Step-by-step explanation:
x, x+2 are the two positive consecutive of integers (x + 2, because the minimum distance between 2 odd numbers is always 2, as there can never be 2 odd numbers directly following each other; and neither can even numbers, by the way).
(x+2)² = 2×x² - 1
x² + 4x + 4 = 2x² - 1
0 = x² - 4x - 5
we can solve this by factoring.
that means we need to find a and b so that
(x - a)(x - b) = x² - 4x - 5 = 0
and x = a and x = b are the 2 solutions of the quadratic equation.
x² - ax - bx + ab = x² - 4x - 5 = 0
x² - (a+b)x + ab = x² - 4x - 5 = 0
a+b = 4
ab = -5
that means that either a or b has to be 5 and the other -1.
so, the result is
(x - 5)(x + 1) = 0
x = 5
or
x = -1
are the possible solutions.
since we are only looking for positive integers, x = -1 is not a valid solution.
and only x = 5 remains as valid solution.
therefore, the 2 positive consecutive odd integers are
5, 7
Answer:
A. a + c ≥ 70; 15a + 4c ≤ 1000
Step-by-step explanation:
<u>Given data:</u>
A community action committee is planning a block party
The party will be successful if at least 70 adults (a) and children (c) attend
Their budget for the party is $1,000
The cost for each adult will be $15
And the cost for each child will be $4
<u>Solution:</u>
<u />
At least 70 adults and children attend.
So the inequality here is a + c ≥ 70
The budget for the party is $1,000.
So the cost for all adults plus the cost for all children cannot exceed $1,000
And hence the inequality here is; 15a + 4c ≤ 1,000
It would be A.) 7. hope this helps
Answer:
Step-by-step explanation:
we are given equation as
Since, we have to solve it by using complete square
so, firstly we will complete square
and then we can solve for x
step-1:
Factor 2 from both sides
step-2:
Simplify it
step-3:
Add both sides 3^2
now, we can complete square
step-4:
Take sqrt both sides
step-5:
Add both sides by 3
we get
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<span><span><span>In geometry, how do defined terms and undefined terms relate to each other?
</span><span><span>Ask for details </span> <span>Follow </span> Report</span> <span>by <span>Da5ncing4bearnelogi </span>05.08.2016</span></span>Answers<span><span>Hussain514 </span> Ambitious</span>In geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane.
POINT (an undefined term)
In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y).
LINE (an undefined term)
In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends without end in two directions. A line is named by a single lowercase written letter or by two points on the line with an arrow drawn above them.
PLANE (an undefined term)
In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or wall. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC).
Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the end point, and all points extending infinitely to one side of the end point.
Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single end point. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.
Everything else builds on these and adds more information to this base. Those added things include all the theorems and other "defined" terms like parallelogram or acute angle. <span>
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