Answer:
x = 10.5
Step-by-step explanation:
Firstly, in geometry, you may have to <u>prove that the two triangles pictured are similar</u>.
Since the two horizontal lines are marked, they are assumed to be parallel.
Therefore, if the lines are parallel, the two bottom angles of each triangle can be treated as the same due to the [Corresponding Angles Theorem], respectively
As such, the two triangles can be seen as <u>SIMILAR</u> as proven by <u>Angle-Angle Similarity.</u>
Now that we've proven both triangles to be similar, we can then set up ratios for the sides:
= 
Note: we are using y as a measure of the <em>entire right side of the triangle</em>, so
<em>y = 6 + x</em>
Continuing on, if you cross-multiply the fractions to solve for y:
8y = 6 * 22
Simplify.
8y = 132
Simplify again.
y = 16.5
<u>We are not done yet!</u> We are solving for x, so remember <em>y = 6 + x</em>
16.5 = 6 + x
Solve for x.
x = 10.5
Answer:
1) 11.9
2) 3.6
3) 18.9
4) 45.4
Step-by-step explanation:
Math
Answer:
186
Step-by-step explanation:
We found a counterexample, so the statement is false.
<h3>
Is the statement true?</h3>
Let's use the matrix:
![\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-2%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C%200%260%260%261%20%5Cend%7Barray%7D%5Cright%5D)
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
![\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%2F2%260%260%260%5C%5C0%26-1%260%260%5C%5C0%260%26-1%260%5C%5C%200%260%260%26-1%20%5Cend%7Barray%7D%5Cright%5D)
If we multiply it by 2, we get:
![\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%26-2%260%260%5C%5C0%260%26-2%260%5C%5C%200%260%260%26-2%20%5Cend%7Barray%7D%5Cright%5D)
The adjoint of that is the original matrix, actually:
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
If you want to learn more about matrices:
brainly.com/question/11989522
#SPJ1
Answer:
5h+5
5(h+1)
Step-by-step explanation:
Equivalent expressions are the ones that look different but are the same. As the statement says that mason works h number of hours during the 5 day week and 5 hours on the weekend, you can write the following expression:
5h+5
h= number of hours Mason works
Then, you can find the common factor to get an equivalent expression:
5(h+1)
According to this, the equivalent expressions are:
5h+5
5(h+1)
