<span>A rectangle has a length the area of the rectangle is 180(2w-9=180).Find the length and the width of the rectangle. Find the perimeter of the rectangle</span>
Answer:
x=7
Step-by-step explanation:
9x -5 = 58 since they are vertical angles and vertical angles are equal
9x-5 = 58
Add 5 to each side
9x-5+5 = 58+5
9x = 63
Divide each side by 9
9x/9 = 63/9
x=7
<span>The correct answer is n</span>²<span>+3.
Explanation<span>:
We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.
Since these are different, this is not linear.
We now find the second differences:
5-3=2; 7-5=2; 9-7=2.
Since these are the same, this sequence is quadratic.
We use (1/2a)n</span></span>²<span><span>, where a is the second difference:
(1/2*2)n</span></span>²<span><span>=1n</span></span>²<span><span>.
We now use the term number of each term for n:
4 is the 1st term; 1*1</span></span>²<span><span>=1.
7 is the 2nd term; 1*2</span></span>²<span><span>=4.
12 is the 3rd term; 1*3</span></span>²<span><span>=9.
19 is the 4th term; 1*4</span></span>²<span><span>=16.
28 is the 5th term: 1*5</span></span>²<span><span>=25.
Now we find the difference between the actual terms of the sequence and the numbers we just found:
4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.
Since this is constant, the sequence is in the form (1/2a)n</span></span>²<span><span>+d;
in our case, 1n</span></span>²<span><span>+d, and since d=3, 1n</span></span>²<span><span>+3.</span></span>
