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marissa [1.9K]
3 years ago
14

The sum of three consecutive even integers is 168. Define an appropriate variable and write an equation that represents the stat

ement. Solve to find the integers. Show all work and write a conclusion.
Mathematics
1 answer:
bulgar [2K]3 years ago
3 0

Answer:

a, a + 1, a + 2

55, 56. 57

Step-by-step explanation:

Let the integers be :

a, a + 1, a + 2 (consecutive integers)

Hence, sum of the integers equals 168

a + (a + 1) + (a + 2) = 168

a + a + 1 + a + 2 = 168

3a + 3 = 168

3a = 168 - 3

3a = 165

a = 165 / 3

a = 55

first integer, a = 55

Second, a +1 = 56

Third, a + 2 = 57

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Three times the quantity five less than x, divided by the product of six and x
Elden [556K]

Answer:

\frac{3(x-5)}{6x}

Step-by-step explanation:

we know that

The phrase "Three times the quantity five less than x" means 3 multiplied by the difference of x minus 5

3(x-5)

The phrase "the product of six and x" means the number 6 multiplied by x

6x

therefore

The phrase" Three times the quantity five less than x, divided by the product of six and x" is equal to the quotient of 3(x-5) and 6x

\frac{3(x-5)}{6x}

7 0
3 years ago
4
taurus [48]

Answer:

x^2 - 2x + 10, option B

Step-by-step explanation:

Complex numbers:

The most important relation that involves complex numbers is given by:

i^2 = -1

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

The solutions are:

x_1 = 1 - 3i, x_2 = 1 + 3i

We have to find the polynomial. All option have a = 1. So

(x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10

The correct answer is given by option b.

6 0
3 years ago
Consider the line y=9x-1.
OLEGan [10]

Step-by-step explanation:

Slope=9

i)

y−y1=m(x−x1)

When line is parallel

y+5=9(x-6)

y+5 = 9x - 54

<h3>59 = 9x-y </h3>

When line is perpendicular

y+5=-1/9(x-6)

9(y+5)= -1(x-6)

9y + 45 = -x+6

<h3>x+9y = -39</h3>

<h2>MARK ME AS BRAINLIST </h2>
5 0
3 years ago
Give the center and radius of the circle. (x - 5)2 + y2 = 16
olasank [31]

Answer:

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Step-by-step explanation:

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3 years ago
Money in a particular savings account increases by 6% after a year. How much money will be in the account after one year if the
Alona [7]

Answer:

Step-by-step explanation:

34,999999

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