Learn Mathematics Solutions

Introduction to learn mathematics solutions:

In mathematics solutions, we can learn many topics like algebra, differential calculus, trigonometry, geometry, etc. Here we can see mathematics functions and mathematics equation in algebra.Mathematics functions are help to learn one or more degree polynomial function with one or more variables. The example to learn mathematics function is, f(x) = 5x + 11, `f(x) = x^2 + 8x - 5`

Mathematics equations are help to learn one or two variables with one or more order values. The example to learn mathematics equation is y = 15x + 5. `y = 5x^2 + 8x - 2`


Examples to learn mathematics equation solutions:


Learn solutions for mathematics equations example problem 1:

Learn the factors for the given mathematics equations,` x^2 - 5x + 4 = y`

Solutions:

Plug y = 0, to find the factor for the given mathematics equation.

We can separate the equation as sum and product of roots,

This is in the form of

`x^2` + (Sum of the roots) x + (Product of the roots) = 0

By comparing the given equation we can get,

Sum of the roots = -5

Product of the roots = 4

The possible number of outcome for product of the roots is `(-4)xx (-1) and (4)xx(1)`

By comparing the product of root value, we can obtain the sum of the roots,

To obtain the value for sum of the roots -5, consider (-4) + (-1)

Now substitute this sum of roots values in the equation, we get

`x^2 - 4x - x + 4 = 0`

Now, bring out x as common in the first two terms and -1 as common in the next two terms

x(x - 4) - 1 (x - 4) = 0

(x - 4) (x- 1) = 0

Thus, the factors for the given mathematics equation is (x - 4) (x - 1)

Learn solutions for mathematics equations example problem 2:

Learn the given mathematics equation by reducing the given expression, 3(5y + 8) = 8 – 5x.

Solutions:

Step 1: Given expression,

3(5y + 8) = 8 - 5x

Step 2: By the use of distribute property

15y + 24 = 8 - 5x

Step 3: Add -24 on either side,

15y + 24 – 24 = 8 - 5x - 24

15y = -16 – 5x

Step 4: Divide by 15 on either side

` (15y) / (15) = (-16)/ (15) - (5x)/ (15)`

Step 5: By simplifying, the expression we get,

` y = (-16)/ (15) - (x)/ (3).`

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Examples to learn mathematics functions solutions:


Learn solutions for mathematics functions example problem 1:

By reducing the expression 8x - 5 = 8y - 12. Find the mathematics function.

Solutions:

Step 1: Given expression

8x - 5 = 8y - 12

Step 2: Add 12 on either side, we get

8x - 5 + 12 = 8y - 12 + 12

8x + 7 = 8y

Step 3: Divide by 8 on either side, we get

`(8x) /8 + 7/8 = (8y) /8`

Step 4: By simplifying the above expression, we get

` x + 7/8 = y`

Step 5: Replace y = f(x), we get

`x + 7/8 = f(x)`

Thus, we obtain the mathematics function is `f(x) = x + 7/8.`