At Keller's Bike Rentals, it costs 20 to rent a bike for 4 hours. How many hours of bike use does a customer get per dollar?

Answer:

sum is 1275

Step-by-step explanation:

$sum = \frac{n}{2} [2a + (n - 1)d] \\ \\ sum = \frac{50}{2} [(2 \times 1) + (50 - 1) \times 1] \\ \\ sum = 25(51) \\ sum = 1275$

7 0

3 years ago

Find the domain and range of the function y = f(x)= √x-2 <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20-%202%7D%20" i

Over [174]

Answer:

3x-x+2=4

Step-by-step explanation:

The domain of f(x)=2^x would be the x values. This would include all values that you can input as x in order to make this problem work. The domain of a function is usually all real numbers. The range of f(x)=2^x would be the y values. This would include all values that would be the output for the y value. An example of this would be if you used 2 as x then the function would read f(x)=2^2. The y would equal 4 which would be included in the range of this function. To find the domain and range of the inverse you would follow the proper steps to get the inverse of the function which would be x=2^y. The domain would be the x values and the range would be the y values. If you put 4 as x which would be your input for the domain you would get 2^4 = 16 for the y which would be the range.

4 0

3 years ago

Write this equation in Standard Form. Y=2/3x+1

Svet_ta [14]

Write everything on one side
2/3x-y+1=0
multiply by 3
2x-3y+3=0
I hope this is what you're looking for

6 0

3 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term $2x^2$ , which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression:

$x_v=\frac{-b}{2a}$

Since in our case $a=2$ and $b=-3$ , we get that the x-position of the vertex is:

$x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

$y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}$

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

$f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6$

See the graph produced in the attached image.

4 0

3 years ago

You invest $5000 into an account that has a 2.7% annual interest rate and is compounded quarterly. Approximately how long will i

allsm [11]

Since the interest is compounded, we will have to use the compound interest formula.

We Weill plug 7500 in for A, because that's the amount of money that we want to have at the end of some amount of time.

5000 will go in for P because that's the starting amount.

2.7% will be converted into a decimal percentage form. You can do this by dividing by 100, which you will get .027, and then plug that in for r, the rate.

Since the interest is compounded quarterly, n = 4.

After a bit of number crunching, you will get to the point where you have to solve for an exponent. You can easily do this by using the natural log ln(). One property of logarithm is that you can take the exponent and place it in front of the log. Now you can divide both sides to separate and solve for t.

4 0

3 years ago