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sveta [45]
4 years ago
7

He main span of the Sunshine Skyway Bridge is 366 meters long. The bridge's main span is 30 meters shorter than the main span of

the Dames Point Bridge. Write and solve an equation to find the length (in meters) of the main span of the Dames Point Bridge. Let $x$ represent the length of the main span.
Mathematics
1 answer:
Digiron [165]4 years ago
3 0

Answer:

360 = x + 30

x = 390 meters

Step-by-step explanation:

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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.


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3 years ago
What is the difference between the x-coordinates of B and C?
Brilliant_brown [7]

Answer:

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Step-by-step explanation:

The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. ... In an ordered pair, such as (x, y), the first value is called the x-coordinate and the second value is the y-coordinate.

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The sum of two numbers is 52. If one number is 76 times the second number, then find the largest number out of the two.
butalik [34]

Answer:

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Step-by-step explanation:

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HELP ASAP!!!!!!<br> Ken and Betty each write a proof of the statement: if m
shepuryov [24]

The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

<h3>What is an angle?</h3>

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have Ken's statements are shown in the table:

Angle AOC = Angle BOD (given)

Angle AOB + Angle BOC = Angle BOC + Angle COD   (angle addition postulate)

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Ken wrote direct proof using deductive evidence.

As we can in betty's proof:

Betty wrote an indirect proof using contradiction.

Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

Learn more about the angle here:

brainly.com/question/7116550

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2 years ago
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