MATHEMATICS MIDDLE SCHOOL

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

Answers

Answer 1

Answer:

Answer:

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

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:

$1^3-4\cdot 1^2-3\cdot 1+18=1-4-3+18=10\neq 0\n \n(-1)^3-4\cdot (-1)^2-3\cdot (-1)+18=-1-4+3+18=16\neq 0\n \n2^3-4\cdot 2^2-3\cdot 2+18=8-16-6+18=4\neq 0\n \n(-2)^3-4\cdot (-2)^2-3\cdot (-2)+18=-8-16+6+18=0$

So, x=-2 is zero. Now

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

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

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Kate prepared 9 kilograms of dough after working 3 hours. How many hours did Kate work if she prepared 12 kilograms of dough? Assume the relationship is directly proportional.

Answers

Answer:

4 hours

Step-by-step explanation:

cross multiply

Martin has 15 texts messages on his phone .Two thirds of them are from his sister how many texts does martin have from his sister? I need three different ways to calculate this answer?

Answers

15/3=5. 5x2=10. 2/3=66.66%. 10%=1.5 5%=0.75 1%=0.15 0.66 rounds to 1 1.5x6=9. 9+0.76+1.5+1.5=10. 2:3=10:15.

Divide 15 by 3 and add that number to itself

Multiply 15 by (2/3) (don't forget parentheses if you are using a calculator)

Draw a pic and shade in two thirds

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|__________|__________|__________|

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|__________|__________|__________|

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|__________|__________|__________|

////=shade in

What is the difference between 9squere unit and 9 cubic units

Answers

9 square units is 9 to the scond power (9*2)while 9 cubic units is 9 cubed to third power (9*3)

What is 18/42 in it's simplest form?

Answers

$(18)/(42)=(3\cdot6)/(7\cdot6)=(3)/(7)$

Well, you can divide both numbers by 6.
18/6=3
42/6=7.
You have the simplest form in the simplest way!!
Your answer is 3/7.
Hope this helped!!

The trucking company also needs to deliver 1 2/3 tons of oak logs and 1 7/12 tons of maple logs. Which load weighs more?

Answers

the oak logs weigh more because 2/3= 8/12

Final answer:

To determine which load is heavier, oak logs weighing 1 2/3 tons or maple logs weighing 1 7/12 tons, we convert these to improper fractions and find that 44/12 tons (oak logs) is heavier than 19/12 tons (maple logs).

Explanation:

To determine which load weighs more, we must compare 1 2/3 tons of oak logs and 1 7/12 tons of maple logs. First, we need to convert these mixed numbers into improper fractions. For the oak logs, we multiply 3 (the whole number) by 3 (the denominator) and add 2 (the numerator), giving us 11/3 tons. For the maple logs, we multiply 1 by 12 (the denominator) and add 7 (the numerator), giving us 19/12 tons.

To compare, we convert these fractions so they have a common denominator:

11/3 tons is equal to 44/12 tons when multiplied by 4/4.

19/12 tons remains unchanged as it already has the common denominator of 12.

Now we compare 44/12 (oak logs) and 19/12 (maple logs). 44/12 tons is greater than 19/12 tons, so the load of oak logs weighs more than the load of maple logs.

Learn more about Comparing Weights here:

brainly.com/question/33449705

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Suppose that an insect population’s density, in thousands per acre, during year n, can be modeled by the recursive formula: a1 = 8 an = 2.9an – 1 – 0.2(an – 1)^2 Which of the following describes what is happening to the insect population for the first five years?