The fifth term of an A.P is 40 and the seventh term is 28 more than the 3rd term. Find the first and 10th term.

Answer:

option 4

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

let width be w then length = 3w ( 3 times the width )

given A = 507

substitute these values into the formula for A

507 = 3w × w , that is

507 = 3w² ( divide both sides by 3 )

169 = w² ( take square root of both sides )

= , that is

13 = w

Then

length = 3w = 3 × 13 = 39 cm

Answer:

The correct option is 4.

Step-by-step explanation:

It is given that 120% of a number is 43.

Let the number be x.

Multiply both sides by 10.

Divide both sides by 12.

The required number is 35.83. Therefore the correct option is 4.

Jada's turtle embarked on an intriguing journey, marking its passage with each step. Initially, it took a decisive stride spanning 10 feet. This pivotal moment laid the foundation for the subsequent segment of its expedition.

In a remarkable turn, the turtle chose to halve its preceding distance, taking a path less traveled and demonstrating an innate sense of mathematical intuition.

This deliberate decision to cover half the initial distance carries profound mathematical implications. Halving signifies a division, a fundamental operation in mathematics.

In this context, it exemplifies the concept of fractions and ratios, crucial elements in various mathematical disciplines. By traversing half of the initial 10 feet, the turtle traveled 5 feet, embodying the notion of proportionality and equivalence. This action aligns with the mathematical principle that dividing a quantity by 2 results in equal parts, illustrating balance and harmony.

Moreover, this scenario offers a valuable lesson in geometry, emphasizing spatial understanding. The turtle's journey can be visualized geometrically, with the initial 10-foot distance representing a line segment. Halving this segment creates two distinct yet symmetrical parts, showcasing the concept of geometric symmetry.

Understanding symmetry is fundamental not only in geometry but also in various branches of science and art, underscoring the turtle's unintentional yet profound contribution to these fields.

Furthermore, the turtle's expedition is symbolic of mathematical recursion, a concept prevalent in various mathematical problems and computer science algorithms. Recursive processes involve breaking a problem into smaller, similar subproblems.

In this case, the turtle repeatedly divides its path by 2, creating a recursive sequence of distances. Recursive thinking is a cornerstone of problem-solving, highlighting the turtle's journey as a metaphor for tackling complex challenges by breaking them down into manageable steps.

In essence, Jada's turtle, with its seemingly simple journey, encapsulates fundamental mathematical concepts such as fractions, ratios, geometry, symmetry, and recursion. Its measured steps echo the principles that underpin a wide array of mathematical phenomena, demonstrating the interconnectedness of mathematics with the world around us.

Through this tale, the turtle becomes not just a traveler but a mathematical muse, inspiring contemplation and understanding of the intricacies of the numerical world.

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Answer:

              -11, -9, -7

the smallest:   2x+1 = -11

Step-by-step explanation:

{z - some integer}

2z+1  - the smallest number

7(2z+1)  - seven times the smallest number

2z+1+2=2z+3  - the middle number

2z+3+2 = 2z+5 - the largest number

2(2z+5) - twice the largest number

7(2z+1) + 2(2z+5)  - the sum of 7 times the smallest and twice the largest

7(2z+1) + 2(2z+5)   = -91

14z + 7 + 4z + 10 = -91

              -17              -17

      18z   = -108

       ÷18        ÷18

        z = -6

2z+1 = 2(-6)+1 = -12 + 1 = -11  

2z+3 = 2(-6)+3 = -12 + 3 = -9

2z+5 = 2(-6)+5 = -12 + 5 = -7        

Final answer:

To solve this problem, we denote the smallest odd integer as 'x' and set up the equation 7x + 2(x+4) = -91. By solving this equation, we find that the smallest integer is -15.

Explanation:

To find the three consecutive odd integers, let us denote the smallest odd integer as x; therefore, the next two consecutive odd integers would be x + 2 and x + 4, respectively. The problem states that the sum of seven times the smallest integer and twice the largest integer equals to -91. So, we can translate this into the equation, 7x + 2(x+4) = -91. Solving this gives us x = -15. Hence the smallest integer is -15. The full solution is as follows:

1. Let the smallest integer be x.
2. Then the other two consecutive odd numbers are x + 2 and x + 4.
3. According to the question, 7x + 2(x + 4) = -91.
4. Solving for x, we get x = -15.
5. Hence, the smallest odd integer sought is -15.

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