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4 years ago

Three times a number decreased by 9

Mathematics

2 answers:

DedPeter [7]4 years ago

7 0

Answer:

I do not know what you want, but the equation is 3x - 9

Step-by-step explanation:

Nady [450]4 years ago

7 0

Answer:

3a - 9

Step-by-step explanation:

Three times a number decreased by 9:

3a - 9

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Three is a zero of the equation x^3−4x^2−3x+18=0. Which factored form is equivalent to the equation?

Novosadov [1.4K]

Answer:

$x_1=-2,\ x_2=x_3=3\\ \\(x+2)(x-3)^2=0$

Step-by-step explanation:

Consider the equation

$x^3-4x^2-3x+18=0$

The zeros of the equation can be the divisors of 18:

$\pm 1,\ \pm2,\ \pm3,\ \pm 6,\ \pm 9,\ \pm 18$

Check them:

$1^3-4\cdot 1^2-3\cdot 1+18=1-4-3+18=10\neq 0\\ \\(-1)^3-4\cdot (-1)^2-3\cdot (-1)+18=-1-4+3+18=16\neq 0\\ \\2^3-4\cdot 2^2-3\cdot 2+18=8-16-6+18=4\neq 0\\ \\(-2)^3-4\cdot (-2)^2-3\cdot (-2)+18=-8-16+6+18=0$

So, x=-2 is zero. Now

$x^3-4x^2-3x+18\\ \\=x^3+2x^2-6x^2-12x+9x+18\\ \\=x^2(x+2)-6x(x+2)+9(x+2)\\ \\=(x+2)(x^2-6x+9)\\ \\=(x+2)(x-3)^2$

Thus, x=3 is the second root (of multiplicity 2)

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4 years ago

Write an expression that can be used to represent the number of miles Peter can travel in his car with the amount of gas left in

harkovskaia [24]

Answer:

$s = k \cdot \left(\frac{n}{100} \right) \cdot m_{max}$

Step-by-step explanation:

The number of miles is directly proportional to the amount of gas, then:

$s \propto m$

$s = k\cdot m$

Where the amount can be modelled as the product of the maximum amount of gas and the percentage of occupied capacity. Hence:

$s = k \cdot \left(\frac{n}{100} \right) \cdot m_{max}$

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