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tigry1 [53]
3 years ago
8

The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ

ers.
Mathematics
1 answer:
Nutka1998 [239]3 years ago
3 0

Answer:

  • equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
  • values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

  (x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

  4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

  x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

  • -18-3 = -21
  • -18-1 = -19
  • -18+1 = -17
  • -18+3 = -15

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

  (x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

  4x +12 = -72 . . . . . collect terms

  4x = -84 . . . . . . . . subtract 12

  x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

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7 0
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Can someone do question b please?
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What s 3/4 multiplied by 9? what is the solution?
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Answer:

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3 0
3 years ago
Read 2 more answers
1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
Lunna [17]

The correct responses found using trigonometric ratios are as follows;

  1. Brooke's cannot bring the boat back without getting water over her boots.
  2. The plan will not be approved
  3. The plane will not disturb
  4. The company can not use the chimney legally
  5. The Long company will build the bridge
  6. The fireman can reach her.
  7. The lift does not take the skiers up to the bar.
  8. Eric will be able to see his Dad's plane.
  9. The 73 m. brace

<h3>How can trigonometric ratios be used to find the right responses?</h3>

1. The depth of the water = 15 × tan(4°) = 1.049 m

The height of Brooke's boot = 1 m

Therefore;

  • Brooke's cannot bring the boat back without getting water over her boots.

2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°

Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;

  • The plan will not be approved.

3. Height reached by the plane = 9 × tan(21°) = 3.455

Therefore;

  • The plane will not disturb.

4. Height of the chimney at the factory = 50 × tan(51°) = 61.745

The minimum chimney height = 65 m.

Therefore;

  • The company can not use the chimney legally.

6. Length of the bridge = 72 × tan(55°) ≈ 102.83

Therefore;

  • The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.

7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7

Therefore;

  • The fireman can reach her.

8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8

Therefore;

  • The lift does not take the skiers up to the bar.

9. Height reached by plane = 26 × tan(9°) ≈ 4.12

The plane flies under the cloud therefore;

  • Eric will be able to see his Dad's plane.

10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83

Therefore;

  • The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.

Learn more about trigonometric ratios here:

brainly.com/question/24349828

#SPJ1

7 0
1 year ago
Please help it urgent!!!!
Veronika [31]

Answer:

<h3>1) 5(7x^{2} - x + 8)</h3>

first box: 5 * 7 = 35

35 x^2

second box: 5 * -1 = -5

-5x

third box: 5 * 8 = 40

40

answer: 35x^{2} - 5x + 40

<h3>2) 2x(4x^2 + 3x + 6)</h3>

first box: 2x * 4x^2

2 * 4 = 8

x * x^2 = x^3

8x^3

second box: 2x * 3x

2 * 3 = 6

x * x = x^2

6x^2

third box: 2x * 6

2 * 6 = 12

12x

answer: 8x^3 + 6x^2 + 12x

<h3>3) (tp + 5)(4p - 6)</h3>

top left box: tp * 4p

p * p = p^2

4tp^{2}

top right box: tp * - 6

-6tp

bottom left box: 5 * 4p

5 * 4 = 20

20p

bottom right box: 5 * - 6

5 * -6 = -11

-11

answer: 4tp^2 - 6tp + 20p - 11

<h3>4) (4a - 8)(8a - 1)</h3>

top left box: 4a * 8a

4 * 8 = 32

a * a = a^2

32a^2

top right box: 4a * -1

4 * -1 = -4

-4a

bottom left box: -8 * 8a

-8 * 8 = -64

-64a

bottom right box: -8 * - 1

-8 * - 1 = 8

8

32a^2 - 4a - 64a + 8

<em>combine like terms</em>

32a^2 - 68a + 8 = answer

4 0
3 years ago
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