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erastova [34]
3 years ago
14

a rectangular swimming pool is 25 feet long anf 12 feet wide. it is surrounded by a fence that is h feet from each side of a poo

l. write the expression for the length of the fence.
Mathematics
1 answer:
timurjin [86]3 years ago
5 0

The length of rectangular swimming pool = 25 feet

The width of the swimming pool = 12 feet

The pool is surrounded by a fence which is h feet from each side

So, length of fence becomes = 25+2h

Width of fence becomes = 12+2h

The expression for the length of the fence is 25+2h feet

2h because 'h' increases for both ends of the length of the pool.

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Copy the expressions which are polynomials. Give reasons why the remaining are
kupik [55]

Answer: a and c are polynomials, b is not.

Step-by-step explanation:

A polynomial p(x) is written as:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀*x⁰

where x is the variable, and the numbers aₙ, aₙ₋₁, ..., a₁, a₀ are the coefficients of the polynomial, such that aₙ is the leading coefficient, and the value of n (always a natural number) is the degree of the polynomial.

Notice that the powers need to be always natural numbers.

Now, let's analyze the options:

a) 3*x - 2

We can rewrite this as:

3*x¹ - 2*x⁰

Then this is a polynomial.

b) p² + 1/p    (in this case the variable is p)

the second term can be written as:

1/p = p⁻¹

Then we have a term with a negative power of p, this means that this is not a polynomial.

c) 3*y² - 2*y/3 + 1

Same as in the first case, we can rewrite this as:

3*y² - (2/3)*y¹ + 1*y⁰

This is a polynomial.

8 0
3 years ago
The coordinates of the endpoints of directed line sergeant ABC are A(-8,7) and C(7,-13). If AB:BC = 3:2 then the coordinates of
cestrela7 [59]

The correct answer is A) (1,-5)

Further explanation:

Given points are:

A(-8,7)=(x1,y1)

C(7,13)=(x2,y2)

IT is also given that

AB:BC=3:2

Which means that B divides the line segment in 3:2

Here,

m=3

n=2

To find the coordinates of B

x_B=\frac{mx_2+nx_1}{m+n}\\ = \frac{(3)(7)+(2)(-8)}{3+2}\\=\frac{21-16}{5}\\=\frac{5}{5}\\=1\\y_B=\frac{my_2+ny_1}{m+n}\\=\frac{(3)(-13)+(2)(7)}{3+2}\\=\frac{-39+14}{5}\\=\frac{-25}{5}\\=-5

The coordinates of point B are (1,-5)

The correct answer is A) (1,-5)

Keywords: Coordinate geometry, mid-point

Learn more about coordinate geometry at:

  • brainly.com/question/4819659
  • brainly.com/question/4691222

#learnwithBrainly

7 0
3 years ago
Solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?
Sedbober [7]

Answer:

Step-by-step explanation:

cos (x/2)=cos x+1

cos (x/2)=2cos ²(x/2)

2 cos²(x/2)-cos (x/2)=0

cos (x/2)[2 cos (x/2)-1]=0

cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)

x/2=2nπ+π/2,2nπ+3π/2

x=4nπ+π,4nπ+3π

n=0,1,2,...

x=π,3π

or x=180°,540°,...

180°∈[0,360]

so x=180°

or

2cos(x/2)-1=0

cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)

x/2=360n+60,360n+300

x=720n+120,720n+300

n=0,1,2,...

x=120,300,840,1020,...

only 120° and 300° ∈[0,360°]

Hence x=120°,180°,300°

7 0
2 years ago
What is the simplest form of ^3√x^10
IrinaK [193]

Answer:

3=-3

A radical is a mathematical symbol used to represent the root of a number. Here’s a quick example: the phrase “the square root of 81” is represented by the radical expression . (In the case of square roots, this expression is commonly shortened to —notice the absence of the small “2.”) When we find  we are finding the non-negative number r such that , which is 9.

While square roots are probably the most common radical, we can also find the third root, the fifth root, the 10th root, or really any other nth root of a number. The nth root of a number can be represented by the radical expression.

 

Radicals and exponents are inverse operations. For example, we know that 92 = 81 and  = 9. This property can be generalized to all radicals and exponents as well: for any number, x, raised to an exponent n to produce the number y, the nth root of y is x.

7 0
2 years ago
For the following equation, compute the x- and y- intercepts to graph the line.
nikklg [1K]
X-intercept: (-5,0)
Y-intercept: (0,4)
To solve for the X-Intercept, substitute 0 for y and solve for x.
To solve for the Y-Intercept, substitute 0 for x and solve for y.

7 0
3 years ago
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