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Inessa [10]
3 years ago
6

Find four consecutive integers whose sum is 290.

Mathematics
2 answers:
Ede4ka [16]3 years ago
8 0
For an instance, n is the smallest number, then the other number will be (n + 1), (n + 2), (n + 3)

Write an equation based on the problem
the sum of the numbers = 290
n + n + 1 + n + 2 + n + 3 = 290
4n + 6 = 290
<em>This is the equation</em>

Solve the equation
4n + 6 = 290
4n = 290 - 6
4n = 284
  n = 284/4
  n = 71
The smallest number is 71

Find the other three numbers
n + 1 = 71 + 1 = 72
n + 2 = 71 + 2 = 73
n + 3 = 71 + 3 = 74
The other numbers area 72,73,74
jarptica [38.1K]3 years ago
3 0

n = number


(n + 1) + (n + 2) + (n + 3) + (n + 4) = 290

⬇️

4n + 10 = 290

4n = 280

n = 70

⬇️

70 + 1 = 71
70 + 2 = 72
70 + 3 = 73
70 + 4 = 74

⬇️

The numbers are 71, 72, 73, and 74
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The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. Th
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The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

<h3>How to determine the length</h3>

The cosine rule is given as;

c = \sqrt{a^2 + b^2 - 2ab cos \alpha }

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}

c = \sqrt{533 - 308 * 0. 7660}

c = \sqrt{533 - 235. 93}

c = \sqrt{297. 072}

c = 17. 24 feet

Using sine rule

\frac{a}{sin A }  = \frac{c}{sin C}

\frac{a}{sin 70}  = \frac{17. 24}{sin 40}

Cross multiply

a × sin 60 = c × sin 70

a × 0. 8660 = 17. 24 × 0. 9397

a = \frac{16. 20}{0. 8660}

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

Learn more about  isosceles trapezoid here:

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DanielleElmas [232]
A.) is the correct answer.
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Answer:

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8 0
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A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height
melisa1 [442]

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

x\geq 0

The height of the food packet cannot be a negative value, so

f(x)\geq 0

We need to replace -15x^2+6000 for f(x) in the above inequality to find the domain.

-15x^2+6000\geq 0 \; \;  [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0

The possible solutions of the above inequality are given by the intervals (-\infty , -2], [-2,2], [2,\infty ). We need to pick test point from each possible solution interval and check whether that test point make the inequality (x+200)(x-200)\leq 0 true. Only the test point from the solution interval [-200, 200] make the inequality true.

The values of x which will make the above inequality TRUE is -200\leq x\leq 200

But we already know x should be positive, because time cannot be negative.

Conclusion:

Domain of the given function is 0\leq x\leq 200

4 0
3 years ago
Read 2 more answers
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