A certain car traveling at 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. in approximately

Let C denote the quantity of compost

T represent the quantity of topsoil

Each cubic yard of compost is priced at $25

Thus, the cost of C cubic yards of compost is 25C

Each cubic yard of topsoil costs $15

Therefore, the cost for T cubic yards of topsoil is 15T

Together, the amount of compost plus topsoil equals 10

C + T = 10 -------> Equation 1

The total cost for compost and topsoil is $180

25C + 15T = 180 --------> Equation 2

Rearranging the first equation to find C

C + T = 10

results in

C = 10 - T

Now substitute into the second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

Using like terms: 250 - 25T + 15T = 180

From which we can simplify to 250 - 10T = 180 by removing 250 from both sides

-10T = 180 - 250

yielding -10T = -70 (dividing both sides by -10)

results in T = 7

Since this parabola intersects the center, its formula is:

y = ax². Given that it opens downward, the coefficient a must be negative.

Thus, the equation can be expressed as:

y = - ax², with the axis of symmetry located at x = 0.

The height measures 84 ft when the parabola's opening is 42 ft wide.
This indicates that for the height y, the corresponding x-values are +21 and -21 (due to symmetry).
To find a, let's substitute y and x with their respective values:

y = - ax²

84 = - a(21)²

84 = - a(441), leading to a = - 84/441 ↔ a = - 4/21.

Therefore, the final equation is: y = -4/21 x².

Answer:

You need to purchase 3 shirts to be able to use your coupon.

Step-by-step explanation:

Each shirt originally costs $17.99.

There is a 20% discount on this specific brand of shirts.

$17.99 × 0.2 = $3.60 (discount per shirt)

Subtracting the discount from the original price:

$17.99 - $3.60 = $14.39 (price per shirt after discount)

To qualify for the $10 off coupon which requires a $40 minimum purchase:

$40 ÷ $14.39 ≈ 2.779, rounded up to 3 shirts

Therefore, you must buy 3 shirts.

3 shirts × $14.39 = $43.17, surpassing the $40 minimum needed to apply the $10 discount.

Answer:

Refer to the explanation below.

Step-by-step explanation:

We start with a small aircraft that flies 760,320 yards within a duration of 2 hours.

A)

The formula for distance is:

To isolate the rate r, we divide both sides by time:

B)

To calculate the rate in yards per hour, divide the total yards by the hours taken. Therefore:

Perform division:

Thus, the aircraft speeds at 380,160 yards every hour.

C)

There are 1,760 yards in a mile.

To compute the speed in miles per hour, we apply dimensional analysis.

We recognize the rate is 380,160 yards per hour:

To cancel "yards" from the numerator, we multiply by 1 mi/1,760 yards. Therefore:

This eliminates yards:

Now, multiply the values across:

Then divide:

The final rate for the plane is 216 miles per hour.

D)

Miles are a more appropriate measurement in this context because the distance is substantial, making it impractical to express using yards. A rate of 380,160 yards per hour is excessive, whereas 216 miles per hour provides a clearer understanding.

Response: 27,576

16 acres

Detailed explanation: