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1 year ago

Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.

Mathematics

1 answer:

Tatiana [17]1 year ago

6 0

Answer:

6 +7x

Step-by-step explanation:

To write an English expression as an algebraic one, you must first understand what the English is telling you. Then the translation is straightforward.

<h3>Algebraic representation</h3>

A plus sign (+) signifies addition. Multiplication is signified several different ways. The simplest is writing the factors next to each other.

<h3>Parsing the English</h3>

The objects involved in the addition are 6 and a product:

6 + product

The product is said to consist of two factors: 7 and "a number". The instructions say to use "x" for "a number", so the product can be written ...

<h3>Algebraic expression</h3>

Then the complete algebraic expression is ...

6 +7x

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3 years ago

<img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B4%7D%20%20-%206%20%7Bx%7D%5E%7B3%7D%20%20%2B%2022%20%7Bx%7D%5E%7B2%7D%20%20-%2

alexira [117]

Answer:

x = 2, 1 + 3i, 1 − 3i

Step-by-step explanation:

Find the Roots (Zeros)

x^4 − 6x^3 + 22x^2 − 48x + 40

Set x^4 − 6x^3 + 22x^2 − 48x + 40 equal to 0. x^4 − 6x^3 + 22x^2 − 48x + 40 = 0

Solve for x.

Factor the left side of the equation.

Factor x^4 − 6x^3 + 22x^2 − 48x + 40 using the rational roots test.

(x − 2) (x^3 − 4x^2 + 14x − 20) = 0

Factor x^3 − 4x^2 + 14x − 20 using the rational roots test.

(x − 2) (x − 2) (x2 − 2x + 10) = 0

Combine like factors.

(x − 2)2 (x^2 − 2x + 10) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

(x − 2)^2 = 0

x^2 − 2x + 10 = 0

Set (x − 2)^2 equal to 0 and solve for x.

Set (x − 2)^2 equal to 0.

(x − 2)^2 = 0

Solve (x − 2)^2 = 0 for x.

x = 2

Set x^2 − 2x + 10 equal to 0 and solve for x.

Set x^2 − 2x + 10 equal to 0. x^2 − 2x + 10 = 0

Solve x^2 − 2x + 10 = 0 for x.

Use the quadratic formula to find the solutions.

−b ± (√b^2 − 4 (ac) )/2a

Substitute the values a = 1, b = −2, and c = 10 into the quadratic formula and solve for x.

2 ± (√(−2)^2 − 4 ⋅ (1 ⋅ 10))/2 ⋅ 1

Simplify.

Simplify the numerator.

x = 2 ± 6i/ 2.1

Multiply 2 by 1

x = 2 ± 6i/2⋅1

Simplify

2 ± 6i/2

x = 1 ± 3i

The final answer is the combination of both solutions.

x = 1 + 3i, 1 − 3i

The final solution is all the values that make (x − 2)2 (x2 − 2x + 10) = 0 true.

x = 2, 1 + 3i, 1 − 3i

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3 years ago