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Shtirlitz [24]
2 years ago
10

The sum of two integers with different signs is 16. What two integers fit this description?

Mathematics
1 answer:
Lana71 [14]2 years ago
3 0
-2 and 18 add to 16
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How does the Binomial Theorem’s use Pascal’s triangle to expand binomials raised to positive integer powers?
MrMuchimi

Answer:

There are  ways for quickly multiply out a binomial that's being raised by an exponent. Like

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = (a + b)(a + b)2 = (a + b)(a2 + 2ab + b2) = a3 + 3a2b + 3ab2 + b3

and so on and so on

but there was this mathematician named Blaise Pascal and he found a numerical pattern, called Pascal's Triangle, for quickly expanding a binomial like the ones from earlier. It looks like this

1                           1      

2                   1     2     1

3                1     3     3   1

4           1     4     6     4     1

5       1     5     10     10     5     1

Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n, where n is the row of the triangle.

Hope this helps!

5 0
2 years ago
Matthew sold 528 sets of dinnerware in a year.If each set contained 14 pieces.How many pieces were sold in all?​
Zina [86]
He sold 7392 sets this year
5 0
2 years ago
What is 6×9÷18+100-11+4
mojhsa [17]

6 × 9 ÷ 18 + 100 - 11 + 4

Use the order of operations to simplify:

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

6 × 9 ÷ 18 + 100 - 11 + 4

There are no parentheses or exponents, so multiplication comes first. Multiply 6 and 9.

54 ÷ 18 + 100 - 11 + 4

Next is division. Divide 54 by 18.

3 + 100 - 11 + 4

Finally, add and subtract from left to right.

103 - 11 + 4

92 + 4

96

<h3>Answer:</h3>

96

4 0
3 years ago
Where does the square root of 40 go on a 1-10 number line?​
kaheart [24]

Answer:

Step-by-step explanation:

36 < 40 < 49\\\\6 < \sqrt{40}  < 7\\

Here is the exact construction of √40 using Pythagorean 's theorem

8 0
2 years ago
The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\&#10;600 = (x+5)(x+4)\\&#10;600 =  x^{2} + 9x + 20&#10;

Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\&#10;x^{2} + 9x - 580 = 0\\&#10;(x + 29)(x - 20) = 0\\&#10;x + 29 = 0, \:\: x - 20 = 0\\&#10;x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
8 0
3 years ago
Read 2 more answers
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