Answer:
It is necessary four parameters.
Step-by-step explanation:
Since the augmented matrix of the consistent system has rank equal to three then the number of free variables is (number of unknows)-rank then there are 7-3=4 free variables. This means that are necessary four parameter to specify all solutions.
With dot plot if it’s symmetrical its the mean and MAD, so i think that.
Answer:
a rectangle is twice as long as it is wide . if both its dimensions are increased 4 m , its area is increaed by 88 m squared make a sketch and find its original dimensions of the original rectangle
Step-by-step explanation:
Let l = the original length of the original rectangle
Let w = the original width of the original rectangle
From the description of the problem, we can construct the following two equations
l=2*w (Equation #1)
(l+4)*(w+4)=l*w+88 (Equation #2)
Substitute equation #1 into equation #2
(2w+4)*(w+4)=(2w*w)+88
2w^2+4w+8w+16=2w^2+88
collect like terms on the same side of the equation
2w^2+2w^2 +12w+16-88=0
4w^2+12w-72=0
Since 4 is afactor of each term, divide both sides of the equation by 4
w^2+3w-18=0
The quadratic equation can be factored into (w+6)*(w-3)=0
Therefore w=-6 or w=3
w=-6 can be rejected because the length of a rectangle can't be negative so
w=3 and from equation #1 l=2*w=2*3=6
I hope that this helps. The difficult part of the problem probably was to construct equation #1 and to factor the equation after performing all of the arithmetic operations.
The rationalized expression in general term is given by: (-8 -4√2) / 3
<h3>What is rationalization?</h3>
Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(8√2 / 6-3√8 ) Multiply by ( 6+3√8)/( 6+3√8)
(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)
8√2(6+3√8) / (6-3√8)² Expand the denominator using the FOIL method.
8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)
8√2(6+3√8) / -36
48√2 + 24√2√8 / -36 ::::. √8 = 2√2
48√2 + 96 / -36
-12(4√2 + 8) / 12x3
(-8 -4√2) / 3 is the result.
Learn more about rationalization in:
brainly.com/question/14261303
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Answer:
-5x + 7
Step-by-step explanation:
-4x - 2y = -2
x - 2y = 9
First, you're going to subtract the equations from each other.
(-4x - 2y = -2) - (x - 2y = 9)
Next, you need to get rid of the equal sign in both equations.
(-4x - 2y = -2) - (x - 2y = 9)
+2 +2 -9 -9
After you get rid of the equal signs, you will distribute the sign to the equation and then subtract everything.
-4x - 2y + 2 - x + 2y + 9
Now, combine the like terms.
(-4x -x) + (-2y + 2y) + (2 + 9)
Finally, calculate the terms and solve.
-5x + 7
