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2 years ago

Please help me thank you

Mathematics

1 answer:

OverLord2011 [107]2 years ago

4 0

Answer:

$x = 2\sqrt{5}$

Step-by-step explanation:

Given

The attached triangle

Required

Find x

Using the sin function

$sin(\theta) = \frac{Opposite}{Adjacent}$

$sin(30) = \frac{\sqrt{5}}{x}$

Make x the subject

$x = \frac{\sqrt{5}}{sin(30)}$

$x = \frac{\sqrt{5}}{1/2}$

Express as:

$x = \sqrt{5}/1/2}$

$x = \sqrt{5}*2/1$

$x = \sqrt{5}*2$

$x = 2\sqrt{5}$

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2 years ago

Find the x- and y- intercepts of parabola y=5x^2-16x+10

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Y-INTERCEPT

$y = 5x^2 - 16x + 10$

The y-intercept is where the equation/curve/parabola cosses the y-axis.

The y-axis is where x = 0. (The x-axis is where y = 0)

To find the y-intercept:

$\text{y-axis} \rightarrow \text{x = 0} \rightarrow y = 5(0)^2 -16(0) + 10 = 10$

The y-intercept must be at (0, 10)

X-INTERCEPT (ROOTS/SOLUTIONS)

$y = 5x^2 - 16x + 10\\\text{make it equal 0}\\y = 0\\\therefore 5x^2 - 16x + 10 = 0$

We need to use the quadratic formula

The quadratic formula helps us find what values of $x$ make the equation = 0

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-16) + \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\\x = \frac{16 + \sqrt{256-200}}{10}\\x = \frac{16 + \sqrt{56}}{10}\\x = \frac{16 + 2\sqrt{14}}{10}\\x = \frac{8 + \sqrt{14}}{5}\\\\\\x=\frac{-(-16) - \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\text{doing the same thing...}\\\text{end up with...}\\x = \frac{8 - \sqrt{14}}{5}\\$