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kiruha [24]
3 years ago
12

Choose the polynomial that is written in standard form 7x^5+8x^8+27x

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

Answer: Option d: -3*x^4*y + 2*x^2*y^2 + 5*y^3

Step-by-step explanation:

In standard form, the first term of the polynomial must be the term with the highest degree and on each subsequent term the degree decreases. In the case of two variables, the degree is equal to the sum of the exponents.

Then the correct option is d.

Where the degree of the first term is (4 + 1) = 5

The degree of the second term is (2 + 2) = 4

The degree of the third therm is 3.

We can see that the degree decreases as the term number increases, then the polynomial written in standard form is:

-3*x^4*y + 2*x^2*y^2 + 5*y^3

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4 0
2 years ago
The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\
600 = (x+5)(x+4)\\
600 =  x^{2} + 9x + 20


Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\
x^{2} + 9x - 580 = 0\\
(x + 29)(x - 20) = 0\\
x + 29 = 0, \:\: x - 20 = 0\\
x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
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3 years ago
Read 2 more answers
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Answer:

The answer is 18.75

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1. AB = 11 and BC = 5. Find AC 2. AC = 16, BC = x + 4, AB = x + 14. Find x
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The wording of the question kinda doesn't make sense in some parts, but I'll try anyway. 1 plus 4 is 5, and since BC is 5, x is 1 for BC. -3 plus 14 is 11, so x is -3 for AB.
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