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Nostrana [21]
3 years ago
7

× + 20 + 2× = 10 - 2× - 15

Mathematics
1 answer:
OlgaM077 [116]3 years ago
6 0

Answer:

The answer is -5

Step-by-step explanation:

\mathrm{Group\:like\:terms}\\x+2x+20=10-2x-15

\mathrm{Add\:similar\:elements:}\:x+2x=3x\\3x+20=10-2x-15

\mathrm{Group\:like\:terms}\\3x+20=-2x+10-15

\mathrm{Add/Subtract\:the\:numbers:}\:10-15=-5\\3x+20=-2x-5

\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}\\3x+20-20=-2x-5-20

\mathrm{Simplify}\\3x=-2x-25

\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\\3x+2x=-2x-25+2x

\mathrm{Simplify}\\5x=-25

\mathrm{Divide\:both\:sides\:by\:}5\\\frac{5x}{5}=\frac{-25}{5}

\mathrm{Simplify}\\x=-5

Hope this helps you greatly!

Have a great afternoon!

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Please help!! What is the solution to the quadratic inequality? 6x2≥10+11x
fredd [130]

Answer:

The solution of the inequation 6\cdot x^{2} \geq 10 + 11\cdot x is \left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right).

Step-by-step explanation:

First of all, let simplify and factorize the resulting polynomial:

6\cdot x^{2} \geq 10 + 11\cdot x

6\cdot x^{2}-11\cdot x -10 \geq 0

6\cdot \left(x^{2}-\frac{11}{6}\cdot x -\frac{10}{6} \right)\geq 0

Roots are found by Quadratic Formula:

r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}

r_{1} = \frac{5}{2} and r_{2} = -\frac{2}{3}

Then, the factorized form of the inequation is:

6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0

By Real Algebra, there are two condition that fulfill the inequation:

a) x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0

x \geq \frac{5}{2}\,\wedge\,x \geq-\frac{2}{3}

x \geq \frac{5}{2}

b) x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0

x \leq \frac{5}{2}\,\wedge\,x\leq-\frac{2}{3}

x\leq -\frac{2}{3}

The solution of the inequation 6\cdot x^{2} \geq 10 + 11\cdot x is \left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right).

3 0
3 years ago
The width of a rectangular prism is six times its length. The height is five times its length. If its length is m units, what is
I am Lyosha [343]

Answer:

30m^3 cubic units.

Step-by-step explanation:

Let m represent length of the rectangular prism.

We have been given that the width of a rectangular prism is six times its length, so width of the prism would be 6m.

We are also told that the height is five times its length, so height of the prism would be 5m.

We know that volume of rectangular prism is height times width times length.

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\text{Volume of rectangular prism}=m\cdot 6m\cdot 5m

\text{Volume of rectangular prism}=30m^3

Therefore, the volume of the given rectangular prism would be 30m^3 cubic units.

8 0
3 years ago
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