Which of the following represents the distributive property?

An airplane travel at a constant speed of 575 miles per hour.write and equation that can be used to determine the number of mile

Oxana [17]

Answer:

$m = 575h$

Step-by-step explanation:

Given

$Rate = 575 miles/hour$

Required

Determine the equation for the model

Represent the number of hours with h and the miles with m.

Using distance formula:

$Distance = Speed * Time$

In this case, it is:

$Miles = Rate * Hour$

So, we have:

$m = 575 * h$

$m = 575h$

3 0

2 years ago

The function f(t)=-16 + 100 models the height of a ball, in feet, dropped from a 100-foot rooftop at time t, in seconds.

Mazyrski [523]

Using it's concept, it is found that the average rate of change of the function during the interval from 0 to 2 seconds is given by:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

<h3>What is the average rate of change of a function?</h3>

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

$r = \frac{f(b) - f(a)}{b - a}$

In this problem, the function is given by:

f(t) = -16t² + 100.

The outputs are given as follows:

f(0) = -16(0)² + 100 = 100.

f(0) = -16(2)² + 100 = 36.

Hence the average rate of change is given by:

r = (36 - 100)/(2 - 0) = -32 ft/s.

And the correct option is:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

More can be learned about the average rate of change of a function at brainly.com/question/24313700

#SPJ1

8 0

1 year ago

Please helppp meeeeee

alexira [117]

Answer: 16) $\bold{\sqrt{x}}$ (17) $\bold{\dfrac{x-4}{2}}$ (18) $\bold{\sqrt{x}-2}$ (19) 3x - 18

Step-by-step explanation:

Inverse is when you swap the x's and y's and then solve for y

16) Given: y = x²

Swapped: x = y²

$\bold{\sqrt{x} =y}$

17) Given: y = 2x + 4

Swapped: x = 2y + 4

x - 4 = 2y

$\bold{\dfrac{x-4}{2}=y}$

18) Given: y = (x + 2)²

Swapped: x = (y + 2)²

√x = y + 2

$\bold{\sqrt{x}-2=y}$

19) Given: $y=\dfrac{1}{3}x+6$

Swapped: $x=\dfrac{1}{3}y+6$

$x - 6 = \dfrac{1}{3}y$

3(x - 6) = y

3x - 18 = y

4 0

2 years ago

A car travels a distance of 230 miles in a time of 4.2 hours. What is its average speed rounded to 1dp?

zhannawk [14.2K]

Its average speed rounded to 1dp is 54.76 miles per hour.

<h3>Average speed</h3>

Using this formula

Average speed=Distance/Time

Where:

Total Distance =230 miles

Time= 4.2 hours

Let plug in the formula

Average speed=230/4.2

Average speed=54.76

Inconclusion Its average speed rounded to 1dp is 54.76 miles per hour.

Learn more about average speed here:brainly.com/question/4931057

5 0

2 years ago

Read 2 more answers

A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions

salantis [7]

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

$Area = length \times width$

Substituting the values we get,

$Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0$

Solve the above equation by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}$

$a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14$

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

3 years ago