Question: What value of c will complete the square below (
) and make the expression a perfect square trinomial?
Answer: c = 225
Step-by-step explanation:
Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that <u>a = x, and b² = c</u>, but we need to find the numerical value of 
.
To do this, note that the middle term, or <u>2ab, corresponds with (is equal to) 30x</u>. We know that a = x, and thus, <u>2ab = 2bx</u>. Now, 2bx and 30x are corresponding terms; thus, <u>2bx = 30x</u>.
Dividing by 
on both sides gives us <u>b = 15</u>. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)
<h3><u>Solution</u><u> </u><u>:</u><u>-</u><u> </u></h3>
1) 4x + 5y
→ 4*6 + 5*1
→ 24 +5 = 29
2) 2x (20-y)
→ 2*6 (20-1)
→ 12 *19 = 228
3) x ÷ 3 + y
→ 6 ÷ 3 + 1
→ 2 +1 = 3
4) 4y ÷ 2 + (8x + 10)
→ 4*1 ÷ 2 +(8*6+10)
→ 2 + (48+10)
→ 2 + 58
→ 60
5 ) 5. Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts for her family, how much money does she have left?
Money made each weekend = $34
Money made in 3 weekend = $34*3 =$102
Money spent = $50
Therefore ,
→Money left = Money made in 3 weekends - Money spent
→ Money left = $102 - $50 = $52
6.Carlos solved 20-(2x6) + 8 divide 4 = 29. Is this the correct answer? ( In attachment it's written 29 and not 28 .)
Given equation is ,
→ 20 - (2 × 6) + 8 ÷ 4 = 29
Solve inside the brackets ,
→ 20 - 12 + 8 ÷ 4
Perform division ,
→ 20 -12 + 2
Perform addition ,
→ 22 - 12
Perform subtraction,
→ 10
<u>No , he is wrong the answer should have been 10 but he got 29 .</u>
<em>I </em><em>hope</em><em> this</em><em> helps</em><em> </em><em>.</em>
Answer:
Step-by-step explanation:
Here, we have to find the sum of 2 fractions:
1st fraction: 
2nd fraction: 
Considering the denominator of 1st fraction:
Using factorization method:
can be written as 
.
Taking <em>5 common</em> from 
and <em>y common</em> from 
:
Now taking 
common:
can be written as 
Now, calculating the sum:
Taking <em>LCM</em> and solving:
Hence, answer is .
Answer:
0, 5, 7, 11, ...
Step-by-step explanation:
1^2 = 1; 1 - 1 = 0; 0 is divisible by 6
5^2 = 25; 25 - 1 = 24; 24 is divisible by 6
7^2 = 49; 49 - 1 = 48; 48 is divisible by 6
11^2 = 121; 121 - 1 = 120; 120 is divisible by 6
