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Evgen [1.6K]
3 years ago
11

What is the completely factored form of d4 − 81?

Mathematics
2 answers:
lilavasa [31]3 years ago
4 0

For this case we must factor the following expression:

d ^ 4-81

Rewriting the expression:

(d ^ 2) ^ 2-9 ^ 2

We factor using the formula of the square difference:

a ^ 2-b ^ 2 = (a + b) (a-b)

Where:

a = d ^ 2\\b = 9

So:

(d ^ 2 + 9) (d ^ 2-9)

From the second term we have:

d ^ 2-3 ^ 2 = (d-3) (d + 3)

Finally, the factored expression is:

(d ^ 2 + 9) (d-3) (d + 3)

Answer:

(d ^ 2 + 9) (d-3) (d + 3)

saw5 [17]3 years ago
3 0
<h2>Answer:</h2>

The complete factorization of the term:

              d^4-81 is:

        (d-3)(d+3)(d^2+9)

<h2>Step-by-step explanation:</h2>

To factor a term means to express is as a product of distinct factors i.e. multiples.

We are asked to factor the algebraic expression which is given by:

d^4-81

We could write this expression as:

(d^2)^2-(3^2)^2=(d^2)^2-(9)^2

We know that:

a^2-b^2=(a-b)(a+b)

i.e.

d^4-81=(d^2-9)(d^2+9)\\\\i.e.\\\\d^4-81=(d^2-3^2)(d^2+9)\\\\i.e.\\\\d^4-81=(d-3)(d+3)(d^2+9)

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Answer:

Step-by-step explanation:

9h+5h(5h-5760)-2+12=y

7 0
2 years ago
Tom made 5,000 mL of soup. He packed 2.5 liters of the soup in his kids' lunches. He froze the rest of the soup. How many millil
MakcuM [25]

Answer:

Amount of frozen soup = 2500 mL

Step-by-step explanation:

We are told that tom made 5,000 mL of soup.

We are also told he packed 2.5 Litres into his kids' lunches.

Now, from conversions,

1 liter = 1000 mL

Thus,

2.5 litres = 2.5 × 1000 = 2500 mL

Now, we are told he froze the rest of the soup.

Thus;

Amount of frozen soup = total amount of soup made - amount given to kids' lunch pack.

Amount of frozen soup =

5000 - 2500 = 2500 ml

7 0
3 years ago
Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are not close
Mrrafil [7]

Answer:

  f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.

Step-by-step explanation:

The set of all polynomials is <em>closed</em> under addition, subtraction, and <em>multiplication</em>, because performing any of these operations on a pair of polynomials will give a polynomial result.

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<em>Comment on the question</em>

The wording is a bit strange, because f(x) and g(x) are elements of a set (of polynomials), so cannot be said to be "closed." "Closed" is a property of a set with respect to some function, it is not a property of an element of the set.

6 0
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a fisherman catches 2 fish the amberjack weighs 3 times as much as the snapper,altogether the fish weigh 44 pounds how much does
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Because of the fact that the amberjack is essentially three snappers, it can be shown as 3s

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s+3s = 4s

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s = 11

Small bonus (finding an amberjack)

Since an amberjack is equal to three snappers, and a snapper is 11 pounds, an amberjack would be 33 pounds.

8 0
3 years ago
For the following exercises, determine whether the functions are even, odd, or neither.
stealth61 [152]

Answer:

The solutions of the equation |2 x-3|=17

are x=10

and x=-7

Step-by-step explanation:

Given equations is |2 x-3|=17.

It is required to find out the values of x satisfying the given equation.

To find it out, use the fact that the solution of this type of equation is 2x-3=17.

Or 2x-3=-17 and simplify the equations using simple mathematical operations.

Step 1 of 2

Solve the equation 2x-3=17,

Add 3 on both sides of the equation 2x-3=17,

2x-3+3=17+3

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Divide by 2 on both sides of the equation 2x=20,

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Step 2 of 2

Solve the equation 2x-3=-17,

Add 3 on both sides of the equation 2x-3=-17,

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Divide by 2 on both sides of the equation 2x=-14,

$$\begin{aligned}&\frac{2 x}{2}=\frac{-14}{2} \\&x=-7\end{aligned}$$

6 0
2 years ago
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