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Harrizon [31]
3 years ago
6

The late fee for library books is $2.00 plus 15 cents each day for a book that is late. How much will you owe if the book is 30

days late?
Mathematics
1 answer:
zaharov [31]3 years ago
8 0
$4.50

Multiply the $0.15 by the 30 days then add $2.00 to your total.
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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
2 years ago
I GIVEEEEE BRAINLILSTTTT
Georgia [21]

Answer:

Step-by-step explanation:

englargment

4 0
2 years ago
Read 2 more answers
Pls help me,this is Canadian MO 1998 question,i'm very confuse with this​
dybincka [34]

The solution to the equation is x = 1.62

<h3>How to solve the equation?</h3>

The equation is given as:

x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}

Next, we split the equations as follows:

y = x

y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}

Next, we graph the equations (see attachment)

From the attached graph, the equations intersect at

(x, y)= (1.62, 1.62)

Remove the y value

x = 1.62

Hence, the solution to the equation is x = 1.62

Read more about equations at

brainly.com/question/2972832

#SPJ1

5 0
1 year ago
Read 2 more answers
Solve 3sinx = 2cos^2x .
goldenfox [79]
3 sin x = 2 ( 1 - sin² x )
3 sin x = 2 - 2 sin² x
2 sin² x + 3 sin x - 2 = 0
Substitution: t = sin x
2 t² + 3 t - 2 = 0
t 1/2 = \frac{-3+/- \sqrt{9+16} }{4} =  \frac{-3+/-5}{4}
t 1 = 1/2
t 2 = - 2 ( this solution is not acceptable )
sin x = 1/2
Answer:
x 1 = π / 6 + 2 kπ,       x 2 = 5 π / 6 + 2 k π,   k ∈ Z 
5 0
3 years ago
An article is marked to sell at profit of 16%. if it is sold for rs 62.50 less ,t
Anettt [7]

Answer:

the price is 250

Step-by-step explanation:

let cp be x.

the marked price is 116x/100=1.16x.

25x/100=6250/100

x=250

6 0
3 years ago
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