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3 years ago

What multiplies to 6 but adds to 17

Mathematics

2 answers:

MAVERICK [17]3 years ago

5 0

The answer is -4 and 21

I am glad to help!

vladimir1956 [14]3 years ago

5 0

You can write this line as the system:

x + y = 17
xy = 6

To solve it, you first need to get the proper value of either x or y. In this case i choose to get the value of x:

x + y = 17
x = 17-y

With this, i an input the value into the second line:

(17-y)y = 6

17y-y^2=6

-y^2+17y-6=0
can be solved with the quadratic formula.

y = (-17 +/- sqrt(-17^2 - 4*-1*-6))/2*-1
y = (-17 +/- sqrt(289 - 24)/-2
The square root is 16.28
y = (-17 +/- 16,28)/-2
y_1 = (-17 + 16.28)/-2 = 0,36
y_2 = (-17 - 16.28)/-2 = 16,64

To skip the work ahead of us, x_1 and x_2 will end up with the exact same numbers, as we could multiply both ways.

The numbers are ca. 0,36 and 16,64

0,36+16,64 = 17

0,36*16,64 = 5,999997 = ca. 6

Sorry for the small amount of rounding, but i hope this works.

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Heyo !!

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<h2>A. What are the 7 numbers in the term of n?</h2>

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EXPLANATION :

Because when you have 3 consecutive numbers, you have to put 7 numbers in the term of the n.

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What composition forms the equation p(x) when given the functions for h(x), f(x), k(x), and g(x)? PLEASE HELP!!!!! thank you!!!!

Flura [38]

Answer: Choice B. k(h(g(f(x))))

For choice B, the functions are k, h, g, f going from left to right.

===========================================================

Explanation:

We have 4x involved, so we'll need f(x)

This 4x term is inside a cubic, so we'll need g(x) as well.

So far we have

g(x) = x^3

g( f(x) ) = ( f(x) )^3

g( f(x) ) = ( 4x )^3

Then note how we are dividing that result by 2. That's the same as applying the h(x) function

$h(x) = \frac{x}{2}\\\\h(g(f(x))) = \frac{g(f(x))}{2}\\\\h(g(f(x))) = \frac{(4x)^3}{2}\\\\$

And finally, we subtract 1 from this, but that's the same as using k(x)

$k(x) = x-1\\\\k(h(g(f(x)))) = h(g(f(x)))-1\\\\k(h(g(f(x)))) = \frac{(4x)^3}{2}-1\\\\$

This leads to the answer choice B.

To be honest, this notation is a mess considering how many function compositions are going on. It's very easy to get lost. I recommend carefully stepping through the problem and building it up in the way I've done above, or in a similar fashion. The idea is to start from the inside and work your way out. Keep in mind that PEMDAS plays a role.

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