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vagabundo [1.1K]

4 years ago

12

A number is written with the following factorization 2x2x2x4x5. Is this factorization is prime factorization? Explain why or why

not. If it is not correct, give the prime factorization of the number.

1 answer:

Ulleksa [173]4 years ago

3 0

The number 2*2*2*4*5 is not in its prime factorization because not all the factors are prime numbers. A prime number is a number that has no other factors except for 1 and itself.
4 is not a prime number, since it can be divided by 2. The number can be broken down into its prime factors by dividing by 2, and it becomes 2*2.

Therefore, the factorization of the number 2*2*2*4*5 can be broken down to 2*2*2*2*2*5.

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When completing the square on the equation c2 + 110 = 12, the resulting solution is:<br> It

Delvig [45]

Answer:

$c=1$ and $c=-12$

Step-by-step explanation:

The correct equation is:

$c^2+11c=12$

To solve by completing the square method.

Solution:

We have:

$c^2+11c=12$

In order to solve by completing the square method we will carry out the following operations to the given equation to get a perfect square binomial.

We can write as:

$c^2+2.\frac{11}{2}c=12$

$c^2+2.\frac{11}{2}c+(\frac{11}{2})^2-(\frac{11}{2})^2=12$

$(c+\frac{11}{2})^2-(\frac{11}{2})^2=12$ [As $c^2+2.\frac{11}{2}c+(\frac{11}{2})^2=(c+\frac{11}{2})^2$ ]

Adding both sides by $(\frac{11}{2})^2$

$(c+\frac{11}{2})^2-(\frac{11}{2})^2+(\frac{11}{2})^2=12+(\frac{11}{2})^2$

$(c+\frac{11}{2})^2=12+\frac{121}{4}$

Taking LCD to add fraction.

$(c+\frac{11}{2})^2=\frac{48}{4}+\frac{121}{4}$

$(c+\frac{11}{2})^2=\frac{169}{4}$

Taking square root both sides.

$\sqrt{(c+\frac{11}{2})^2}=\sqrt{\frac{169}{4}}$

$c+\frac{11}{2}=\pm\frac{13}{2}$

Subtracting both sides by $\frac{11}{2}$ :

$c+\frac{11}{2}-\frac{11}{2}=\pm\frac{13}{2}-\frac{11}{2}$

$c=\pm\frac{13}{2}-\frac{11}{2}$

So, we have:

$c=\frac{13}{2}-\frac{11}{2}$ and $c=-\frac{13}{2}-\frac{11}{2}$

$c=\frac{2}{2}$ and $c=\frac{-24}{2}$

$c=1$ and $c=-12$ (Answer)

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4 years ago

You decide finance a $12,000 car at 3% compounded monthly for 4 years. What will your monthly payments be? How much interest wil

dexar [7]

Answer:

Step-by-step explanation:

The cost of the car is $12,000

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the cost of the car

r represents the interest rate

n represents number of monthly payments. Therefore

a = 12000

r = 3%/12 = 0.03/12 = 0.0025

n = 12 × 4 = 48

Therefore,

P = 12000/[{(1+0.0025)^48]-1}/{0.0025(1+0.0025)^48}]

12000/[{(1.0025)^48]-1}/{0.0025(1.0025)^48}]

P = 12000/{1.127 -1}/[0.0025(1.127)]

P = 12000/(0.127/0.0028175)

P = 12000/45.075

P = $266.22

The monthly payment is $266.22

The total amount that would be paid over the life of the loan is

266.22 × 48 = $12778.56

The amount of interest paid is

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3 years ago

Diana is buying plates and cups for a party. She wants the same number of each. Plates are sold in packs of eight and cups are s

Citrus2011 [14]

Answer:

What is the least number of plates and cups she can buy?

The least number of cups of plates and cups she can buy is 24

How many packs of plates?

3 packs of plates

How many packs of cups?

2 packs of cups

Step-by-step explanation:

What is the least number of plates and cups she can buy?

We solve this using the Lowest Common Multiple method

The L.C.M of 8 and 12

Multiples of 8: 8, 16, 24, 32, 40

Multiples of 12: 12, 24, 36, 48

Therefore,

LCM(8, 12) = 24

Hence, the least number of cups and plates she can buy is 24

How many packs of plates?

Plates are sold in packs of eight

Hence: 24 ÷ 8 = 3 packs of plates

How many packs of cups?

Cups are sold in packs of 12

Hence: 24 ÷ 12 = 2 packs of cups

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3 years ago

Interest earned: $40, Principal: $400, Time: 2 years. Find the rate.

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Answer:

840

Step-by-step explanation:

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3 years ago

Read 2 more answers

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andrezito [222]

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3 years ago