Answer:
The absolute value
Step-by-step explanation:
we know that
The modulus of a real number, is equal to the absolute value of the real number
so
The modulus of a positive number is simply the number and the modulus of a negative number is found by ignoring the minus sign.
Then
modulus of n is always positive number .such that n belongs to real number R.
Modules of n is denoted by |n|
<u><em>Examples:
</em></u>
|-4|=4
|2.5|=2.5
|-100.1|=100.1
Answer:
the theater needs to sell at least 100 tickets
Step-by-step explanation:
wants to make at least $1000 and they already have $50, so you take the $9.50 per ticket and add that to the $50.
$1000=$9.50t+$50
1000/50=9.5t
950=9.5t
950/9.5=t
t=100
There are several ways to solve a system of equation; one of these ways is the use of matrix.
<em>Jerry made a mistake at step 2</em>
From the attachment, the step 1 is represented as:
![\mathbf{\frac 12R_1 \left[\begin{array}{cccc}1&1&1&0\\5&3&-2&-4\\3&2&1&1\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%2012R_1%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%260%5C%5C5%263%26-2%26-4%5C%5C3%262%261%261%5Cend%7Barray%7D%5Cright%5D%20%7D)
The equation in step 2 is given as:
This means that:
We subtract the elements of row 2 from the elements of row 1, multiplied by 5
So, we have:
![\mathbf{R_2 = 5\left[\begin{array}{cccc}1&1&1&0\end{array}\right] } - \left[\begin{array}{cccc}5&3&-2&-4\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7BR_2%20%3D%205%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%260%5Cend%7Barray%7D%5Cright%5D%20%7D%20-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%263%26-2%26-4%5Cend%7Barray%7D%5Cright%5D%20%7D)
Expand
![\mathbf{R_2 = \left[\begin{array}{cccc}5&5&5&0\end{array}\right] } - \left[\begin{array}{cccc}5&3&-2&-4\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7BR_2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%265%265%260%5Cend%7Barray%7D%5Cright%5D%20%7D%20-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%263%26-2%26-4%5Cend%7Barray%7D%5Cright%5D%20%7D)
Subtract corresponding cells
![\mathbf{R_2 = \left[\begin{array}{cccc}0&2&7&4\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7BR_2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%262%267%264%5Cend%7Barray%7D%5Cright%5D%20%7D)
So, the new row 2 elements should be:
![\mathbf{ \left[\begin{array}{cccc}0&2&7&4\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%262%267%264%5Cend%7Barray%7D%5Cright%5D%20%7D)
However, the row 2 elements of Jerry's steps are:
![\mathbf{R_2 = \left[\begin{array}{cccc}0&-2&-7&-4\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7BR_2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%26-2%26-7%26-4%5Cend%7Barray%7D%5Cright%5D%20%7D)
This means that:
Jerry made a mistake; and the mistake is at step 2
Read more about matrix at:
brainly.com/question/21848291
Answer:
G. ABD = 74
H. DBC = 206
I. XYW = 33.75
J. WYZ = 46.25
Step-by-step explanation:
For G and H: You have a straight line (ABC) with another line coming off of it, creating two angles (ABD and DBC). A straight line has an angle of 180 degrees. This means that the two angles from the straight line when combined will give you 180 degrees. Solve for x.
ABD + DBC = ABC
(1/2x + 20) + (2x - 10) = 180
1/2x + 20 + 2x - 10 = 180
5/2x + 10 = 180
5/2x = 170
x = 108
Now that you have x, you can solve for each angle.
ABD = 1/2x + 20
ABD = 1/2(108) + 20
ABD = 54 + 20
ABD = 74
DBC = 2x - 10
DBC = 2(108) - 10
DBC = 216 - 10
DBC = 206
For I and J: For these problems, you use the same concept as before. You have a right angle (XYZ) that has within it two other angles (XYW and WYZ). A right angle has 90 degrees. Combine the two unknown angles and set it equal to the right angle. Solve for x.
XYW + WYZ = XYZ
(1 1/4x - 10) + (3/4x + 20) = 90
1 1/4x - 10 + 3/4x + 20 = 90
2x + 20 = 90
2x = 70
x = 35
Plug x into the angle values and solve.
XYW = 1 1/4x - 10
XYW = 1 1/4(35) - 10
XYW = 43.75 - 10
XYW = 33.75
WYZ = 3/4x + 20
WYZ = 3/4(35) + 20
WYZ = 26.25 + 20
WYZ = 46.25
Answer:
1.07142857143 (1 rounded)
Step-by-step explanation:
3/14 of 5 is 1.07142857143
