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3 years ago

Use the grouping method to factor the polynomial below completely. 3x^3 + 9x^2 + 4x + 12

Mathematics

1 answer:

Alex3 years ago

4 0

Answer:

$(x+3)(3x^{2}+4)$

Step-by-step explanation:

$3x^{3}+9x^{2}+4x+12\\3x^{2}(x+3)+4(x+3)\\(x+3)(3x^{2}+4)$

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Find the sum of natural number from 1 to 30

Ierofanga [76]

Answer:

1. sum of term = 465

2. nth term of the AP = 30n - 10

Step-by-step explanation:

1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore

sum of term = n/2(a + l)

where

a = 1

l = last term = 30

n = number of term

sum of term = 30/2(1 + 30)

sum of term = 15(31)

sum of term = 465

2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......

The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;

a = 20

d = 30

nth term of an AP = a + (n - 1)d

nth term of an AP = 20 + (n - 1)30

nth term of an AP = 20 + 30n - 30

nth term of the AP = 30n - 10

The nth term formula can be used to find the next term progressively. where n = number of term

The sequence will be 20, 50, 80, 110, 140, 170, 200..............

6 0

3 years ago

To find the Volume of a Cylinder, we use the formula:

kolezko [41]

Answer:

the correct anser is B

Step-by-step explanation:

Calculate the area of the shape on all the corners

6 0

2 years ago

What is the value of x?

user100 [1]

Answer:

1/2

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable

7 0

2 years ago

Read 2 more answers

One operator is holding a laser pointer at a height of 9 feet whose beam is reflected on a horizontal reflecting surface at a po

lutik1710 [3]

Answer:

The height (in feet) at which the laser will impact the wall is 6.75 feet

Step-by-step explanation:

The given parameters are;

The height from which the laser beam operator is holding the laser = 9 feet

The horizontal distance away from the pointer the beam is reflected = 8 feet

Given that we have;

$f(x) = \dfrac{9}{8} \times \left | x - 8\right | = y$

When x = 8, the point of reflection, the height, f(x) is given as follows;

$f(x) = \dfrac{9}{8} \times \left | 8 - 8\right | = 0$

When x = 7, the point of reflection, the height, f(x) is given as follows;

$f(x) = \dfrac{9}{8} \times \left | 7 - 8\right | = \dfrac{9}{8}$

Therefore, given that the point of reflection is at an elevation of 0 relative to the 9 feet of the laser source (pointer), by tan rule, we have;

$tan(\theta) = \dfrac{Opposite \ side}{Adjacent \ side} =\dfrac{9}{8} = \dfrac{h}{7}$

Where;

h = The height at which the laser meets the wall

$h = \dfrac{9 \times 7}{8} =7.875$

Given that the wall the laser meets is at the point x with elevation 9/8, the height, y, at which the laser meets the wall is therefore;

$y = \dfrac{9 \times 7}{8} - \dfrac{9}{8} = \dfrac{54}{8} = 6.75 \ feet$

The height (in feet) at which the laser will impact the wall = 6.75 feet.

7 0

3 years ago

What number is in the tenth's place? 41.53

zysi [14]

Answer: The number in the tenth's place is <u>5</u>

Step-by-step explanation:

There is no ones place in decimals

41.<u>5</u>3

the tenth's place come first then the hundredth's and so on.

6 0

1 year ago

Read 2 more answers