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4 years ago

What is the prime factorization of 54

Mathematics

1 answer:

nadya68 [22]4 years ago

8 0

The prime factorization is 3.

Steps:

1. Break 54 into 2 parts, I broke them into 2 and 27.

2. Since 2 is prime, leave it as is and break 27 into 2. I got 3 and 9.

3. 3 is prime so leave it alone. Break 9 into 3 and get 3 and 3. Your prime factor is 3.

Now, you need the prime factorization, which, if I remember correctly, is the prime factors that you left and did not break apart. List these in order from least to greatest. Your prime factorization should end up looking like this:

2 x 3 x 3 = 54

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What is the value of the fourth term in a geometric sequence for which a1=30 and r=1/2

lisov135 [29]

Answer:

a(4) = 15/4

Step-by-step explanation:

The general formula for a geometric series with common ratio r and first term a(1) is

a(n) = a(1)*r^(n - 1)

and so, if a(1) = 30 and r = 1/2, we have

a(n) = 30*(1/2)^(n - 1)

and the fourth term is then:

a(4) = 30*(1/2)^(4 - 1) = 30/8 = 15/4

8 0

3 years ago

Write a rule for g described by the transformation of the graph of f...

Svetlanka [38]

Answer:

$g(x) = 4-4\sqrt{x}$

Step-by-step explanation:

Given

$f(x) = 4\sqrt{x}+1$

1. 5 units down translation

2. Reflection in the x-axis

Required

Determine the resulting function g

1. 5 units down translation

This is defined by the rule:

A down translation is:

$f'(x) = f(x) - b$

Where b is the number of units.

So, we have:

$f'(x) = 4\sqrt{x} + 1 - 5$

$f'(x) = 4\sqrt{x} -4$

2. Reflection in the x-axis

For a function f(x),

When reflected over the x-axis, it becomes -f(x)

So:

$g(x) = -f(x)$

$g(x) = -(4\sqrt{x} - 4)$

$g(x) = -4\sqrt{x} +4$

$g(x) = 4-4\sqrt{x}$

4 0

3 years ago

(x+3)/(x-2)=5. ........

DochEvi [55]

Times both sides by (x-2)
x+3=5(x-2)
x+3=5x-10
minus x both sides
3=4x-10
add 10 both sides
13=4x
divide by 4
13/4=x

5 0

3 years ago

Which of the following fractions is an improper fraction?<br> 2/3<br> 6/11<br> 21/25<br> 8/7

kirza4 [7]

Answer:

8/7

Step-by-step explanation:

The Numerator is bigger than the denominator which in turn can be converted to a mixed fraction.

3 0

3 years ago

Please help me with vivid explanation

Ivanshal [37]

Answer:

864 m²

Step-by-step explanation:

First calculate the total area of the rectangular field

The area of a rectangle is given by the product of the length and the width

let A be the total area

A = 100*120

A = 12000 m²

Calculate the area of the small rectangles

Let A' be the total area of the four small rectangles and A" the area of one small rectangle

A' = 4 A"
A' = 4 [( $\frac{120-4}{2}$ )*( $\frac{100-4}{2}$ )]
A' = 4*58*48
A' = 11136 m²

Substract the A' from A to get the area of the road

Let A"' be the area of the road

A"' =A-A'

A"' = 12000-11136

A"' = 864 m²

3 0

3 years ago