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Artyom0805 [142]
2 years ago
15

Find x, y, and z. Please help :)

Mathematics
1 answer:
Ivan2 years ago
3 0

Answer:

x = 55°, y = 70° and z = 125°

Step-by-step explanation:

Step 1 - Calculate ∠x:

As all angles on a line add up to 180°

125 + x = 180

x = 180 - 125

x = 55

Step 2 - Calculate ∠y:

As the triangle is an isosceles triangle, as evident by the two sides of equal length:

180 = y + 55 + 55

180 = y + 110

y = 180 - 110

y = 70

Step 3 - Calculate z:

180 - 55 = z

z = 125

Meaning that x = 55°, y = 70° and z = 125°

Hope this helps!

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1. 2 4/5v-2/3(4v+1 1/6)
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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]

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a =3 , b = 10

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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

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Subtract 100 from both sides, we get

100-12c -100= 196-100

Simplify:

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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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