This scenario forms a right-angled triangle where Ruby's height of 5 feet is the height of the triangle. Her 6 feet long shadow is the length of the triangle and the distance from the top of her head to the end of the shadow is the hypotenuse.

This can therefore be solved by the Pythagorean formula:

c² = a² + b²

where ;

c = hypotenuse

a = height

b = length

c² = 5² + 6²

c² = 25 + 36

c² = 61

c = √61

c = 7.81 feet

7 0

3 years ago

A football field is 53 1/3 yards wide how many feet wide is a football field

Olin [163]

Just look up 53 1/3 yards in feet. This would mean that the football field is 160 feet.

3 0

3 years ago

PLEASE HELP ME (PICTURE) 4 3 2 6

elena55 [62]

Since the triangles are similar, they will have proportional sides. With this knowledge, we can make the proportion $\frac{8}{10} =\frac{x}{5}$ to solve for x.

Firstly, cross multiply: $40=10x$

Next, divide by 10 on both sides, and your answer will be 4 = x, or the first option.

3 0

3 years ago

Read 2 more answers

Let A = (1, 0, 3) and B = (−3, 2, 1).

Romashka-Z-Leto [24]

Answer:

a) $(-\frac{\sqrt{24}}{6} ,\frac{\sqrt{24}}{12} ,-\frac{\sqrt{24}}{12})$

b) $(-1,1,2)$

c) $-2x+y-z=1$

Step-by-step explanation:

AB, OB, OA are vectors.

$AB = OB - OA = (-3, 2, 1) - (1, 0, 3) = (-4, 2, -2)\\||AB|| = \sqrt{(-4)^2+2^2+(-2)^2}=\sqrt{24}\\$

Normalizing AB: $\frac{AB}{||AB||} = (\frac{-4}{\sqrt{24}},\frac{2}{\sqrt{24}}, \frac{-2}{\sqrt{24}})=(-\frac{\sqrt{24}}{6} ,\frac{\sqrt{24}}{12} ,-\frac{\sqrt{24}}{12})$

OM, OA, OB are vectors.

$OM = \frac{1}{2}OA+\frac{1}{2}OB=(\frac{-3+1}{2} ,\frac{2+0}{2}, \frac{1+3}{2} )=(-1,1,2)$

So, $M = (-1,1,2)$

$-4x+2y-2z=(-4)(-1)+(2)(1)+(-2)(2)=4+2-4=2$

Hence,

$-2x+y-z=1$

5 0

3 years ago