A) We are told that at 2 hours, the velocity is 18 km/h and at 4 hours, the velocity is 4 km/h. Since we are relating two variables - let's give them names.

Let x = time and y = velocity. Since the velocity depends on the time (that is, the time influences velocity), this is a linear function. Any linear function can be written in slope intercept form as y = mx + b. The problem wants the situation in standard from of Ax + By = C, which can be found from slope intercept form.

So now we can make our line. Consider the ordered pairs of (2,18) and (4, 4) with them in (x, y) form. Finding the slope, m, between these points is as such:

m = y₂-y₁ / x₂-x₁

m = 4 - 18 / 4 - 2

m = -14 / 2 = -7.

Our slope is -7.

We take m = -7, x = 4, and y = 4 (it goes 4 km/h in 4 hrs) and use those three things to find the y-intercept.

y = mx + b

4 = -7 * 4 + b

4 = -28 + b

32 = b

So our equation of the line is y = -7x + 32. To put the equation into standard form, we need to place all the variables on one side of the equals sign, all the numbers on the other.

y = -7x + 32

7x + y = 32

In standard form, the equation for this situation is 7x + y = 32

***

To find out the velocity at 8 hours, we evaluate our function at x = 8. Either equation (standard form or slope intercept) works; we use standard form.

7x + y = 32

7*8 + y = 32

56 + y = 32

y = -24

At a time of eight hours, the bicycle is moving at -24 km/h.

5 0

4 years ago

25^(x+2) = (1/5)^(4x)

dangina [55]

The first step for solving this equation is to write $25^{x+2}$ in exponential form with a base of 5.
$5^{2x+4}$ = $( \frac{1}{5}) ^{4x}$
Write $( \frac{1}{5}) ^{4x}$ in exponential form with a base of 5.
$5^{2x+4}$ = $5^{-4x}$
Since the bases on both sides of the equal are the same,, set the exponents equal.
2x + 4 = -4x
Move the constant to the right side of the equation and then change its sign.
2x = -4x - 4
Now move the variable to the left side and change its sign.
2x + 4x = -4
Collect the terms with an x variable.
6x = -4
Lastly,, divide both sides of the equation by 6 to get your final answer.
x = $- \frac{2}{3}$
Let me know if you have any further questions.
:)

8 0

3 years ago

Find the volume of the solid figure.

olasank [31]

It’s 90 after you multiply the length, width, and height

8 0

3 years ago