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Leona [35]
1 year ago
14

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 ...

  7x

<h3>Algebraic expression</h3>

Then the complete algebraic expression is ...

  6 +7x

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Lilit [14]
The product of trigonometric functions can be converted into sum ans vice versa. The given function is a product and we can convert it to a sum.One way is to expand the given expression and simplify it to find the result.

The second and easier option is to just remember the formulas of product to sum conversion identities. The 4 formulas for this case are listed below in the image.

Since we have the product of cos and sin, the sum will involve two sine functions connected by addition.

So the correct answer is option A

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2 years ago
What's the greatest common factor of 49 + 25?
Feliz [49]
The GCF is one. I hope this helps love! :)
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3 years ago
Which ordered pair is a solution to the system of linear equations below?<br> y= 1/4x+2<br> y= x-1
adelina 88 [10]

Answer:

The answer is (4,3)

Step-by-step explanation:

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8 0
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A farmer divided his piece of land into 2 equivalent groups and the quality of the soil is the same in both of these groups. He
Dimas [21]

Answer:

  1. Observational would mean that he (farmer) has no direct impact or change on the statistical study.
  2. Experiment would mean that he imposed a certain treatment up a group in this case it would be the land.
  3. Hence we can determine that the the study was an experimental one.
7 0
2 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

3 0
3 years ago
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