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Ahat [919]
3 years ago
10

Please help me with this math question, It's worth 30 points for whoever want's to answer.

Mathematics
1 answer:
swat323 years ago
8 0

Answer:

hello I can help you in this

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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}

or

\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}

or

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}

or

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
Answer this really quick
ivann1987 [24]

Answer:

the equation is y = ax + b (a ≠ 0)

see in the graph, the line passed through (0;3) and (1;5)

=>b = 3

   a + b = 5

<=> a = 2

     b = 3

=> the equation is y = 2x + 3

Step-by-step explanation:

7 0
2 years ago
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The U.S. Energy Department states that 60% of all U.S. households have ceiling fans. In addition, 29% of all U.S. households hav
hram777 [196]

Answer:

Very sorry if this is no help

Step-by-step explanation:

5 0
2 years ago
Correct Answers only!
Illusion [34]

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 80000 × 15/100 × 4

I = $48000

He saves = 48000 +80000 = $128000

6 0
4 years ago
Help with this question, please
Leya [2.2K]

Answer:

12.57 inches

Step-by-step explanation:

the formula is l = x/360 (2 pi r) so you solve from there

8 0
2 years ago
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