Hello! So Brian is 6 feet tall and casts a 4 foot shadow and the tree’s shadow is 20 feet. To find the height of the tree, we can write and solve a proportion. Set it up like this:
6/4 = x/20
This is because we are looking for the height of the tree, and having it set up like this will help us get to the right answer. Let’s cross multiply. 6 * 20 is 120. 4 * x is 4x. That simplified to 120 = 4x. Now, divide each side by 4 to isolate the x. 4x/4 cancels our. 120/4 is 30. Let’s cross multiply to check out answers. 6 * 20 is 120. 30 * 4 is 120. 120 = 120. There. x = 30. The tree is 30 feet tall.
88.32 should be the answer. I don't know if you are supposed to round your answer though. If you are you should be able to figure that out :)
If the value of |A| is 48 the possible values for x in the matrix is 4 or -2.
<h3>How to use determinant to find a value in a matrix?</h3>
The determinant of the matrix A is as follows:
|A| = 48
Therefore,
48 = (3x × 2x) - (4x × 3)
48 = 6x² - 12x
6x² - 12x - 48 = 0
3x² - 6x - 24 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2 -4(x + 2) = 0
(x - 4)(x +2) = 0
Therefore,
x = 4 or -2
learn more on determinant here: brainly.com/question/19206601
Answer:
<h3>The answer is 10 units</h3>
Step-by-step explanation:
The distance between two points can be found by using the formula
<h3>
![d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} }](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%28%20%7Bx1%20-%20x2%7D%29%5E%7B2%7D%20%2B%20%20%28%7By1%20-%20y2%7D%29%5E%7B2%7D%20%20%7D%20)
</h3>
where
(x1 , y1) and (x2 , y2) are the points
From the question , the points are
A(13, 2) and B(7, 10)
The distance between them is
<h3>
![|AB| = \sqrt{( {13 - 7})^{2} + ({2 - 10})^{2} } \\ = \sqrt{ {6}^{2} + ( { - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100}](https://tex.z-dn.net/?f=%20%7CAB%7C%20%20%3D%20%20%5Csqrt%7B%28%20%7B13%20-%207%7D%29%5E%7B2%7D%20%2B%20%20%28%7B2%20-%2010%7D%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%7B6%7D%5E%7B2%7D%20%2B%20%28%20%7B%20-%208%7D%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B36%20%2B%2064%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B100%7D%20)
</h3>
We have the final answer as
<h3>10 units</h3>
Hope this helps you