Write an equation that defines m(x) as a trinomial where m(x)=(3x-1)(3-x)+4x^2+18

Mathematics

1 answer:

AlladinOne [14]3 years ago

5 0

Answer:

m(x) = x² + 10x + 15

Step-by-step explanation:

Rewrite m(x) = (3x-1)(3-x) + 4x² + 18 as a trinomial (three-term equation) by simplifying the equation. Expand the brackets by multiplying the binomials and collect like terms.

m(x) = (3x-1)(3-x) + 4x² + 18 Multiply brackets with terms FOIL (first, outside, inside, last)

m(x) = (9x - 3x² - 3 + x) + 4x² + 18 The brackets can be removed

m(x) = 9x - 3x² - 3 + x + 4x² + 18 See what terms have the same variables

m(x) = -3x² + 4x² + 9x + x + 18 - 3 Like terms are rearranged together

m(x) = x² + 10x + 15 Collected like terms

You might be interested in

A banner is hung for a party. The

rewona [7]

Answer:

8.5 feet

Explanation:

The function that can determine the distance from a point on the bottom edge of the banner to the floor is:

$f(x)=0.25x^2-x+9.5$

That function is a quadratic function which means that it is a parabola. Given that the coefficient of the quadratic term (0.25) is positive, the parabola open upwards, and the vertex is the lowest point of the parabola and it represents how high above the floor is the lowest point on the bottom edge of the banner.

So, you need to find the vertex of the parabola.

I will complete squares to find the form A(x -h)² + k, where h and k are the coordinates of the vertex (h, k).

$f(x)=0.25x^2-x+9.5\\ \\ 4(f(x))=4(0.25x^2-x+9.5)\\ \\ 4f(x)=x^2-4x+38\\ \\ 4f(x)-38=x^2-4x\\ \\ 4f(x)-38+4=x^2-4x+4\\ \\ 4f(x)-34=(x-2)^2\\ \\ 4f(x)=(x-2)^2+34\\ \\ f(x)=(1/4)(x-2)^2+8.5$

Hence, the vertex (h,k) is (2, 8.5), meaning that the lowest point on the bottom edge of the banner is at 2 feet from the left edge of the banner and 8.5 feet above the floor.

3 0

3 years ago

Solve these liner inequalities 2(x+1)>3(x-8)

raketka [301]

The answer for that problem is X<26

4 0

3 years ago

Which is bigger .72 or .725?

aleksley [76]

.72
.725 would be less because it has more behind the decimal.
.72 would be more because there are only 2 numbers behind the decimal

3 0

3 years ago