Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 723 hours, what was the speed of the bus?

You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)

In each instance, when it sheds a shell, its size increases by a factor of 1 1/3. To determine the growth after the first molt, multiply 1 cm by 1 1/3 to get 1 1/3 cm. To find the next size, repeat the multiplication: 1 1/3 cm times 1 1/3 cm equals 16/9. This process will continue by multiplying by 1 1/3. We can express it mathematically as (initial size) * 1 1/3 *(number of shells) equals length or 1 cm * 1 1/3 * n equals L. Given that the final length is 10 cm, accordingly, 1 1/3 * n equals 10 cm, leading to n being 7.5 shells, which translates to either about 7 or 8 shells.

Mel descends 50-35=15 feet in 5-2=3 seconds. Thus, her descent rate is 15/3=5 ft/sec.
Victor descends 60-50=10 feet in 4-1=3 seconds. Hence, his descent rate is 10/3=3⅓ ft/sec. Mel is faster, traveling at 5 ft/sec.

Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

True, since p = a + 4 implies a = p – 4.

B. f(x) ≤ 0 over the interval [0, 2]. D. f(x) > 0 over the interval (–2, 0). E. f(x) ≥ 0 over the interval [2, ).