Answer:
square root of 25 <square root of 51 <square root of 81
5 <7.14 <9
Answer:
y = 3(x + 15)^2 - 625
Step-by-step explanation:
y = 3x^2 + 90x + 50
To complete the square, the coefficient of the x^2 term must be 1. We have 3x^2, so we factor out a 3 from the first two terms.
y = (3x^2 + 90x) + 50
y = 3(x^2 + 30x) + 50
To complete the square, square half of the coefficient of the x term. The x term is 30x. Half of 30 is 15. 15 squared is 225.
Since you are adding 225 inside the parentheses, and the quantity in parentheses is being multiplied by 3, you have really added 3 * 225 = 675 to the polynomial, so you must subtract 675 from the polynomial to keep it equal.
y = 3(x^2 + 30x + 225) + 50 - 675
Now we change the trinomial which is perfect square into the square of a binomial.
y = 3(x + 15)^2 - 625
Answer:
8 and 3
Step-by-step explanation:
8+3=11
8-3= 5
We know that b
<span>⩾ 1, so b is never 0.
a)
notice, the first figure starts off with 4 tiles and has 10 bordering tiles.
the second figure starts off with 14 tiles and has 14 bordering tiles
the third figure has starts off with 28 tiles and has 20 bordering tiles.
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![\bf \stackrel{\textit{first row, b = 1}}{4(1-1)+10}\implies \stackrel{\textit{border tiles}}{4(0)+10\implies 10} \\\\\\ \stackrel{\textit{second row, b = 2}}{4(2-1)+10}\implies \stackrel{\textit{border tiles}}{4(1)+10\implies 14} \\\\\\ \stackrel{\textit{third row, b = 3}}{4(3-1)+10}\implies \stackrel{\textit{border tiles}}{4(2)+10\implies 18}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bfirst%20row%2C%20b%20%3D%201%7D%7D%7B4%281-1%29%2B10%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bborder%20tiles%7D%7D%7B4%280%29%2B10%5Cimplies%2010%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7B%5Ctextit%7Bsecond%20row%2C%20b%20%3D%202%7D%7D%7B4%282-1%29%2B10%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bborder%20tiles%7D%7D%7B4%281%29%2B10%5Cimplies%2014%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7B%5Ctextit%7Bthird%20row%2C%20b%20%3D%203%7D%7D%7B4%283-1%29%2B10%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bborder%20tiles%7D%7D%7B4%282%29%2B10%5Cimplies%2018%7D)
<span>
b)
She's correct, check a).
</span>
![\bf \stackrel{\stackrel{starting~tiles}{\downarrow }}{4}(\stackrel{\stackrel{row~number}{\downarrow }}{b}-1)+10~~=~~\textit{number of tiles per border}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Cstackrel%7Bstarting~tiles%7D%7B%5Cdownarrow%20%7D%7D%7B4%7D%28%5Cstackrel%7B%5Cstackrel%7Brow~number%7D%7B%5Cdownarrow%20%7D%7D%7Bb%7D-1%29%2B10~~%3D~~%5Ctextit%7Bnumber%20of%20tiles%20per%20border%7D)
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c)
n(b - 1) + 10</span>