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lesya692 [45]
3 years ago
9

For what values of x is the area of the rectangle greater than the perimeter?

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
4 0
Area = 7(x + 2) = 7x + 14
Perimeter = 2(7 + x + 2) = 2(9 + x) = 18 + 2x
7x + 14 > 18 + 2x
7x - 2x > 18 - 14
5x > 4
x > 4/5
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Find the vertex of the parabola.<br> F(x) = 5x^2 - 30x +49
Juli2301 [7.4K]

X=-b/2a is the formula for finding the axis of symmetry
So x= -30/2(5)
X=-30/10
X=-3

Because the axis of symmetry is -3, we know where to place our line, and we also know that the parabola is open downwards, which means that the vertex will be maximum. To find the vertex, plug in your values with the axis of symmetry as a midway point. Plug that in for x and so you should have the following:
F(x)
Y(f(x) and y variables are interchangeable) =5(-3)^2-30(-3)+49

Solve for y(f(x))
5(-3)^2-30(-3)+49
(-3)^2=3^2
3^2*5+30*3+49
Multiply
3^2*5+90+49
Add numbers
3^2*5+139
9*5=45
45+139=184
Y=184

So, your vertex would be
(-3,184) and it would be maximum. From there you can plug in the rest of your table of values.
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3 years ago
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Answer:

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Simplify the expression below. Then classify the resulting expression
evablogger [386]

Answer:

Simplified = 5

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Step-by-step explanation:

<h2>PART I: Simplify the expression</h2>

<u>Given expression:</u>

 3x² + 6x + 5 - 3x (2 + x)

<u>Expand parenthesis by distributive property:</u>

= 3x² + 6x + 5 - 3x (2) - 3x (x)

= 3x² +6x + 5 - 6x - 3x²

<u>Put like terms together:</u>

= 3x² - 3x² + 6x - 6x + 5

= 0 + 0 + 5

= \boxed{5}

<h2>PART II: Classify polynomial</h2>

<u>Concept:</u>

Polynomial is classified by the number of terms a polynomial has.

  • Monomial: a polynomial with only one term
  • Binomial: a polynomial with two terms
  • ...

<u>Classify the given expression:</u>

Original = 3x² + 6x + 5 - 3x (2 + x)

Simplified = 5

5 is a constant and it has only one term

Therefore, it is a <u>monomial</u>.

Hope this helps!! :)

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