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2 years ago

Reduced form of 2ab^2-a^2 b^2/5

Mathematics

1 answer:

Ket [755]2 years ago

7 0

Answer:

$2ab^2-\frac{a^2b^2}{5}=\frac{10ab^2-a^2b^2}{5}$

Step-by-step explanation:

Given the expression

$2ab^2-\frac{a^2b^2}{5}$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:2ab^2=\frac{2ab^25}{5}$

$2ab^2-\frac{a^2b^2}{5}=\frac{2ab^2\cdot \:5}{5}-\frac{a^2b^2}{5}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{2ab^2\cdot \:5-a^2b^2}{5}$

$=\frac{10ab^2-a^2b^2}{5}$

Thus,

$2ab^2-\frac{a^2b^2}{5}=\frac{10ab^2-a^2b^2}{5}$

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3 years ago

Solve the equation. 2.2= z - 1.1 z=?

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Answer:

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Step-by-step explanation:

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Read 2 more answers

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

Quadrilateral EFGH with diagonals EG and HF must be a parallelogram if (1) EF FG  and GH HE  (2) EG FH  (3) EG FH  (4) EF HG

qwelly [4]

Answer:

EF = HG and EF || HG

Step-by-step explanation:

A quadrilateral is a polygon shape with four sides and four angles.

A parallelogram is a quadrilateral with two pairs of parallel sides. The following are properties of a parallelogram:

Opposite sides are equal and parallel.
Opposite angles are equal to each other.
Consecutive angles are supplementary
The diagonals of a parallelogram bisect each other.

If Quadrilateral EFGH with diagonals EG and HF is a parallelogram then EF = HG and EF || HG

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3 years ago