We solve the equation, ( a + a + 1 )^2 = 112 + a^2 + ( a + 1 )^2;
Then, ( 2a + 1 )^2 = 112 + a^2 + a^2 + 2a +1;
4a^2 + 4a + 1 = 113 + 2a^2 + 2a;
Finally, 2a^2 + 2a - 112 = 0;
a^2 + a - 56 = 0;
We use <span>Quadratic Formula for this Quadratic Equation;
The solutions are a1 = 7 and a2 = -8;
But a is a natural number; so, a = 7;
The natural consecutive numbers are 7 and 8.</span>
Answer:
22
Step-by-step explanation:
Generate the terms of sequence T using the nth term formula n² - 3
a₁ = 1² - 3 = 1 - 3 = - 2
a₂ = 2² - 3 = 4 - 3 = 1
a₃ = 3² - 3 = 9 - 3 = 6
a₄ = 4² - 3 = 16 - 3 = 13
a₅ = 5² - 3 = 25 - 3 = 22
22 is common to sequence S and T
Yes,this is a doozy.
<u>-3 (y - 5) = 15</u>
Eliminate the parentheses on the left side:
-3(y) -3(-5) = 15
-3y + 15 = 15
Subtract 15 from each side:
-3y = 0
Divide each side by -3 :
<em> y = 0</em>
Answer:
1723
Step-by-step explanation:
Ones place, tens place, hundreds place, thousands place
<h3>
Answer:</h3>
(2x + 1)(x + 3)
<h3>
Step-by-step explanation:</h3>
It is probably easier to try the answer choices than to try to factor the expression yourself.
(2x + 2)(x + 1) = 2x² +4x +2
(2x + 3)(x + 1) = 2x² +5x +3
(2x + 1)(x + 3) = 2x² +7x +3 . . . . . correct choice
_____
<em>Constructed solution</em>
If you want to factor this yourself, you can look for factors of "ac" that add to give "b". That is, you want factors of 2·3 = 6 that add up to give 7. You don't have to look very far.
... 6 = 1·6 = 2·3 . . . . . . the first factor pair adds to give 7
Now, rewrite the x term using the sum of these numbers.
... 2x² +(1 +6)x +3
... 2x +x +6x +3 . . . . eliminate parentheses
... (2x +x) +(6x +3) . . . . group pairs of terms
... x(2x +1) +3(2x +1) . . . . factor each pair
... (x +3)(2x +1) . . . . . . matches the last selection
