You travel 50 miles in 4 hours. What is your average speed of

Alex787 [66]

Answer:

Answer is 7. Did this is simple:

3 0

3 years ago

Solve the inequality both algebraically and graphically. Draw a number line graph of the solution and give interval notation.

Lemur [1.5K]

Finding the solution algebraically

To answer this inequality, we can follow the next steps:

1. Multiply by 7 both sides of the inequality:

$7\cdot\frac{(x-7)}{2}$

2. Multiply by 2 both sides of the inequality:

$7\cdot2\cdot^{\cdot}\frac{(x-7)}{2}$

3. Apply the distributive property at the left side of the inequality:

$7\cdot x-7\cdot7$

4. Add 49 to both sides of the inequality:

$7x-49+49$

5. Finally, divide both sides of the inequality by 7:

$\frac{7x}{7}$

We can graph this inequality in the number line as follows:

Notice the parenthesis indicating that the solution is the number below 131/7 (but not equal to 131/7). In interval notation the solution is:

$(-\infty,\frac{131}{7})$ $(-\infty,18\frac{5}{7})$

Or, approximately:

$(-\infty,18.7142857143)$

The number 131/7 in decimal is equivalent to 18.7142857143, so the graph of the solution is given by graph A (we can see that there are seven divisions between 18 and 19; since we have that the shaded division is in the 5th division, then, we have 5/7 = 0.714285714286, that is, the decimal part of the above number).

We can express the number 131/7 as a mixed number as follows:

$\frac{131}{7}=\frac{126}{7}+\frac{5}{7}=18+\frac{5}{7}=18\frac{5}{7}$

Again, notice also the symbol for the left part of the interval notation is a parenthesis since the interval is open at the point 131/7 = 18 + 5/7.

Finding the solution graphically

To find the solution graphically, we can represent the inequality as two lines as follows:

$y=\frac{x-7}{2},y=\frac{41}{7}$

Then, if we graph the first line, we can find the x- and the y-intercepts to find two points to graph the line. We have that the x- and the y-intercepts are:

The x-intercept is (that is, when y = 0):

$0=\frac{x-7}{2}\Rightarrow x-7=0\Rightarrow x=7$

Then, the x-intercept is (7, 0), and the y-intercept (the point on the graph when x = 0) is:

$y=\frac{x-7}{2}\Rightarrow y=\frac{0-7}{2}\Rightarrow y=-\frac{7}{2}$

Then, the y-intercept is (0, -7/2).

The other line is given by:

$y=\frac{41}{7}=\frac{35}{7}+\frac{6}{7}=5\frac{6}{7}$

With this information, we can graph both lines:

And we can see that the point where the two lines coincide is:

$(\frac{131}{7},\frac{41}{7})$

Then, the values for x of the line (x-7)/2 [that is, the values of y = (x-7)/2] that are less than y = 41/7, represented as:

$\frac{(x-7)}{2}$

Are those values of x less than 131/7, or the solution is also (we express the solution as a fraction or a mixed number as follows) (the same solution):

$(-\infty,\frac{131}{7})or(-\infty,18\frac{5}{7})$

In summary, we have that the solution to the inequality is:

As an inequality:

$x$

In interval notation:

$(-\infty,18\frac{5}{7})or(-\infty,\frac{131}{7})$

And the representation of the solution on the number line is (option A):

4 0

1 year ago

Rafael is taking a test that contains a section of 12 true-false questions. how many of the possible groups of answers to these

stiv31 [10]

Answer: There are 495 possible different sets of answers the could contain exactly 8 correct answers of false.

Basically, we are looking for the number of different ways of selecting 8 objects out of a set of 12 objects. Our objects are answers of false and the set is the test.

This is a combination problem. The formula would be:

12! / (8! x 4!) = 495

5 0

3 years ago

The graph of F(x), shown below, resembles the graph of G(x) x2, but it has

Bingel [31]

Correct answer is: F(x)=-x^2-3

Step-by-step explanation:

We are given a function:

The graph of is also shown in the given question figure.

It is a parabola with vertex at (0,0).

Sign of is positive, that is why the parabola opens up.

General equation of parabola is given as:

Here, in G(x), a = 1

Vertex (h,k) is (0,0).

As seen from the question figure,

The graph of F(x) opens down that is why it will have:

Sign of as negative. i.e.

And vertex is at (0,-3)

Putting the values of a and vertex coordinates,

Hence, the equation of parabola will become:

7 0

3 years ago

Find the payment necessary to amortize a 6.3% loan of 7500 compounded semiannually, with 6 semiannual payments. Find the payment

Lorico [155]

Answer:

Semiannual payment = $ 1391.37

Total payment = $ 8348.22

Interest paid = $ 848.22

Step-by-step explanation:

Since, the semiannual payment formula of a loan,

$P=\frac{PV(\frac{r}{2})}{1-(1+\frac{r}{2})^{-n}}$

Where,

PV = present value of the loan,

n = number of semiannual payments,

r = annual rate,

Here, PV = 7500, r = 6.3% =0.063, n = 6,

By substituting the value,

The semiannual payment would be,

$P=\frac{7500(\frac{0.063}{2})}{1-(1+\frac{0.063}{2})^{-6}}$

$\approx \$ 1391.37$

Also, total payment = semiannual payment × total semiannual periods

= 1391.37 × 6

= $ 8348.22,

Also, the interest paid = total payment - present value

= 8348.22 - 7500

= $ 848.22

6 0

3 years ago