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3 years ago

A race car travels 100 feet in .5 seconds. At this rate of speed, how many feeet will the race car travel in a minute?

2 answers:

7 0

$\text{Hello there!}\\\\\text{We know that a car travels 100 ft every .5 seconds}\\\\\text{Lets find how far it goes every second}\\\\100*2=200\,\text{ft per second}\\\\\text{We're trying to find how far it goes in a minute, so multiply by 60}\\\text{Since 60 seconds = 1 minute}\\200*60=12000\\\\\boxed{12,000 ft}$

soldier1979 [14.2K]3 years ago

5 0

Answer:

Step-by-step explanation:

$\frac{100ft}{0.5s} * 60s$

$\frac{100 * 60}{0.5}$

$\frac{6000}{0.5}$

$12000ft$

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3 years ago

The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

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Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

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$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

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3 years ago

Nathan usually drinks 38 ounces of water per day. He read that he should drink 60 ounces of water per day. If he starts drinking

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Answer:

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Step-by-step explanation:

First, we need to find how much extra water Nathan drinks.

$60-38=22$ extra ounces.

To find the percent increase:

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3 years ago

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Therefore, what will be charged with taxes will be:

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45.0,05 = 2,25

Now that we know that the tax was 2.25, we just have to add it to the total purchase to find out how much Carmen paid:

2.25 + 70 = 72.25

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