24 is what percent of 56

Mathematics

1 answer:

zhuklara [117]4 years ago

8 0

24 divided by 56 will give you the answer.

= 0.42

Answer : 42%

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3 years ago

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Write the equation of a circle M(7, -10) and radius 2

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(x -7)^2 + (y+10)^2 = 4

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enyata [817]

9514 1404 393

Explanation:

1) 2x^2 -5x -3 = 0 . . . . standard form equation

To convert this to factored form, you can look for factors of the product (2)(-3) that have a sum of -5. It can help to start by listing the ways that -6 can be factored. Since we want the sum of factors to be negative, we want to have larger negative factors.

-6 = (1)(-6) = (2)(-3)

The sums of these factor pairs are -5 (what we want) and -1 (not relevant). We can call these factors p=1 and q=-6.

If a = 2 is the leading coefficient of our standard form quadratic, we want to use these factors in the form ...

(ax +p)(ax +q)/a . . . . . factored form of the quadratic

(2x +1)(2x +(-6))/2 . . . .fill in the values we know

(2x +1)(x -3) . . . . . . . factor 2 from the second binomial

So, the factored form of the quadratic equation is ...

(2x +1)(x -3) = 0 . . . . factored form equation

2) f(x) = x^2 +7x +10 . . . . standard form quadratic function

Using the thinking process described above, we are looking for factors of 10 that have a sum of 7. We know those are 2 and 5. So, the factored form of the function is ...

f(x) = (x +2)(x +5) . . . . . . factored form quadratic function

The leading coefficient is 1, so we have no further work to do.

Roots, x-intercepts, zeros

The graph attached below shows this function crosses the x-axis when x=-2 and x = -5. These values of x are variously called "roots", "x-intercepts", and "zeros" of the function. They are values for which the factors and the function are zero. (x+2=0 when x=-2, for example)

Solutions

Often, we are interested in solving the equation ...

f(x) = 0

For that equation, the solutions are the zeros or x-intercepts or roots. The graph attached also shows solutions for ...

f(x) = 4

Those solutions are x = -6 and x = -1. The function value is not zero for these values of x, so the roots, x-intercepts, or zeros are not solutions to this equation.