Answer:
x = 5
Step-by-step explanation:
Step 1: Distributive property
Using this property means when you have something like the equation on the right side ( 4 ( x + 3 ) ) you multiply both the values in the parentheses by the number outside:
4 ( x + 3 )
( 4 x X ) + ( 4 x 3 )
4x + 12
8x + 2 = 2x + 4x + 12
Step 2: combine like terms
Combining like terms is when you find like terms with the same variables and such and add them together:
8x + 2 = 12 + ( 2x + 4x )
8x + 2 = 12 + 6x
Step 3:Using inverse operations
This means that you need to get a variable one one side and a constant on the other:
8x + 2 ( -2 ) = 12 ( -2 ) + 6x
8x = 10 + 6x
8x ( -6x ) = 10 + 6x ( -6x )
2x = 10
Step 4: solve for the variable
The last thing you need to do is divide both sides by the constant with the variable ( 2x ) to get x by itself:
2x ( /2 ) = 10 ( /2 )
x = 5
The answer is <span>a.)(x - 4)2 = 3.
(x - a)</span>² = b can be expressed as:
x² - 2ax + a² = b ⇒ x² - 2ax + a² - b = 0
Our equation is x² - 8x + 13 = 0.
The general formula is x² - 2ax + (a² - b) = 0
Thus:
8x = 2ax and a² - b = 13
Divide both sides of the first equation (8x = 2ax) by x:
8 = 2a ⇒ a = 8 ÷ 2 = 4
Replace a in the second equation (a² - b = 13):
4² - b = 13 ⇒ b = 4² - 13 = 16 - 13 = 3
Now when we have a and b, let's just replace them in the general equation:
(x - a)² = b
(x - 4)² = 3
Answer:
Step-by-step explanation:
a) We have 15! as the product of 1 to 15 natural numbers. Since 17 is prime there will be no factor common to these
By actual division we find
15! (mod 17) =16
From this we deduce
even 16! mod 17 = 16 = -1
According to Wilson theorem
(17-1)! = -1 mod 17
Thus verified 17 is prime
Hence 15! (mod 17) =-1=16
-----------------------
b) 2(26!) is divided by 29
Since 29 is prime
(29-1)! = -1 mod 29
28! = -1 mod 29 = 28
When divided this gives 25 as remainder
Yes, the blank numbers that can be written as a product of blank factors are called the prime factorization of a number. It can also be composite numbers where it can be written also as the product of prime factors.
Answer:
Step-by-step explanation:
Law of Sines recall Sin(A) /a = Sin(B) /b
does the above make sense?
Next we need to find the angle of A
notice that 16+75=91 :o
so angle A is only 89° ..(b/c all the way around then inside of a triangle is 180) so this is NOT a right triangle but that's okay, b/c law of sines still works fine.
then we want to find length of line AB
and if 89 = A then a = BC
and if 75 = B the b = AB (note that in the given triangle this is angle C, i'm using B , b/c you can see the difference between capital B and lower case b much easier than you can with C, & c :/ )
capitals are the angles while lower case are the length of the sides
then
Sin(89) / 29 = Sin(75) / b
solve the parts that can be put into numbers or solve for 'b' first, that means isolate 'b' all by itself on one side of the equal sign .
0.034477 = 0.965925/ b
b = 0.965925 / 0.034477
b = 28.0165
b = 28.0 ( to the nearest 10th)
we have the parts to plug in now
Sin(75) /
