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3 years ago

Factor the trinomial below.

Mathematics

2 answers:

Ratling [72]3 years ago

8 0

The answer is A.

Explanation:

9x^2 + 12x + 4

= (3x)^2 + 2(3x)(2) + (2)^2

= (3x+2)(3x+2)

lbvjy [14]3 years ago

5 0

Answer:

A. (3x+2)(3x+2)

Step-by-step explanation:

The trinomial below is a quadratic which comes in the form of ax^2+bx+c

This is pretty self-explanatory when you factor a quadratic equation where a=1

However, in this case, a=9, b=12, and c=4

This is a special polynomial, but in case you can't recognize that, here's how you can factor it:

Now, there are many ways to solve this, I'm going to use a method known as Master Product.

First, we multiply a and c together.

ac=9*4=36

next, we find p and q so that ac = pq and p + q = b

Therefore we are trying to find 2 numbers that multiply to 36 and add to 12.

9 and 4 may be tempting, but it actually adds to 13.

The correct answer would be 6 and 6.

So p=6 and q=6

Next, we can use this to split our polynomial.

Rewrite it as ax^2+px+qx+c

Our new expression would then be

9x^2+6x+6x+4

Now, we just need to factor by grouping.

(9x^2+6x)+(6x+4)

Take GCF out

3x(3x+2)+2(3x+2)

You know this is factorable as the numbers within the parentheses is the same.

Hence you keep one as the numbers in the parentheses and use the numbers in front to get the other bracket.

So if it was ax(bx+c)+d(bx+c) it would become (ax+d)(bx+c)

Rewrite:

(3x+2)(3x+2)

This is a choice, so we can confidently choose A.

Hope that helps, let me know if you have any questions :)

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tatyana61 [14]

Answer:

10.5

Step-by-step explanation:

$KET\cong KIT...... (given)$

$\therefore KE \cong KI.... (csct)$

$\therefore m(KE) =m(KI)$

$\therefore 10x-34= 4x + 29$

$\therefore 10x-4x= 34 + 29$

$\therefore 6x= 63$

$\therefore x=\frac{63}{6}$

$\therefore x=10.5$

4 0

3 years ago

Joe is at the ice cream shop, and his house is 10 blocks north of the shop. The park is 10 blocks south of the ice cream shop. W

Furkat [3]

Answer:

The distance between the ice cream shop and Joe's house is the same as the distance between the ice cream shop and the park. So Joe is not closer to the park or his house, he is in the middle.

Step-by-step explanation:

We consider that the ice cream shop is the zero value in the number line. We assume that going north is positive (right side of the number line) and going south is negative (left side of the number line).

The house position is 10 block north of the ice cream shop, so it is represented by the integer 10.

The park is 10 blocks south of the ice cream shop, so it is represented by the integer -10.

The lower absolute value of the integer, the closer position from the ice cream shop.

If we calculate the absollute value of the House position:

|10|=10

Then, we calculate the the absollute value of the Parkposition

|-10|=10

In conclusion, the distance between the ice cream shop and Joe's house is the same as the distance between the ice cream shop and the park. Joe is in the middle.

5 0

3 years ago

q(x)= x 2 −6x+9 x 2 −8x+15 q, left parenthesis, x, right parenthesis, equals, start fraction, x, squared, minus, 8, x, plus, 1

AURORKA [14]

According to the theory of rational functions, there are no vertical asymptotes at the rational function evaluated at x = 3.

<h3>What is the behavior of a functions close to one its vertical asymptotes?</h3>

Herein we know that the rational function is q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15), there are vertical asymptotes for values of x such that the denominator becomes zero. First, we factor both numerator and denominator of the equation to see evitable and non-evitable discontinuities:

q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15)

q(x) = [(x - 3)²] / [(x - 3) · (x - 5)]

q(x) = (x - 3) / (x - 5)

There are one evitable discontinuity and one non-evitable discontinuity. According to the theory of rational functions, there are no vertical asymptotes at the rational function evaluated at x = 3.

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

8 0

1 year ago

Recall that for use of a normal distribution as an approximation to the binomial distribution, the conditions np greater than or

vagabundo [1.1K]

Answer:

The minimum sample size needed for use of the normal approximation is 50.

Step-by-step explanation:

Suitability of the normal distribution:

In a binomial distribution with parameters n and p, the normal approximation is suitable is:

np >= 5