Answer:
The measure of a = b = 116 degrees
Step-by-step explanation:
Here, we have value of angles to calculate.
If a and b are both supplementary to c, what this means is that when we add either a or b to c, we get 180
Hence; Mathematically;
a + c = 180 and b + c = 180
What we have here is that a and b must be equal since they are both supplementary to the same angle value
Now, we are told further in the question that the measure of angle a is 12 less than 2 times the measure of c;
Mathematically, this means that;
a = 2c - 12
So we now want to find the measure of b
Let’s substitute for a
2c -12 + c = 180
3c -12 = 180
3c = 180 + 12
3c =192
c = 192/3
c = 64
Thus; a = 2c - 12 = 2(64) -12 = 128 -12 = 116
Answer:
- determinant: -15
- x = 3; y = 4; z = 1
Step-by-step explanation:
The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.
<h3>coefficient matrix, determinant</h3>
The first attachment shows the coefficient matrix and its determinant.
__
<h3>solution</h3>
The solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.
This multiplication is shown in the second attachment. It tells us ...
![\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Ctextbf%7BX%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C4%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Answer: The TV is 24 inches tall
Step-by-step explanation: The question has provided the diagonal and the width of the rectangle shaped television. From this bit of information, we can deduce that the diagonal of the rectangle (television) is also the Hypotenuse (26 inches) while the the other two sides are the Length and the Width (10 inches).
For every right angled triangle, we can apply the Pythagoras theorem to solve for any unknown side. The theorem states that
AC² = BC² + AB²
Where AC is the hypotenuse (longest side)
26² = 10² + AB²
676 = 100 + AB²
Subtract 100 from both sides of the equation
576 = AB²
Add the square root sign to both sides of the equation
√576 = √AB²
24 = AB
Therefore, the height of the television is 24 inches
