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tatiyna
2 years ago
8

One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know tha

t the perimeter of the rectangle is 58 meters
Mathematics
2 answers:
Wittaler [7]2 years ago
6 0
Set the shorter side of rectangle as X m
The longer side = (4X-6) m
58 = (X + 4X -6)2
58=10X -12
70 = 10X
X = 7
The shorter side is 7 m
And the longer side is 4 x 7 -6 = 22 m
Lerok [7]2 years ago
6 0

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

<u>Equation 1</u>

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

<u>Equation 2</u>

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

<u>Solve by substitution</u>

Substitute Equation 1 into Equation 2 and <u>solve for x</u>:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and <u>solve for y</u>:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

<u>Conclusion</u>

The dimensions of the rectangle are:

  • width = 7 meters
  • length = 22 meters

Therefore, the length of the longer side is 22 meters

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Answer:

21. is 18 dollars

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Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X &gt; 4) = 1/2.
Anettt [7]

Answer:

a=2

b=6

Step-by-step explanation:

Assuming a uniform distribution and that a ≤ x ≤ b, if f(x) = 1/4, then:

f(x) =\frac{1}{4}=\frac{1}{b-a}\\b-a = 4

If P(X > 4) = 1/2, then:

\frac{1}{2} = 1-(\frac{x-a}{b-a})=1-(\frac{4-a}{4})\\a-4+4 =\frac{1}{2}*4\\ a=2\\b=4+a\\b=6

The values for a and b are, respectively, 2 and 6.

3 0
3 years ago
What is the domain of the function f(w) = 0.5(35 – 2w)? Explain your answer.
Igoryamba
The domain is all real numbers, the function is a variant of linear, which could be expressed in the form of y=mx+b as y = -w + 17.5, therefore all real numbers is the domain and the range.
5 0
3 years ago
Which of the following is equivalent to 5x - x + 3x = 30? A 8x = 30 o 7x = 30 с 3x + 5= 30 x = 30​
lyudmila [28]

Answer:

Step-by-step explanation:

5x -x + 3x =30,  first you combine like terms 5x + 3x-x=30

8x-x =30

8-1=7

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4 0
2 years ago
Read 2 more answers
I don’t understand :(
viktelen [127]

Answer:

The quotient when x^3-4x^2-8x+8 is divided by x+2 is x^2-6x+4 with no remainder, so x+2 is a factor of p(x).

Step-by-step explanation:

As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form (x-a). In this case, we may use synthetic division, since x+2 is equal to x-(-2). I will use synthetic division here as it is slightly faster than long division.

The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.

The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.

Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.

This is the answer: the quotient is x^2-6x+4, and the remainder is zero (which indicates that x+2 is a factor of p(x)).

--

Edit: long division

We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since x \times x^2 is equal to x^3, the first term in the quotient will be x^2. Since x^2 \times (x+2) is equal to x^3+2x^2, we must now subtract that from x^3-4x^2-8x+8.

We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.

<em>I know this might be difficult to follow, so please comment if you have any questions.</em>

4 0
3 years ago
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