Step-by-step explanation:
The sum of angles in a triangle = 180°
Therefore,
(7x - 6)° + (5x - 10)° + 52° = 180°
Collect the like terms and add
7x + 5x - 6 - 10 + 52 = 180°
12x + 36 = 180°
12x = 180 - 36
12x = 144
x = 144 / 12
x = 12°
From the above diagram,
Angle A = 7x - 6
A° = 7(12) - 6
A° = 84 - 6
A = 78°
D because they all increase by the same number (+1)
The <em><u>correct answer</u></em> is:
negative six and thirty-three fortieths
Explanation:
To multiply (2 5/8)(-2 3/5), we first change each mixed number to an improper fraction. To do this, we multiply each whole number by the denominator and add the numerator:
(2*8)+5 = 16+5 = 21; this makes 2 5/8 = 21/8
(2*5)+3 = 10+3 = 13; this makes -2 3/5 = -13/5
This gives us
(21/8)(-13/5) = (21*-13)/(8*5) = -273/40
40 will go into 273 6 times; this gives us the number -6. There is then 270-240 = 33 left over; this gives us 33/40, and a total of -6 33/40.
Answer:
5,040 different passwords are possible
Step-by-step explanation:
Assuming that 4-digit means using only numeric values.
This is a permutations problem.
n = number of values used with number values only this is 10
r = the number used in each case without repeating in this case 4
nPr = n! / (n - r)!
nPr = 10! / (10-4)!
nPr = 10! / 6!
The ! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24
A quick hack for dividing factorials is to use cancelling.
10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)
= 5040
Change the left side to improper fractions.
9
--
4
====
3
--
2
Now use the fraction rule. Invert the denominator and multiply that by the numerator.
9 2
== * ==
4 3
18/12 = 3/2 which for now is left alone.
Now work with the fraction on the right side.
1 5/6 = 11/6
Now equate the two results
27/8 = 11/6 // x/1
Simplify the right side
3/2 = 11/6 * 1 / x Remember to invert and multiply that's why you need the 1 underneath the x
3/2 = 11/6x Cross multiply
3* 6x = 11 * 2
18 x = 22
18 x = 22
x = 11/9
x = 1.2222
What are the choices or are there any? The other choice is x = 1.2222
x = 22/18 or
x = 1.22222222 or
x = 11/9
All three are possible and all three are correct and all three are equal. Since I do not have choices, I don't know which one will be acceptable.
Check
I'll do this in decimals. It is much easier.
2.25/1.5 = 1.83333333 / 1.22222222
1.5 = 1.5 so these numbers do check.
