Timothy built a base for a circular tabletop. The base can support a tabletop with a radius of at least 6 inches, but not more t

Answer:

4. A)

3. A)

2. D)

1. C)

Step-by-step explanation:

4. Two families combined must have at least 3 pets.

3. $1500 represents your total, making everything else straightforward, as the keywords at least indicate that the a sum of $1500 must be greater or equal to $1500.2. Find the correspondents, then identify the inequality to apply. Here, use less than or equal because overpaying is unnecessary.1. Eight dollars

for each

pizza and twelve dollars for each pizza yields 12x and 8x. The remainder follows logically, as we have our initial costs of $45 and $5, so Company A’s total would be less than Company B's total, leading directly to our conclusion.I’m happy to assist with any further queries.

The distance from my home to my friend's residence is 14 miles Step-by-step explanation: Let me clarify the solution process: - When heading to my friend's house, my driving speed is 35 miles per hour. - In returning home, the driving speed increases to 40 miles per hour. - The total duration of the trip was 45 minutes. - Our goal is to determine the distance separating my home from my friend's house. - First, we will convert 45 minutes into hours since the driving speed is expressed in miles per hour. Knowing that 1 hour equals 60 minutes, it follows that 45 minutes equates to hours. - Let’s assume that the distance between my home and my friend's place is d; thus, the time taken to reach my friend's house will be and the time for the ride back will be. Since the distance between the two is d, the corresponding equations will be: d = 35 ×, and d = 40 ×. - Setting both equations equal we derive:. - After dividing both sides by 35, it leads to. - This indicates that the total time of the round trip is hours. - Utilizing this information, we then substitute back into the equations to compute d, leading to the conclusion that the distance from my home to my friend's is indeed 14 miles.

Answer:

6 knots

Step-by-step explanation:

Let the velocity be v knots

thus, the time required to traverse 500 M is given by 500 / v hours

Fuel consumption per hour is equal to 216 plus half the cube of the speed (v^3).

Let F denote the fuel consumption for the journey

= [500/v][216 + 0.5v^3]

= 500[216/v + 0.5v^2]

The derivative of F with respect to v is: dF/dv = 500[ - 216/v^2 + v]

The second derivative, d^2F/d^2v = 500[432/v^3 + 1], indicates positivity.

Setting dF/dv to zero helps find the minimum.

500[ -216/v^2 + v] = 0

or v = 216/v^2

or v^3 = 216

By solving, we arrive at v = [216]^(1/3) = 6 knots

To address this issue, we will utilize the formula for determining the distance from a point to a line.

The formula is:

distance = | a x + b y + c | / sqrt (a^2 + b^2)

 

We have the line equation:

y = 2 x + 4

Rearranging it results in:

<span>y – 2 x – 4 = 0 --> a = -2, b = 1, c = -4</span>

 

The coordinates given are:

(-4, 11) = (x, y)

 

Substituting into the distance formula:

distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 + (1)^2]

distance = 15 / sqrt (5)

distance ≈ 6.7

 

<span>Thus, the tree is approximately 6.7 ft from the zip line.</span>

Answer:

Sarah purchased 2 drinks and 6 candies.

Step-by-step explanation:

Let

x ----> the quantity of drinks Sarah bought.

y ----> the number of candies acquired by Sarah.

We know that

the total spent on drinks and candies was $35.50

therefore,

-----> equation A

She bought 3 times more candies compared to drinks.

thus,

-----> equation B

To resolve the equations graphically

The solution lies at the intersection of the two graphs

utilizing a graphing tool

The result is the coordinate (2,6)

therefore,

Sarah bought 2 drinks and 6 candies.