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2 years ago

Mario walked at a rate of 2/3 miles every 10 minutes what is his unit rate every mile per hour

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

5 0

Mario's unit rate is given by 900 miles/hour.

Explanation:

We have been given that Mario walked at a rate of 2/3 miles every 10 minutes.

We have the relation between speed, time and distance, which is given by

$\text{Speed}= \frac{\text{Distance}}{\text{Time}}$

We have,

Distance = $\frac{2}{3} \text{ miles}$

Time = 10 minutes

On substituting these values in the above formula, we get

$\text{Speed} = \frac{2/3}{10}\\\\ \text{Speed} =\frac{2}{10\cdot 3}\\\\ \text{Speed} =[tex]\frac{1}{15}$ \text{ miles/min}[/tex]

We have to find the unit rate in mile per hour, so we need to multiply it by 60

Thus, unit rate is given by

$\frac{1}{15} \times 60\\ = 4 \text{ miles/hour}$

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Solve x2 - 8x - 9 = 0. Rewrite the equation so that it is of the form x2 + bx = c.

barxatty [35]

Answer:

x=9,-1 and $x^2+(-8)x=9$

Explanation:

we have been given with the quadratic equation $x^2-8x-9$

we compare the given quadratic equation with general quadratic equation

general quadratic is $ax^2+bx+c=0$

from given quadratic equation a=1,b= -8,c= -9

substituting these values in the formula for discriminant $D=b^{2}-4ac$

$D=(-8)^2-4(1)(-9)=100$

Now, to find the value of x

Formula is $x=\frac{-b\pm\sqrt{D}}{2a}$

Now, substituting the values we will get

$x=\frac{-(-8)\pm\sqrt{100}} {2}= \frac{8\pm10}{2}=9,-1$

And rewritting the given equation by shifting 9 to right hand side of the given equation and taking minus inside the bracket so as to convert it in the form of

$x^2+bx=c$

4 0

2 years ago

Read 2 more answers

A scientist had a bottle that contains 56.6 ML of a solution. she used 3.2 ML of the solution for an experiment then she poured

hjlf

1. 56.6 - 3.2 = 53.4
2. 53.4 divided by 2 = 26.7
3. 26.7 - 6 = 20.7
Answer: 20.7 mL

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2 years ago

Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not

4vir4ik [10]

<u>Answer:</u>

x = 4 (extraneous solution)

<u>Step-by-step explanation:</u>

$\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\$

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back $x=4$ , we will get two fractions with zero denominator which would be undefined.