Mathematics, 19.07.2019 03:50 drago12

Three quadratic functions are being compared to determine which has the smallest y-intercept. the first quadratic function can be modeled by the equation a(x) = (x + 5)2 − 7. the second function, b(x), can be modeled by the values presented in the table. the third quadratic function, c(x), is graphed below. which quadratic function has the smallest y-intercept and what is this value? x b(x) −3 0 0 6 3 0 a(x) has the smallest y-intercept: −7. b(x) has the smallest y-intercept: −3. c(x) has the smallest y-intercept: −2. a(x) has the smallest y-intercept: −5.

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To find the smallest y-value, you substitute x=0 into each other the functions.

For function a(x), do a(0):
a(0) = (0+5)2-7 = 3

For function b(x), it gives you (0,6).

For function c(x), just look at where the line crosses the x-axis. It crosses it as -2, and there's a point at (0,-2).

So since -2 is the smallest, function c(x) has the smallest y-intercept: -2

Answer from: Quest

the simplified form is

$\frac{x^2(2x+3)}{2(4x-3)}$

step-by-step explanation:

we want to simplify the expression,

$\frac{\frac{6x+9}{15x^2} }{\frac{16x-12}{10x^4} }$

let us change the middle bar to a normal division sign to obtain,

$\frac{6x+9}{15x^2}\div\frac{16x-12}{10x^4}$

we multiply the first fraction by the reciprocal of the second fraction to obtain,

$\frac{6x+9}{15x^2}\times \frac{10x^4}{16x-12}$

we factor to obtain,

$\frac{3(2x+3)}{3\times5\times x^2}\times \frac{2\times5\times x^2\times x^2}{4(4x-3)}$

we cancel the common factors to get,

$\frac{(2x+3)}{1}\times \frac{ x^2}{2(4x-3)}$

we simplify to get,

$\frac{x^2(2x+3)}{2(4x-3)}$

the correct answer is b

Answer from: Quest

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

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