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Fynjy0 [20]
3 years ago
6

Choose any four consecutive even numbers. (For example: 6, 8, 10, 12). Multiply the two middle numbers together. (e.g. 8 x 10 =

80) Multiply the first and last numbers. (e.g. 6 x 12 = 72) Now subtract your second answer from the first. (e.g. 80 - 72 = 8) Try it with your own numbers. Why is the answer always 8?
Mathematics
1 answer:
Ludmilka [50]3 years ago
6 0

Answer:

Step-by-step explanation:

let the consecutive even numbers be  2n-2,2n,2n+2,2n+4 where n>0 and n is an integer.

2n(2n+2)-(2n-2)(2n+4)

=4n²+4n-(4n²+8n-4n-8)

=4n²+4n-4n²-8n+4n+8

=8

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The graph of f(x) = 2x^2 + 20x + 48 is shown
Free_Kalibri [48]

Answer:

a) The equation in intercept form by factoring is (x+6)(x+4)

b) From the given graph x- intercepts are (-4,0) and (-6,0) and zeros (roots) of the function are -6 and -4.

c) The solutions of  2x^2+20x+48=0 is (x+6)(x+4)=0 that is x= -6 and x = -4.

Step-by-step explanation:

The given quadratic  equation is f(x)=2x^2+20x+48

Put the function f(x) = 0 , then f(x)=2x^2+20x+48=0

a) The equation in intercept form by factoring is ,

Consider the given function,

f(x)=2x^2+20x+48=0

\Rightarrow 2x^2+20x+48=0

taking 2 common, we get,

\Rightarrow 2(x^2+10x+24)=0

\Rightarrow x^2+10x+24=0

The above is a quadratic equation of the form ax^2+bx+c=0

Solving quadratic equation using middle term splitting method,

\Rightarrow x^2+6x+4x+24=0

\Rightarrow x(x+6)+4(x+6)=0

\Rightarrow (x+6)(x+4)=0

Thus, The equation in intercept form by factoring is (x+6)(x+4).

b) From the given graph x- intercepts are (-4,0) and (-6,0) .

Zeroes / roots of a function are those points where the value of the function is zero.

Put f(x) = 0  as solved above

that is (x+6)(x+4)=0

\Rightarrow (x+6)=0 or \Rightarrow (x+4)=0

\Rightarrow x=-6 or \Rightarrow x=-4

Thus, zeros (roots) of the function are -6 and -4.

For checking put x = -6 and -4 in the function we get f(x) =0 .

c) The solutions of  2x^2+20x+48=0 is (x+6)(x+4)=0 that is x= -6 and x = -4 as shown above.


8 0
3 years ago
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