A number is tripled and is added to two, giving the same result as eight less the number doubled

2 answers:

8 0

2 + 3n = 2n - 8

subtract 2n from 2n and 3n

2 + n = -8

subtract 2 from 2 and -8

n = -10

n equals to -10 is the answer

Olenka [21]3 years ago

3 0

Answer: 8

8 x 3 = 24 - 8 = 16

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Find a quadratic model for the set of values: (-2, -20), (0, -4), (4,-20) Show your work

Usimov [2.4K]

A quadratic function:
$y=ax^2+bx+c$

First, take the point (0,-4) and plug the values (x,y) into the equation:
$-4=a \times 0^2+b \times 0 +c \\
-4=c$

So the equation is $y=ax^2+bx-4$ .

Now plug the values of the other two points into the equation and set up a system of equation:
$-20=a \times (-2)^2+b \times (-2)-4 \\
-20=a \times 4^2+b \times 4-4 \\ \\
-20+4=4a-2b \\
-20+4=16a+4b \\ \\
-16=4a-2b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \div 2 \\
-16=16a+4b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 4 \\ \\
-8=2a-b \\
\underline{-4=4a+b} \\
-12=6a \\
\frac{-12}{6}=a \\
a=-2 \\ \\
-8=2a-b \\
-8=2 \times (-2)-b \\
-8=-4-b \\
-8+4=-b \\
-4=-b \\
b=4$

The function is:
$\boxed{y=-2x^2+4x-4}$

5 0

3 years ago

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