Factor Completely: x2 + 16(x + 4)(x - 4)
(x - 4)(x - 4)
(x + 4)(x + 4)
Prime

Answers

Answer 1

Answer: I think the correct answer from the choices listed above is the last option.The expression x^2 + 16 is a prime expression which cannot be further simplified over the real numbers. But when considering the complex numbers, the factor would be:

(x + 4i)(x - 4i)

Answer 2

Answer:

We have (x + 4i)(x - 4i) as the fullyfactored form of x² + 16.

To factor completely the expression x² + 16, we can use the fact that the sum of squares, in this case, x² + 16, cannot be factored further using real numbers.

However, it can be factored using complex numbers.

The expression x² + 16 represents a quadratic trinomial with no real roots. Instead, it can be factored using complex numbers and the imaginary unit, denoted by 'i.'

The square root of -1 is represented by 'i,' and we can use this concept to factor the expression.

The factorization of x² + 16 can be done as follows:

x² + 16 = (x + 4i)(x - 4i)

Here, we have used the difference of squares formula, which states that a² - b² can be factored as (a + b)(a - b).

In this case, a = x and b = 4i.

It's important to note that the factors (x + 4i) and (x - 4i) cannot be further simplified using real numbers, as 'i' represents an imaginary number.

Therefore, we have (x + 4i)(x - 4i) as the fullyfactored form of x² + 16.

Learn more about complex numbers click;

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Mofor had $21 to spend on two notebooks. After buying them he had $13. How much did each notebook cost?

Answers

His total cost was 8 dollars, so you divide that by two.

8/2 = 4

So, each notebook was $4.00.

Answer and explanation please

Answers

Answer:

$\sf log 162 = p + 4q$

Step-by-step explanation:

Given:

p = log 2
q = log 3

To find :

log 162 in terms of p and q.

Solution:

In order to find the logarithm of 162 in terms of p and q, we can use the properties of logarithms.

We can start by expressing 162 as a product of prime factors:

$\sf 162 = 2 * 3 * 3 * 3 * 3$

Now, we can use the properties of logarithms to simplify this expression:

$\sf log 162 = log (2 * 3 * 3 * 3 * 3)$

Since log(ab) = log(a) + log(b), we can split this into separate logarithms:

$\sf log 162 = log 2 + log (3 * 3 * 3 * 3)$

Now, we can use the fact that q = log 3:

$\sf log 162 = log 2 + log (3^4)$

Using the property $\sf \boxed{\sf log(a^b) = b * log(a)}$ , we get:

$\sf log 162 = log 2 + 4 log 3$

Now, substitute the values of p and q:

$\sf log 162 = p + 4q$

So, the logarithm of 162 in termsof p and q is:

$\sf log 162 = p + 4q$

Answer:

log 162 = 6p + 2q

Step-by-step explanation:

To write log 162 in terms of p and q, we can use the following steps:

- First, we can write 162 as a product of powers of 2 and 3, such as 162 = 2 x 3^4.

- Next, we can use the property of logarithms that log ab = log a + log b to write log 162 = log 2 + log 3^4.

- Then, we can use another property of logarithms that log a^n = n log a to write log 3^4 = 4 log 3.

- Finally, we can substitute p = log 2 and q = log 3 to get log 162 = p + 4q.

We can write 162 as follows:

```

162 = 2^6 * 3^2

```

Therefore,

```

log 162 = log (2^6 * 3^2)

```

Using the logarithmic properties of addition and multiplication, we can simplify this to:

```

log 162 = 6 * log 2 + 2 * log 3

```

Finally, substituting p = log 2 and q = log 3, we get the following expression:

```

log 162 = 6p + 2q

```

Therefore, log 162 can be written as **6p + 2q** in terms of p and q.

