How do I do #11? (Each part of it)

Find X <br><br> Simplify answer type exact number or use radicals as needed

satela [25.4K]

On a right triangle, to find one missing side you can use this equation
a^2 + b^2 = c^2

a and b are the sides next to the right angle, and c is the hypotenuse (side not connected to right angle).

You first need to find the length of the dotted line before finding x. This is because to be able to use the above formula, you have to know the length of two out of three of the sides.

To solve the length of the dotted line, note that it also makes a triangle with the 5 unit line and the 5 √5 unit line. You can plug these numbers into the formula.
(5)^2+b^2=(5 √5)^2
25+b^2=125
b^2=100
b=10

Now that you know the length of the dotted line is 10 units, you can now solve for x

(20)^2+(10)^2=x^2
400+100=x^2
500=x^2
x= √500, which equals 22.361

5 0

3 years ago

A rectangle or piece of paper has a width is 3 inches less than its link it is cut in half along a diagonal to create two congru

kolezko [41]

The length and width of the rectangle is 11 in and 8 in respectively.

Step-by-step explanation:

Given,

The width of a rectangle is 3 in less than the length.

The area of each congruent right angle triangle = 44 in²

To find the length and width of the rectangle.

Formula

The area of a triangle with b base and h as height = $\frac{1}{2}$ bh

Now,

Let, the width = x and the length = x+3.

Here, for the triangle, width will be its base and length will be its height.

According to the problem,

$\frac{1}{2}$ ×(x+3)×x = 44

or, $x^{2} +3x = 88$

or, $x^{2} +3x-88 = 0$

or, $x^{2}$ +(11-8)x-88 = 0

or, $x^{2}$ +11x-8x-88 =0

or, x(x+11)-8(x+11) = 0

or, (x+11)(x-8) = 0

So, x = 8 ( x≠-11, the length or width could no be negative)

Hence,

Width = 8 in and length = 8+3 = 11 in

3 0

3 years ago

Can someone PLEASE help me with Trigonometry???

Svetach [21]

$\bf sin^2(2\theta)-7sin(2\theta)-1=0\\\\
-------------------------------\\\\
sin(2\theta)=\cfrac{7\pm\sqrt{49-4(1)(-1)}}{2(1)}\implies sin(2\theta)=\cfrac{7\pm\sqrt{49+4}}{2}
\\\\\\
sin(2\theta)=\cfrac{7\pm\sqrt{53}}{2}\implies 2\theta=sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)
\\\\\\
\theta=\cfrac{sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)}{2}$

but anyway, the numerator will give the angles, and θ is just half of each

$\bf \theta=\cfrac{sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)}{2}\\\\
-------------------------------\\\\
sin^{-1}\left( \frac{7+\sqrt{53}}{2} \right)\implies sin^{-1}(7.14)\impliedby \textit{greater than 1, no good}
\\\\\\
sin^{-1}\left( \frac{7-\sqrt{53}}{2} \right)\implies sin^{-1}(-0.14) \approx -8.05^o
\\\\\\
\theta=\cfrac{-8.05}{2}\implies \theta=-4.025$

ok... that's a negative tiny angle, is in the 4th quadrant, if we stick to the range given, from 0 to 360, so we have to use the positive version of it, 360-4.025

so the angle is 355.975°

now, the 3rd quadrant has another angle whose sine is negative, so... if we move from the 180° line down by 4.025, we end up at 184.025°

and those are the only two angles, because, on the 2nd and 1st quadrants, the sine is positive, so it wouldn't have an angle there

7 0

3 years ago

The sum of 43.9 and a number is 49.65, as shown below. What number should go in the box to complete the addition problem? 43.9 p

Ber [7]

43.9 + n = 49.65
43.9-43.9 + n = 49.65 -43.9
n = 5.75

6 0

3 years ago

A ball is thrown from an initial height of 3 feet with an initial upward velocity of 21 ft/s. The ball height h (in feet) after

Alexxx [7]

Answer:

Step-by-step explanation:

The position equation is given as

$s(t)=-16t^2+21t+3$ and we are looking for the times when the position of the ball is 9 feet. That means that we simply plug in a 9 for s(t) and factor to solve for t:

$9=-16t^2+2t+3$ and

$0=-16t^2+21t-6$ and this is what we factor to find t:

t = .42 sec and then again on its way back down at t = .89 sec

5 0

3 years ago