The question has omitted options but i will solve, so you will just check my answer from the options you have.
Answer: The equation to find the value of x = 3x+ 2= 5x-4
The value of x= 3
Step-by-step explanation:
Step 1
The sum of 3 times the value of x and 2 is equal to four less than five times the value of x can be expressed as
3x+ 2= 5x-4
Step 2
Solving this equation to find the value of x , we have that
3x+ 2= 5x-4
3x-5x= -4-2
-2x= -6
x= -6/-2
x=3
Answer: Check if numbers are prime. Composite numbers prime factorization (decomposing, breaking numbers down to prime factors). Inscribe them as a product of prime factors, in exponential notation.
Step-by-step explanation:
a triangular number n is the sum of all natural numbers <= n.
t1 = 1
t2 = 1+2 = 3
t3 = 1+2+3 = 6
t4 = 1+2+3+4 = 10
...
so,
tn = tn-1 + n
47.
1×8 + 1 = 9 is a square number.
3×8 + 1 = 25 is a square number
6×8 + 1 = 49 is a square number
10×8 + 1 = 81 is a square number
48.
1/3 = 0 remainder 1
3/3 = 1 remainder 0
6/3 = 2 remainder 0
10/3 = 3 remainder 1
15/3 = 5 remainder 0
21/3 = 7 remainder 0
28/3 = 9 remainder 1
so, there seems to be a pattern 1 0 0 1 0 0 1 0 0 1 ...
49.
1/4 = 0 remainder 1
4/4 = 1 remainder 0
9/4 = 2 remainder 1
16/4 = 4 remainder 0
25/4 = 6 remainder 1
36/4 = 9 remainder 0
49/4 = 12 remainder 1
so, there seems to be a pattern 1 0 1 0 1 0 1 0 1 0 1 ...
50.
polygonal numbers is the real name for this.
the formula for dimensions = 5 is
(3n² − n)/2
for dimensions = 6 it is
2n² - n
so, dimensions=5 (and therefore dividing also by 5) we get the remainders
1/5 = 0 remainder 1
5/5 = 1 remainder 0
12/5 = 2 remainder 2
22/5 = 4 remainder 2
35/5 = 7 remainder 0
51/5 = 10 remainder 1
70/5 = 14 remainder 0
92/5 = 18 remainder 2
117/5 = 23 remainder 2
145/5 = 29 remainder 0
here the pattern is 1 0 2 2 0 1 0 2 2 0 1 0 2 2 0 ...
dimensions=6 (and therefore dividing also by 6) we get the remainders
1/6 = 0 remainder 1
6/6 = 1 remainder 0
15/6 = 2 remainder 3
28/6 = 4 remainder 4
45/6 = 7 remainder 3
66/6 = 11 remainder 0
91/6 = 15 remainder 1
120/6 = 20 remainder 0
153/6 = 25 remainder 3
190/6 = 31 remainder 4
231/6 = 38 remainder 3
276/6 = 46 remainder 0
325/6 = 54 remainder 1
here the pattern is 1 0 3 4 3 0 1 0 3 4 3 0 1 0 3 4 3 0 ...
Answer:
1 / (x-2)(x+3)
Step-by-step explanation:
Given in the question the expression:
(x + 1) / (x² + x - 6) ÷ (x² + 5x + 4) / (x+4)
factorisation of (x² + x - 6) = (x-2)(x+3) by using quadratic equation
(x + 1) / (x-2)(x+3) ÷ (x² + 5x + 4) / (x+4)
Taking reciprocal to convert ÷ into ×
(x + 1) / (x-2)(x+3) x (x+4) / (x² + 5x + 4)
factorisation of (x² + 5x + 4) = (x+1)(x+4) by using quadratic equation
(x + 1) / (x-2)(x+3) x (x+4) / (x+1)(x+4)
cancel (x + 1) from both expression
1 / (x-2)(x+3) x (x+4) / (x+4)
cancel (x+4)
1 / (x-2)(x+3) Simplified form
