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3 years ago

Add or subtract the polynomials (8x3+3x-2)+(9x2-7+3x-2x3)

Mathematics

2 answers:

crimeas [40]3 years ago

4 0

Answer:

10x^3+9x^2-9

Step-by-step explanation:

8x^3+2x-2+9x^2-7+2x-2x^3 - Combine like terms

10x^3+9x^2-9

LekaFEV [45]3 years ago

3 0

Answer:

$\boxed{\boxed{\sf 6x^3+9x^2+6x-9}}$

Step-by-step explanation:

$\sf \left(8x^3+3x-2\right)+\left(9x^2-7+3x-2x^3\right)$

$\sf 8x^3+3x-2+9x^2-7+3x-2x^3$

Note: If there is a negative sign in front of parentheses, each term within the expression changes sign.

$\Longrightarrow \sf 8x^3+3x-2+9x^2-7+3x-2x^3$

Now, we need to organize expression into groups like terms:

$\Longrightarrow \sf (8x^3, -2x^3)\: (3x, 3x)\:(-2,-7)$

$\longmapsto\sf 8x^3-2x^3=6x^3$

$\longmapsto\sf 3x+3x=6x$

$\longmapsto\sf -2-7=-9$

$\boxed{\sf 6x^3+9x^2+6x-9}$

_____________________________

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Y=-x^2+6x-4 Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

Inessa [10]

Answer:

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

x-intercepts:

$(3-\sqrt{5},0) \\\\(3+\sqrt{5},0)$

y-intercept: (0, -4)

Explanation:

1. Equation:

$y=-x^2+6x-4$

2. Axis of symmetry:

That is the equation of a parabola, whose standard form is:

$y=ax^2+bx+c$

Where:

$a=-1;b=6;c=-4$

The axis of symmetry is the vertical line with equation:

$x=-b/2a$

Substitute $a=-1,\text{ and }b=6$

$x=-6/[(2)(-1)]=-6/(-2)=3$

Thus, the axis of symmetry is:

$x=3$

3. Vertex

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

$y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5$

Therefore, the vertex is (3, 5)

4. Find the x-intercepts

The x-intercepts are the roots of the equation, which are the points wher y = 0.

$y=-x^2+6x-4=0$

Use the quadratic equation:

$x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}$

5. Find the y-intercept

The y-intercet is the value of y when x=0:

$y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4$

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Step-by-step explanation:

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Add these two expressions. (–45t + 53s) and (–3 – 75s + 2t) 65t + 415s – 3 –145t – 115s – 3 –115t + 113s – 3 115t – 415s + 2

serious [3.7K]

Answer:

- 43t - 22s - 3

Step-by-step explanation:

(–45t + 53s) + (–3 – 75s + 2t)

Opening the brackets

-45t + 53s -3 - 75s + 2t

Collecting like terms

-45t + 2t + 53s - 75s -3

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Semenov [28]

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