Piece of rope that is 15 ft long what is the area

Find the value of x in the isosceles triangle shown below.

guajiro [1.7K]

Answer:

B) $x = \sqrt{60}$

Step-by-step explanation:

1. As you can see from the image, there are two right triangles in the isosceles triangle. The base of each right triangle is 2 (because 4 ÷ 2 = 2), and the hypotenuse is 8.

2. Let's use Pythagorean Theorem to find the height of each right triangle, which will also give us the height of the isosceles triangle: $a^2 + b^2 = c^2$ , where a = height, b = base, and c= hypotenuse.

$a^2 + 2^2 = 8^2$
$a^2 + (2*2) = (8*8)$
$a^2 + 4 = 64$ (Simplify both sides of the equation)
$a^2 + 4 - 4 = 64 - 4$ (Subtract 4 from both sides)
$a^2 = 60$
$\sqrt{a^2} = \sqrt{60}$ (Take square root of both sides
$a = \sqrt{60}$

3. The√(60) is the height of each right triangle, and it's also the height of the isosceles triangle. Therefore, the answer is B) x = √60.

8 0

3 years ago

The sum of two numbers is 35 the smaller number is 7 less than the larger number what are the numbers

Keith_Richards [23]

14 and 21

14 + 7 is 21 and 21 + 14 is 35.

5 0

3 years ago

If Charlie liked dogs, and Macy's hat was green, how fast was the car, that the dog's dad was driving?

Likurg_2 [28]

Answer: The car wasn't going fast at all because dogs can't drive

Step-by-step explanation:

4 0

3 years ago

What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix? Enter the equation in the box.

antiseptic1488 [7]

Check the picture below. So the parabola looks more or less like so.

let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.

Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.

$\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5$

6 0

3 years ago

−10)−3 = A) 0.01 B) 1000 C) −0.001 D) −1000

nordsb [41]

Answer:

A

Step-by-step explanation:

I am kinda positive this is it but it might not be

8 0

3 years ago

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