Mr. Barrientos can run 2 ½ miles in 2 hours. How many miles can he run in 6 hours? Show your work.

Need this one ASAP please

babunello [35]

Answer:

28..

Step-by-step explanation:

divide 35 by 1 1/4...

7 0

3 years ago

Read 2 more answers

PLEASE HELP (30 POINTS) Solve the rational equation x/3 = x^2/x + 5 , and check for extraneous solutions.

anygoal [31]

Option C: $x=0$ and $x=\frac{5}{2}$ are the solutions.

Explanation:

The equation is $\frac{x}{3} =\frac{x^{2} }{x+5}$

We shall determine the value of x, by simplifying the equation.

$\begin{aligned} x(x+5) &=3 x^{2} \\ x^{2}+5 x &=3 x^{2} \\ 2 x^{2}-5 x &=0 \\ x(2 x-5) &=0 \end{aligned}$

Thus, $x=0$ and $x=\frac{5}{2}$ are the solutions.

Now, let us check whether the solutions are extraneous solutions.

Let us substitute $x=0$ in the original equation to check whether both sides of the equation are equal.

$\begin{aligned}&\frac{0}{3}=\frac{0^{2}}{0+5}\\&0=\frac{0}{5}\\&0=0\end{aligned}$

Thus, both sides of the equation are equal.

Hence $x=0$ is a true solution.

Now, Let us substitute $x=\frac{5}{2}$ in the original equation to check whether both sides of the equation are equal.

$\begin{aligned}\frac{\left(\frac{5}{2}\right)}{3} &=\frac{\left(\frac{5}{2}\right)^{2}}{\left(\frac{5}{2}\right)+5} \\\frac{5}{6} &=\frac{\left(\frac{25}{4}\right)}{\left(\frac{15}{2}\right)} \\\frac{5}{6} &=\frac{5}{6}\end{aligned}$

Thus, both sides of the equation are equal.

Hence, $x=\frac{5}{2}$ is a true solution.

Thus, solutions are not extraneous.

Hence, Option C is the correct answer.

8 0

3 years ago

A bowl has 9 green grapes and 13 grapes. Henry randomly chooses a grape, and eats it, and then choose a another grape What is th

Sunny_sXe [5.5K]

Answer:

$\frac{72}{462}$ or $\frac{12}{77}$ (simplified)

Step-by-step explanation:

Based on the information provided within the question it can be said that in order to calculate the probability of both grapes being green we need to find the probability of each grape being green separately and then multiply those probabilities together

In the first choice, there are a total of 22 grapes (9+13), 9 of which are green. Therefore the probability of the first chosen grape being green is $\frac{9}{22}$

In the second choice,since we removed one grape there is now a total of 21 grapes (22-1), 8 of which are green. Therefore the probability of the second chosen grape being green is $\frac{8}{21}$

Now we multiply both probabilities together to calculate the probability that both grapes are green in a sequence.

$\frac{9}{22} * \frac{8}{21} = \frac{72}{462} or \frac{12}{77}$

7 0

3 years ago

A rectangular swimming pool is 30 cm wide and 40 cm in length. Find the total area and perimeter of the swimming pool.

Shkiper50 [21]

Answer:

Area: 1,200 square centimeters. Perimeter: 140 centimeters.

Step-by-step explanation:

Since you have to multiply the length and width in order to find the area, multiply 30 and 40 together and you can find 1,200. Next, to find the perimeter you have to add all the lengths of the rectangular swimming pool, which will result in 140 centimeters.

3 0

2 years ago

Given the speeds of each runner below, determine who runs the fastest.

Fantom [35]

495/34

13/1sec
495/34sec
5280/506
666/60
Convert all to same measurements( feet/sec) then simplify
13, 14.6, 10, 11.1

8 0

2 years ago