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3 years ago

What is the value of x?

Mathematics

1 answer:

fredd [130]3 years ago

3 0

Answer: 4

Step-by-step explanation:

Well, first you need to use the 30-60-90 special triangle property to find out the length of the hypotenuse triangle with the side with the length 2√3.

The 30-60-90 property states that if the hypotenuse is x, then the leg opposite to 30 degrees has the length of x/2 and the leg opposite to 60 degrees has the length of (x√3)/2. So if the leg opposite to 60 degrees has a length of 2√3, the hypotenuse can be found with this equation: 2√3=(x√3)/2, and when you solve this equation, you should get x=4.

Now that you have figured out the hyptenuse of the 30-60-90 triangle, you can use that leg to find the length of the other leg in the 45-45-90 triangle. Since both of the legs are opposite to the same degree angle, they are both congruent, and the value of x in the problem is 4.

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Read 2 more answers

A quadratic equation is shown below:

sweet [91]

Answer:

Part A:

( 1.8333, -0.08333)

Part B:

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Step-by-step explanation:

The quadratic equation

$3x^{2}-11x+10=0$ has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

$\frac{d}{dx}(3x^{2}-11x+10)=6x-11$

Setting the derivative to 0;

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The vertex is thus located at the point;

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Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

$x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}$

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

$x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}$

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