You can do this.
A right rectangular prism is just a shoebox, or a cardboard box
that's all closed up, or even an ice cube.
Set any one of those things on the table, and then cut it parallel to
the table.
The shape of the cut is a rectangle.
Carets normally are used for an exponent so for example
2^3=8
Hope it helps feel free to ask question
Answer: 81
To get this answer, you do two things
1) Take half of the x coefficient 18 to get 9
2) Square the result from the previous step to get 9^2 = 9*9 = 81
This value is added on to get x^2+18x+81 which factors to (x+9)^2 confirming we have a perfect square trinomial
<h3>
Answer: Largest value is a = 9</h3>
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Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
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Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get 
So the greatest integer possible for 'a' is a = 9.
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Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
Answer:
x = 175/7
Step-by-step explanation:
Combining the like terms in 4x-14+3x=161, we get
7x = 175, and so:
x = 175/7