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Brrunno [24]
1 year ago
14

find the three consecutive odd integers such that the sum of twice the first and three times the second is 67 more than twice th

e thirdz​
Mathematics
1 answer:
Elenna [48]1 year ago
4 0

Answer:

  23, 25, 27

Step-by-step explanation:

It can be convenient to work "consecutive integer" problems by using a variable to represent the middle one.

__

<h3>setup</h3>

Let x represent the middle integer. Then (x-2) is the first of the three odd integers, and (x+2) is the third. The given relation is ...

  2(x -2) +3x = 67 +2(x +2)

<h3>solution</h3>

  5x -4 = 2x +71 . . . . . simplify

  3x = 75 . . . . . . . . add 4-2x

  x = 25 . . . . . . . divide by 3

The three integers are 23, 25, 27.

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Using the Associative Property which expression is equivalent to (2+x)+4=
Anna35 [415]

Answer:

x+6

Step-by-step explanation:

The given expression is (2+x)+4.

The associative property is :

(a+b)+c= a+(b+c)

Here,

a = 2, b = x and c = 4

So,

(2+x)+4 = 2+(x+4)

= x+6

So, the equivalent expression is x+6.

6 0
3 years ago
Find an expression for the nth term ( tn ) in each of the following sequences:
Alexandra [31]

Answer:

The expression for the nth term is Tn = 8n -7

Step-by-step explanation:

Here, we are to find an expression for the nth term of the sequence.

Mathematically, the nth term of an arithmetic sequence can be expressed as;

Tn = a + (n-1)d

for T2, the equation is

a + d = 9

for T4, the equation is

a + 3d = 25

we can substitute the equation of T2 into T4 but we first need to rewrite T4

a + d + 2d = 25

9 + 2d = 25

2d = 25 -9

2d = 16

d = 16/2

d = 8

now since a + d = 9

a = 9-d

a = 9-8

a = 1

So the expression for the nth term would be;

1 + (n-1)8

1 + 8n - 8

= 8n -8+1

= 8n -7

6 0
3 years ago
If 2 variables have a negative correlation, then the slope of the line of best fit will be ______.
Lana71 [14]
Negative, because Correlation and slope have the same direction (Sxy will be negative)
5 0
3 years ago
What is the length of AB?
Dovator [93]

Answer:

AB = 5

Step-by-step explanation:

The side opposite the 30 degree angle will have the shortest length. The side opposite the 60 degree angle will be  √3  times as long, and the side opposite the 90 degree angle will be twice as long.

In this case we just divide 10 by 2

4 0
2 years ago
Read 2 more answers
Se tiene la sucesión 3, 8, 13, 18, 23 … ¿Cuáles son los siguientes dos términos y cuál es la regla general?
V125BC [204]

Respuesta:

28; 33

A (n) = 5n - 2

Explicación paso a paso:

A partir de los datos dados, 3, 8, 13, 18, 23…, podemos ver que cada valor sucesivo de la serie aumenta en 5;

Por lo tanto, los siguientes dos términos de la serie deberían ser:

23 + 5 = 28

28 + 5 = 33

La serie es una progresión aritmética:

Recuerde la fórmula general:

A (norte) = a + (norte - 1) d

Donde, a = Primer término = 3; d = diferencia común = 5

n = enésimo término

A (n) = 3 + (n-1) 5

A (n) = 3 + 5n - 5

A (n) = 5n - 2

6 0
3 years ago
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