The three consecutive integers are 5, 6, and 7.
What are consecutive integers?
Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.
Finding the Consecutive Integers
Let the three consecutive integers be a, a + 1, and a + 2.
These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.
⇒ 2a + 3(a+1) - (a+2) = 21
2a + 3a + 3 - a -2 = 21
5a - a + 3 - 2 = 21
4a + 1 = 21
4a = 20
a = 20/4
a = 5
∴ a+1 = 5+1
a+1 = 6
And, a+2 = 5 + 2
a +2 =7
Hence, the three consecutive integers come out to be 5, 6, and 7
Learn more about consecutive integers here:
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The <em>quadratic</em> function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).
<h3>How to analyze quadratic equations</h3>
In this question we have a graph of a <em>quadratic</em> equation translated to another place of a <em>Cartesian</em> plane, whose form coincides with the <em>vertex</em> form of the equation of the parabola, whose form is:
g(x) = C · (x - h)² - k (1)
Where:
- (h, k) - Vertex coordinates
- C - Vertex constant
By direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.
x = 2
g(2) = (2 - 5)² + 1
g(2) = 10
x = 8
g(8) = (8 - 5)² + 1
g(8) = 10
The <em>quadratic</em> function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).
To learn more on parabolae: brainly.com/question/21685473
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To find the volume of this one we need to break it down
now i see half of a cylinder and rectangle:)
but first lets find the volume of the rectangle...
In order to find the Volume of a rectangle we need to use this formula...
Length x width x height
in this case...
length = 10in
width = 6 in
height = 8in
lets solve:)
10 x 6 x 8 = 480
or we write it like this
480in³
now time to find the volume of the half cylinder:)
But first lets remember the volume for a cylinder
Volume =

So lets find our measurements

= 3.14
r² = 5² or 25
h = 6
so lets plug in our values just like our formula said:)
3.14 x 25 x 6
now lets easily solve
<span>3.14 x 25 x 6 = 471
</span>now since we found an entire cylinder and we only want half of a cylinder lets divide our answer in half
471 ÷ 2 = 235.5
so we write it like this 235.5units³
But we have to add both of our multiples together so lets do that
Volume of rectangle = <span>480in³
</span>volume of half sphere = 235.5units³
480 + 235.5 = 715.5
answer = 715.5units³
I hope this helped and everyone learned something new
anyways don't forget to
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The pass rusher, which is typically line up on the line of scrimmage.
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