186 + k = (0 + 358) + 186

Answer:

Dimensions of rectangle are length = 7 cm and width = 2 cm

Step-by-step explanation:

Let l = length and w = width of the rectangle.

Given that, length is 5 cm less than 6 times width. Rewriting it in equation form,

L =  6 w - 5  cm

Also given that area of rectangle is 14 cm²

Now using formula for area of rectangle,

Area of rectangle = length × width

Area of rectangle = l × w

Substituting the values,

14 = (6 w - 5) × w

Simplifying by using distributive rule,

14 = 6 w² - 5 w

To find the value of b, use the quadratic formula. So rewriting the equation in quadratic form ax²+bx+c=0

Subtracting 14 on both sides,

0 = 6 w² - 5 w - 14

Rewriting,

6 w² - 5 w - 14  = 0

Now applying quadratic formula,

Rewriting the formula in terms of w,

From the 6 w² - 5 w - 14  = 0, value of a = 6 , b = - 5 and c = - 14.

Substituting the values,

Simplifying,

Since √361 = 19,

There will be two values of w,

and

Simplifying,

and

and

Reducing the fraction in lowest form, divide first expression by 12 and second expression by 2.

and

Since the length of width cannot be negative, so value of w = 2 cm

To find the value of length, Use equation L =  6 w - 5  cm

L =  6 (2) - 5  cm

L =  12 - 5  cm

L =  7  cm

Therefore l = 7 cm and w = 2 cm are the dimensions of the rectangle.

Step-by-step explanation:

id-8253381513

password-9999

The function f(n) = 8n - 5 + (-1)ⁿ × 3 indeed generates the given sequence 51, 43, 35, 37, 19.

The given sequence is 51, 43, 35, 37, 19. To identify the underlying function describing this sequence, let's analyze the pattern between the terms.

Subtraction: If we look at the differences between consecutive terms, we get the following sequence of differences: -8, -8, 2, -18.

Alternating Behavior: The differences between terms seem to alternate between subtracting 8 and adding 2.

Possible Linear Function: The alternating behavior suggests that this sequence might be generated by a linear function with some sort of periodic or alternating component.

Linear Function with Alternating Component: A possible function to describe this sequence could be:

  f(n) = 8n - 5 + (-1)ⁿ × 3

  Here, n represents the position in the sequence (starting from n = 1), and (-1)ⁿ introduces the alternating component. When n is even, (-1)ⁿ becomes 1, and when n is odd, (-1)ⁿ becomes -1.

Now, let's test this function with the given values:

- For n = 1: f(1) = 8(1) - 5 + (-1)¹ × 3 = 8 - 5 + (-1) × 3 = 3 - 3 = 0

- For n = 2: f(2) = 8(2) - 5 + (-1)² × 3 = 16 - 5 + 1 × 3 = 11 + 3 = 14

- For n = 3: f(3) = 8(3) - 5 + (-1)³ × 3 = 24 - 5 - 3 = 19 - 3 = 16

- For n = 4: f(4) = 8(4) - 5 + (-1)⁴ × 3 = 32 - 5 + 3 = 27 + 3 = 30

- For n = 5: f(5) = 8(5) - 5 + (-1)⁵ × 3 = 40 - 5 - 3 = 35 - 3 = 32

For similar questions on sequence

brainly.com/question/30762797

#SPJ1