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Pani-rosa [81]
3 years ago
10

What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?

Mathematics
1 answer:
Annette [7]3 years ago
5 0
6x-2>4x-6
2x-2>-6
2x>-4
X>_ -2
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Easy geometry. help please
olchik [2.2K]

(x, y) --> (x + 5, y - 1)

A(3, -1) --> A'(3 + 5, -1 - 1) --> A'(8, -2)

B(6, 1) --> B'(6 + 5, 1 -1) --> B'(11, 0)

C(2, 4) --> C'(2 + 5, 4 - 1) --> C'(7, 3)

D(-1, 3) --> D'(-1 + 5, 3 - 1) --> D'(4, 2)

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Novosadov [1.4K]

84. Area of a triangle is (base x height) / 2

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Given that α and β are the roots of the quadratic equation <img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B6x-7%3Dp" id="Tex
siniylev [52]

Answer:

\large \boxed{\sf \ \ \ p=-11 \ \ \ }

Step-by-step explanation:

Hello,

\alpha \text{ and } \beta \text{ are the roots of the following equation}

   2x^2+6x-7=p

It means that

   2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\

And we know that

\alpha= 2\cdot \beta

So we got two equations

   2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\6\beta^2+6\beta =0\\\\\beta(\beta+1)=0\\\\ \beta =0 \ or \ \beta=-1

For \beta =0, \ \ \alpha =0, \ \ p = -7

For \beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11

I assume that we are after two different roots so the solution for p is p=-11

b) \alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1

So a quadratic equation with the expected roots  is

x(x-1)=x^2-x

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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3 years ago
Which is the best estimate for the area of the figure above?
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Answer:

So I'd say 20in^2 or 22in^2.

Step-by-step explanation:

I decided to make it into a full pentagon shape to just estimate.

So a pentagons sides are all equal so I counted the amount in boxes on the sides of the regular shape and most of them would be 3.5 if you changed the shape into a pentagon.

And I got:

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snow_tiger [21]

Isolate the variable by dividing each side by the factors that don't contain the variable

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