Answer:
1) The value of
is 12.
2) The length of the diagonal is 49.
Step-by-step explanation:
1) If the glass is a rectangle, then both diagonal must have the same length, that is, the following equation must be solved:
(1)
We need some algebraic handling to determine the value of
:


![[5+(-2)] \cdot x = 36](https://tex.z-dn.net/?f=%5B5%2B%28-2%29%5D%20%5Ccdot%20x%20%3D%2036)


The value of
is 12.
2) If we know that
, then the length of the diagonal (
) is:


The length of the diagonal is 49.
Answer:
36°
Step-by-step explanation:
The computation of the measure of the angle is shown below:
As we know that
The trigonometric function in the right angle is
sinα = OS ÷ H
And,
cosα = AS ÷ H
Here
α represent the one of the angles
OS and AS represent the opposite sides
And, H represent the hypotenuse
So
sinx = 8.5 ÷ 14.5
x = arcsin = 8.5 ÷ 14.5
= 35.88
= 36 degrees
-x + y > 5 <em>add x to bot sides</em>
y > x + 5 → y = x + 5
for x = 0 → y = 0 + 5 = 5 → (0, 5)
for x = -5 → y = -5 + 5 = 0 → (-5, 0)
The dotted line (sign >, not ≥).
We shade above the line (y > ...).
Answer:
The matrix is not invertible.
Step-by-step explanation:
We are given the following matrix in the question:
![A =\left[\begin{array}{ccc}-5&0&1\\-1&3&2\\0&10&6\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%260%261%5C%5C-1%263%262%5C%5C0%2610%266%5Cend%7Barray%7D%5Cright%5D)
Condition for invertible matrix:
A matrix is invertible if and only if the the determinant is non-zero.
We can find the determinant of the matrix as:
![|A| = -5[(3)(6)-(2)(10)]-0[(-1)(6)-(2)(0)] + 1[(-1)(10)-(3)(0)]\\|A| = -5(18-20)+(-10)\\|A| = 10-10\\|A| = 0](https://tex.z-dn.net/?f=%7CA%7C%20%3D%20-5%5B%283%29%286%29-%282%29%2810%29%5D-0%5B%28-1%29%286%29-%282%29%280%29%5D%20%2B%201%5B%28-1%29%2810%29-%283%29%280%29%5D%5C%5C%7CA%7C%20%3D%20-5%2818-20%29%2B%28-10%29%5C%5C%7CA%7C%20%3D%2010-10%5C%5C%7CA%7C%20%3D%200)
Since the determinant of the given matrix is zero, the given matrix is not invertible.