per hour.
This indicates that Nina rides faster than Sophia by 2.706 miles per hour (12.706 - 10).
Cheers.
The correct answer is "His teacher advised it because he did not have time to tutor Euler privately." I completed the assignment and got it correct.
