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frosja888 [35]
3 years ago
13

The sum of two consecutive odd integers is 28. What are the integers?

Mathematics
1 answer:
Fantom [35]3 years ago
4 0
The correct option is B): "<span>Let x = 1st integer. Let x + 2 = 2nd integer.</span><span>"
Given that "The sum of two consecutive odd integers is 28."
 
Now the difference between two odd numbers is 2. So this means that one odd number has to be greater than the other by 2.

Let the smaller number be 'X' therefore the bigger number will be 'x+2' thus x + (x+2) = 28
 
therefore, x + x + 2 = 28 now we subtract "2" from both the sides
therefore, 2x = 26 now dividing throughout by 2 we get:

x = 13 therefore, x + 2 = 13+2
                                    = 15
 
therefore, the numbers are 13 AND 15</span>
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A piece of wire of length 6363 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the
Lerok [7]

Answer:

a.

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

Or

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

7 0
3 years ago
G.O is going on a hike in the mountains on a hot summer day ha has 4/5 gallon of water that he split into 4 bottles what fractio
kirill [66]

Answer:

\frac{1}{5} fraction of gallon is in each bottle.

Step-by-step explanation:

As per the given condition: G.O is going on a hike in the mountains on a hot summer day he has 4/5 gallon of water that he split into 4 bottles.

⇒ in 4 bottle  he has \frac{4}{5} gallon of water.

Unit rates defined as when are expressed as a quantity of 1, such as 3 feet per second or 4 miles per hour, then they are called unit rates.

By unit rate definition,

In 1 bottle he has = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} gallon of water.

therefore, the gallon in each bottle in fraction is, \frac{1}{5}

7 0
3 years ago
José sets up computers. He has been working
lakkis [162]
Correct answer should be= 1.5 hours.
3 0
3 years ago
PLS HELP ME ASAP!!!!!!!!!!!!!!
Anton [14]
The answer to that question is C
8 0
3 years ago
Read 2 more answers
Which expression is the correct translation of the following word phrase?
Llana [10]
Hey, there! 

The parentheses would make it multiplication 
The word sum means add 
A number was unknown, so we will label it as "x" 

So, let's see what we're working with here! 

If you chose "Option A" the question would be "five multiplied by a number and the sum of 3" (that doesn't give you the right answer" 
For B. same thing with option A 
For "Option C" its not asking you "a number with sum of three times five" 

So, this leaves "Option D." as your answer because 3 is getting multiplied by the sum of some number and five

Good luck on your assignment and enjoy your day!

~MeIsKaitlyn:)


3 0
3 years ago
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