Answer:
<h2>x = 14, z = 65</h2>
Step-by-step explanation:
The angles (5x - 5)° and (6x + 31)° are supplementary angles.
Supplementary Angles add up to 180°.
Therefore we have the equation:
5x - 5 + 6x + 31 = 180 <em>combine like terms</em>
(5x + 6x) + (-5 + 31) = 180
11x + 26 = 180 <em>subtract 26 from both sides</em>
11x = 154 <em>divide both sides by 11</em>
x = 14
The angles (5x - 5)° and z° are vertical angles.
Vertical angles are congruent.
Therefore we have the equation:
z = 5x - 5 <em>put x = 14 to the equation</em>
z = 5(14) - 5
z = 70 - 5
z = 65
Answer:


Step-by-step explanation:
The law of indices can be used to simplify mathematical expressions involving arithmetical operation on variables with powers.
x
= 
Thus, the given expression can be simplified as follows:
a³b² a²b = a³ x a² x b² x 
=
x 
= 

Thus,
a³b² a²b = 

If both triangles ABE = CBD then <C = <A
Hope it helps.
Answer:
26*26*26 = 17576 ways to select 3 letters
10*10= 100 ways to select 2 numbers
So then the total number of ways are:
possible ways
Step-by-step explanation:
For this case we assume that we have 26 letters from A to Z and 10 numbers from 0 to 9 .
And we want to calculate the number of possible passwords possible if the password consists of 3 letters followed by 2 digits.
And for this case we can use the multiplication principle of combinatories, since we don't have any restriction about the letters of the numbers we can have repetition of letters or numbers.
For the number of possible letters:
26*26*26 = 17576 ways to select 3 letters
10*10= 100 ways to select 2 numbers
So then the total number of ways are:
possible ways
Answer:
$24166.67
Step-by-step explanation:
$25 per hour and works 35 hours per week
Norma Jean makes 35 * 25 (<em>without sales) = </em>$875
<em> </em>Total commission made by Norma<em> </em>= 4500-875 = $3625
<em>let total number of sales by Norma be x</em>
15% is the same as 15/100
<em>so </em>(15/100) * x =3625 <em> multiplying both sides by 100</em>
15x = 362500<em> making x subject of formula</em>
x = 362500/15
x = 24 166.67
Norma should sell total items worth $24166.67