Okay, let's break this down step-by-step:

* log 162 = log (2^4 * 3^2) (by prime factorization)

* log (2^4 * 3^2) = 4log2 + 2log3 (by properties of logarithms)

* Let p = log 2 and q = log 3

* Substituting:

* log 162 = 4p + 2q

Therefore, log 162 can be written as 4p + 2q, where p = log 2 and q = log 3.

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To express log 162 in terms of p (log 2) and q (log 3), you can use logarithm properties, particularly the change of base formula. The change of base formula states that:

log_b(a) = log_c(a) / log_c(b)

In your case, you want to find log 162:

log 162 = log 2^1 * 3^4

Now, we can use the change of base formula with base 10 (or any other base):

log 162 = (log 2^1 * 3^4) / (log 10)

Since log 10 is simply 1 (logarithm of 10 to any base is 1), we can simplify further:

log 162 = (log 2^1 * 3^4) / 1

Now, apply the properties of logarithms to split the logarithm of a product into a sum of logarithms:

log 162 = (log 2^1) + (log 3^4)

Now, we can replace log 2 with p and log 3 with q:

log 162 = p + (4q)

So, log 162 in terms of p and q is:

log 162 = p + 4q

To write log 162 in terms of p and q, we can use the following steps:

- First, we can write 162 as a product of powers of 2 and 3, such as 162 = 2 x 3^4.

- Next, we can use the property of logarithms that log ab = log a + log b to write log 162 = log 2 + log 3^4.

- Then, we can use another property of logarithms that log a^n = n log a to write log 3^4 = 4 log 3.

- Finally, we can substitute p = log 2 and q = log 3 to get log 162 = p + 4q.

A skateboard company tracks the sales of their short boards and long boards. The company's records show the sales of short boards decrease every three months as represented by expression A, where t is the number of years that the boards have been for sale.expression a:624(o.94)^4t
The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.
expression b :725(1.12)^3t
Select the statements that give a correct interpretation of the above expressions.

Expression A grows at a rate of 5% every three months, while expression B decays at
a rate of 12% every four months.

Expression A has an initial value of 0.95, while expression B has an initial value of 1.12.

Expression A decays at a rate of 5% every three months, while expression B grows at
a rate of 12% every four months.

Expression A has an initial value of 624, while expression B has an initial value of 725.

Expression A decays at 5% every three years, while expression B grows at a rate of 12% every four years.

Answers

Answer:

Expression A decays at a rate of 5% every three months, while expression B grows at rate of 12% every four months

Expression A has initial value of 624, while expression B has initial value of 725

Step-by-step explanation:

plato correct

i really need help with this you have to choose all the ones that apply please help

Someone reported my question, I'm sorry Batman.
why does y=mx+b ?

Answers

Answer:

The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y. The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept

Step-by-step explanation:

lol thx for the points

Consider the following food chain: Plants are eaten by grasshoppers, which are eaten by mice, which are eaten by snakes. What would happen to the other members of the food chain if the plant population was wiped out?
a. The populations of grasshoppers, mice, and snakes would increase.
b. The populations of grasshoppers and mice would increase, while the population of snakes would decrease.
c. The populations of grasshoppers would decrease, while the population of mice and snakes would increase.
d. the number of plants will increase, the number of grasshoppers will increase, the number of snakes will increase

Answers

Answer;

-The populations of grasshoppers, mice, and snakes would decrease.

Explanation;

-The food web or a food chain describes the series of relationships that occur between predators and prey in an ecosystem.

-Several types of life forms form the food web. Green plants that can make their own food through photosynthesis are the web's producers. They form the bottom of the chain. Animals that get food from other animals and plants are consumers. Decomposers feed off dead plants and animals because decomposers cannot make their own food.

-If producers were removed in a food chain then, all the other animals in the food web would die too, because their food supplies would have died out. The populations of the consumers would fall as the population of the producer fell.

Answer:

Step-by-step explanation:

The distance between each base on a baseball field is 90 feet. what is the approximate distance from second base to home plate 90 ft

127.3 ft

140.2

180 ft