To divide a number by 1,000, move the decimal point _____.four places to the right
four places to the left
three places to the right
three places to the left

Answers

Answer 1

Answer: 3 places to the left. for example if you divide 5000 by 1000, you get 5 by using this method.

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When factored completely, the expression p^4 - 81 is equivalent to(1) (p^2 + 9)(p^2 - 9)
(2) (p^2 - 9)(p^2 - 9)
(3) (p^2 + 9)(p + 3)(p - 3)
(4) (p + 3)(p - 3)(p + 3)(p - 3)

Answers

p⁴ - 81
p⁴ + 9p² - 9p² - 81
p²(p²) + p²(9) - 9(p²) - 9(9)
p²(p² + 9) - 9(p² + 9)
(p² - 9)(p² + 9)
(p² + 3p - 3p - 9)(p² + 9)
(p(p) + p(3) - 3(p) - 3(3))(p² + 9)
(p(p + 3) - 3(p + 3))(p² + 9)
(p - 3)(p + 3)(p² + 9)

The answer is (3).

Final answer:

The expression p^4 - 81, when factored completely, is equivalent to (p^2 + 9)(p^2 - 9) using the difference of squares formula.

Explanation:

When the expression p^4 - 81 is factored completely, it becomes equivalent to (p^2 + 9)(p^2 - 9). This can be calculated using the rule of difference of squares which states that a^2 - b^2 = (a - b)(a + b). Here, p^4 can be considered as a square of p^2 and 81 as a square of 9. Hence p^4 - 81 = (p^2)^2 - 9^2. Applying difference of squares formula we get (p^2 - 9)(p^2 + 9).

Learn more about Factoring Expressions here:

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Which of the following expressions is the conjugate of a complex number with −5 as the real part and 4i as the imaginary part? 5 + 4i / 5 − 4i / −5 − 4i/ −5 + 4i

Answers

The mathematical expression of the given complex number above is -5 + 4i. The conjugate of this complex number is that which has an opposite operation. The given is an addition operation. That is -5 - 4i. Therefore, the answer is the third among the choices.

Which ordered pair could you remove from the relation {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)} so that it becomes a function?

Answers

Answer:

Either of (2,2) or (2,3) should be removed to get the relation as a function.

Step-by-step explanation:

We know that a relation is a function if each element of the first set is mapped to a unique element of the other set.

i.e. corresponding to each x value we have a single y-value.

We are given a relation as:

{(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)}

As we could observe that there are two images corresponding to '2' i.e. 2 is mapped to 2 and 3 both as could be seen from the ordered pair (2,2) and (2,3).

Hence, if any one of (2,2) and (2,3) will be removed we will get our relation as a function.

Each x value should have only one y value

therefore you should remove wither (2,2) or (2,3)

Use the distributive property to multiply 5(b+8)a.5b+40
b.5b+8
c.5b+13
d.8b+40

Answers

Answer:

Is a. 5b+40

Step-by-step explanation:

The distributive property explains that the multiplication of a number by a sum is equal to the multiplication of the number by each of the addends. So in this case we can multiply the number 5 by each one of the addends, this is:

$5*(b+8)=5*b+5*8=5b+40$

From the above the answer is a. 5b+40

The answer is 5b+40

5+b=5b
5×8=40

=5b+40

26. A public park is in the shape of a triangle. The side of the park that forms the base of the triangle is 2000 yards long, and the area of the park is 7500 yards2 . What is the length of the side of the park that forms the height of the triangle?

Answers

Answer:

7.5 yards

Step-by-step explanation:

Since the area of a triangle is found by the equation: $(bh )/(2)$ , in which b=base h=height, and $bh$ is base times height, we can work backward from the value of the area to find the height of the park