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Kaylis [27]
3 years ago
5

How many pairs of while number have a sum of 110

Mathematics
2 answers:
Naddik [55]3 years ago
8 0
56

The way you figure this out is to first recall that Whole Numbers = 0, 1, 2, 3, 4, ...

Then, just start pairing numbers up:

0, 110
1, 109
2, 108
3, 107

and so forth.

What you realize is that you have a bunch of pairs of numbers that start with (0, 110) and end with (55, 55)

Once you get beyond 55, the pairs start repeating themselves:

(54, 56) is the same as (56, 54)

So, if you start with zero and go up to 55, you would have a total of 56 unique pairs of numbers that would sum to 110.

Hope this helps!

Good luck
Vesnalui [34]3 years ago
3 0
There is a lot of numbers
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sdas [7]

The answer is the option C and the option D, which are:

C. Double the number of pages in the book.

D. The age of my friend.

The explanation for this problem is shown below:

By definition, a variable is an unkown quantity. In the Option A the quantity is given: 60 seconds in a minute. In the option B you know the quantity too, which is 15 years old. But the option C and the option D does not give any quantity, you don't know the number of pages in the book or the age of the friend yet. Therefore, the answer is the options C and D.

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3 years ago
Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is
olganol [36]
<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0
3 years ago
Why did Washington respond so forcefully to the Whiskey Rebellion?
jeka57 [31]

Answer:

he felt that the new government had to show that it was capable of keeping order

Step-by-step explanation:

3 0
3 years ago
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Jobisdone [24]

price after discount- $44-$11=$33

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bill after discount and tip- $37.95

amount of tax- $2.83

total bill- $40.78

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A line passes through the points (-1, -6) and (-4, 3). What is the equation of this line in slope-intercept form?
g100num [7]

Since we have two ordered pairs, we can find the slope by plugging them into (y2-y1)/(x2-x1) which translates to (3-(-6))/(-4-(-1))=9/-3=-3

Since the slope is -3, we have the equation y=-3x+b, but we don't know b. So we plug in values for x and y and solve for b.

-6=-3(-1)+b

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So the y-intercept is -9 and the full equation is y=-3x-9 which means A is the only correct answer.

Hope this helped!

4 0
3 years ago
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