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3 years ago

Four families equally share 5 pies. How much pie will each family receive?

Mathematics

1 answer:

german3 years ago

8 0

1 1/4 because if you give each family a pie there is on pie left so you would have to split that into fourths.

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

andrezito [222]

Answer:

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

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

Simplify:

$x_2 = -2$

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

3 0

3 years ago

Cube roots till 30... pleaseeee!

masha68 [24]

Answer:

1, 8, 27?

Wasn't sure if you were asking for the cube numbers instead?

5 0

2 years ago

Read 2 more answers

Find the magnitude of vector v that has an initial point of (1, 3) and a terminal point of (7, 1)

solmaris [256]

Answer:

It's totally correct with no doubt

3 0

3 years ago

mr and mrs gracia took their three children to see a matinee on saturday. they spent a total of 55.50, which included 29.95 at t

andrezito [222]

First, you would subtract 29.95 from 55.50, and you get 25.55. because 5 people went, and the cost for each was the same, you would divide 25.55 by five, and get $5.11 per person.

3 0

3 years ago

I need help with elimination with substitution. The equations are 3x+4y=19 and 3x+6y=33

olganol [36]

For elimination, multiply one whole equation by negative one (-1), then add or subtract according to your signs. After that, it will be a one-step equation.

3x + 4y = 19 3x + 4y = 19 3x + 4y = 19 -2y = -14 y = 7
3x + 6y = 33 -1 (3x + 6y = 33) -3x - 6y = -33 -14 / -2

Then you would go back and substitute the value of (y) back into either equation and then solve for the remaining variable (x). Finally, use both values to make an ordered pair.

3x + 4y = 19 3x = -9 x = -3 (-3 , 7)
3x + 4(7) = 19 (-9 / 3)
3x + 28 = 19

Good Luck

4 0

3 years ago