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3 years ago

Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

Mathematics

2 answers:

Afina-wow [57]3 years ago

8 0

both sides will be 12√2

About 45 degrees

elixir [45]3 years ago

7 0

Answer:

Both the sides of the triangle are 12√2

Step-by-step explanation:

The given triangle is a right angle triangle having on acute angle = 45°

Since it a right angle triangle so other angle will be same as 45°.

therefore opposite sides of these angles will be same.

Now we apply the sine rule in the given triangle

$sin45=\frac{x}{24}$

x = 24×sin 45 = $24.\frac{1}{\sqrt{2} }=\frac{24}{\sqrt{2} }$

Now to convert this value in radical form we have to multiply numerator and denominator by √2.

$x=\frac{24}{\sqrt{2}}.\frac{\sqrt{2} }{\sqrt{2} }=\frac{24\sqrt{2} }{2}=12\sqrt{2}$

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Can someone please help mee (20 points and i will give brainliest!!!)

FromTheMoon [43]

Answer:

a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes $y=(0)^2-0-6$ which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$ . In this case a=1, b=-1, c=-6. So plugging those values in you get $x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}$ , which simplifies to $x=\frac{1\pm5}{2}$ . This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of $y=(x-h)^2+k$ where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

$y+6=x^2-x$

Complete the square by adding (b/2)^2

$y+6+0.25 = x^2-x+0.25$

Rewrite as square binomial

$y+6.25 = (x-0.5)^2$

Isolate y

$y=(x-0.50)^2-6.25$

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation $y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}$ . which simplifies to $x=\frac{-1\pm5}{-2}$ which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

$y=-(x^2-x-6)$

Add 6 to both sides (on the left side add -6 since -1 was factored out).

$y-6=-(x^2-x)$

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

$y-6-0.25 = -(x^2-x+0.25)$

Rewrite as square binomial

$y-6.25=-(x-0.5)^2$

Add 6.25 to both sides

$y=(x-0.50)^2+6.25$

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

4 0

1 year ago

Read 2 more answers

The diameter of the circle is 8 cm. what is the circles area?

iren [92.7K]

Answer:

Step-by-step explanation:

diameter = 8 cm

radius = 8/2 = 4 cm

Area of circle = πr²

= 3.14*4*4 = 50.24 cm²

8 0