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Stels [109]
3 years ago
13

To rewrite the expression ab+a+b+1, Jozelle first writes (ab+a) + (b+1). What property justifies this?

Mathematics
1 answer:
rodikova [14]3 years ago
7 0

Answer:

I believe it is associative property of addition or commutative

Step-by-step explanation:

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PLEASE HELP!!! 100 POINTS!
arlik [135]

Answer:

  x = 0; y = -6; z = 1

Step-by-step explanation:

You want to find the solution to the system of equations ...

  • 9x+y-3z=-9
  • 10x-y+2z=8
  • -10x-y+4z=10

<h3>Solution</h3>

This set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.

The attachment shows the solution to be ...

  (x, y, z) = (0, -6, 1)

__

<em>Additional comment</em>

Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.

Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.

  (9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]

  19x -z = -1 . . . . simplified

  (9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]

  -x +z = 1 . . . . simplified

At this point, we could graph the two equations, or we can proceed algebraically.

Adding these two equations gives ...

  (19x -z) +(-x +z) = (-1) +(1)

  18x = 0   ⇒   x = 0

Using the second of the reduced equations, we find ...

 -x +z = 1

  0 +z = 1   ⇒   z = 1

And using the second of the original equations, gives us ...

  10(0) -y +2(1) = 8

  -y = 6 . . . . . subtract 2

  y = -6 . . . . multiply by -1

Then the solution is (x, y, z) = (0, -6, 1), as above.

6 0
1 year ago
the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions
KIM [24]
Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft

6 0
3 years ago
When a new machine is not functioning properly, 15% of the items produced are defective. Assume that we will randomly select 5 p
cestrela7 [59]

Answer:

P(X<=2) = 0.9736

Step-by-step explanation: Please find the attached file for the solution

7 0
3 years ago
Write a equation of the lines passes through the given points (-2,7) (1,1) the equation is?
vredina [299]

The point-slope form:

y-y_1=m(x-x_1)

m - slope

(x₁, y₁) - point

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (-2, 7) and (1, 1). Substitute:

m=\dfrac{1-7}{1-(-2)}=\dfrac{-6}{3}=-2

y-7=-2(x-(-2))\\\\\boxed{y-7=-2(x+2)}   <em>point-slope form</em>

\boxed{y=-2x+3}     <em> slope-intercept form</em>

\boxed{2x+y=3}       <em>standard form</em>

7 0
3 years ago
What is the percent change from 1800 to 1926
Crank
The percentage change is 6.54%
You have to divide 1800÷1926, then multiply by 100 and you'd get 93.46, then subtract 100-93.46 which equals 6.54% :)
4 0
3 years ago
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