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Dennis_Churaev [7]
3 years ago
10

There are five consecutive odd integers. The sum of the three smallest is 3 more than the sum of the two largest. Find the integ

ers. 15 points
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
6 0

Answer:

11 13 15 17 19

Step-by-step explanation:

We will solve this word problem using 2k+1 which is one of the general forms of an odd integer.

Let 2k+1 be the first odd integer.

(2k+1) + (2k+3) + (2k +5) =  (2k+7) + (2k +9) + 3 (the +3 is to accommodate for the left side being 3 more than the right)

Solve for k

6k + 9 = 4k + 19

6k - 4k + 9 = 4k-4k + 19

2k + 9 = 19

2k + 9 - 9 = 19 - 9

2k = 10

2k/2 = 10/2

k = 5

To get the first digit in the series plug in 5 for k

2k+1

2(5) + 1

10 + 1 = 11

So our series is 11, 13, 15, 17, 19

Let's test it.

11 + 13 +15 = 39

17 + 19 = 36

So we are correct, the first 3 integers are 3 more that the sum of the last 2.

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A² + 6 from 7<br> plzz answer i gave u half of my points plz
omeli [17]

Answer:

a = 1

Step-by-step explanation:

First, you subtract 6 from both sides and you end up with a² = 1. Since one cannot be squared or square rooted, a = 1. I hope this helps!

7 0
3 years ago
Write an equation parallel to the line determined by the points (15, -6) and (-3, 13), through: (4, 2)
gulaghasi [49]

Answer:

The answer is

<h2>y =  -  \frac{19}{18} x +  \frac{76}{2}</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

That's

Slope of the through points

(15, -6) and (-3, 13) is

<h3>m =  \frac{13 -  - 6}{ - 3 - 15}  =  -  \frac{19}{18}</h3>

Since the lines are parallel their slope are also the same

So slope of parallel line = - 19/18

Equation of the line using point (4,2) and slope -19/18 is

<h3>y - 2 =  -  \frac{19}{18} (x - 4) \\ y - 2 =  -  \frac{19}{18}  x +  \frac{38}{9}  \\ y =  -  \frac{19}{18} x +  \frac{38}{9}  + 2</h3>

We have the final answer as

<h3>y =  -  \frac{19}{18} x +  \frac{76}{2}</h3>

Hope this helps you

7 0
2 years ago
Read 2 more answers
Debi walks laps around the mall for exercise during the winter months. The table represents the number of steps recorded on her
cupoosta [38]
Where’s the table? Then I can help u.
4 0
3 years ago
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Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. Pleas
Anna71 [15]

Answer:

y = \frac{1}{3}x + 4

Step-by-step explanation:

First, to figure out the equation of a line you must find the slope then plug in the coordinates.

In order to find the slope of the equation, you know that it is perpendicular to the equation y = -3x + 7.

Perpendicular slopes are basically reciprocals with opposite signs; you flip the number and give it the opposite symbol.

For example, the perpendicular slope of 2 would -1/2, because flipping the fraction 2/1 is 1/2 and the opposite sign of + would be -.

Therefore, the perpendicular slope of -3 would be 1/3, be 3/1 flipped upside down is 1/3 and the opposite sign of - is +.

Then you plug in the slope into the equation of a line along with the coordinate.

A line is y = mx + b

Since you found the slope, m = 1/3

They also give you the coordinate (3,5), meaning when x = 3, the y =5.

You plug everything into the equation to solve for b:

5 = (1/3)(3) + b

b = 5 - (1/3 * 3) = 5 - 1 = 4

Since you have values for m and b, the equation can now be constructed as

y = 1/3x + 4

6 0
2 years ago
The sum of the exterior angles of a polygon is always 180 degrees.<br><br> True<br> or<br> False
Bezzdna [24]
False. it said ,"The sum of the exterior angles of a polygon is always 360 degrees<span>. ... By an inductive proof, this is </span>true<span> for all </span>polygons." that is what i think.
5 0
3 years ago
Read 2 more answers
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