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3 years ago

Please Help asap 40 points

Mathematics

1 answer:

tester [92]3 years ago

7 0

Answer:

Step-by-step explanation:

34 to the 4

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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

Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. Wh

Alinara [238K]

Answer:

158.33 minutes = 2.63 hours

Step-by-step explanation:

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3 years ago

Solve 6x + 3) = 21.

LiRa [457]

Answer:

18x^2 - 9

Step-by-step explanation:

y = f(x)= 6x^3 - 9x + 4

dy/dx = d/dx(6x^3) - d/dx(9x) + d/dx (4)

=6.d/dx(x^3) - 9.d/dx (x) + d/dx. (4)

=6.3x^2 - 9.1 + 0 =18x^2 - 9

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3 years ago

Fill the blank space in the pattern.<br> 1,5,25,-,625

vazorg [7]

Answer:

-125,-626

Step-by-step explanation:

please mark brainliest

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3 years ago

What is the equation of the line:

kipiarov [429]

Answer:

Final answer is y=3x-2.

Step-by-step explanation:

We have been given a graph and using that graph we need to find the equation of line.

Equation of line is given by formula y=mx+b

Where b is the y-intercept.

We see that graph crosses y-axis at (0,-2) so that means b=-2

Now plug b=-2 into formula y=mx+b. We get:

y=mx-2 ...(i)

Now find any point from the graph say (1,1) and plug into (i) to find value of slope m

1=m*1-2

1=m-2

1+2=m

3=m

Now plug m=3 into (i). We get:

y=3x-2

Hence final answer is y=3x-2.

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3 years ago