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Alecsey [184]
3 years ago
9

I need help with multi step inequalities

Mathematics
1 answer:
vodomira [7]3 years ago
6 0

either

-(3x+3)-2x (less than) -4(x-2)-2

-3x+3-2x (less than) -4x +8-2

-5x+3 (less than)-4x+6

Or if you need it simplified

-5x +3 (less than) -4x+6

+4x                           4x

-x+3 (less than) 6

    -3                  -3

-x(less than) 3

(-x/-1) Less than (3/-1)

x (less than) -3

(didnt have the less than greater than sign so typed it)

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What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round nonint
leonid [27]

The right answer is c. –2.24, 2, 2.24


This question needs to be solved in two ways. First, using a graphing calculator. Next, using a system of equations.


1. Using a graphing calculator.


We have the following polynomial equation:

x^3-5x+5=2x^2-5


By ordering this equation we have:

x^3-2x^2-5x+10=0


So, we can say that this equation comes from a function given by:

f(x)=x^3-2x^2-5x+10


Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of f(x) which are:


x_{1}=-2.236 \\ \\ x_{2}=2 \\ \\ x_{3}=2.236


Finally, rounding noninteger roots to the nearest hundredth we have:


\boxed{Root_{1}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=2.24}


2. Using a system of equations.


The ordered equation is:

x^3-2x^2-5x+10=0


By arranging to factor out we have:

x^3-5x-2x^2+10=0


Then, by factoring:

x(x^2-5)-2(x^2-5)=0


Term (x^2-5) is a common factor, thus:


(x-2)(x^2-5)=0 \\ \\ (x-2)(x-\sqrt{5})(x+\sqrt{5})=0 \\ \\ Finally: \\ \\ \boxed{Root_{1}=-\sqrt{5}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=\sqrt{5}=2.24}

6 0
3 years ago
Read 2 more answers
Find how many quarts of 6% butterfat milk and 1% butterfat milk should be mixed to yield 75 quarts of 3% butterfat milk.
IgorC [24]

Answer:

30 gallons of 6% milk, and 45 gallons of 1% milk.

Step-by-step explanation:

x=quarts of 6% butterfat

<h2>First, write an equation.</h2>

0.06x+0.01(75-x)=0.03*75

<h2>Multiply both sides by 100.</h2>

0.06x*100+0.01*100(75-x)=100*0.03*75

<h2>Simplify</h2>

6x+75-x=3*75

6x+75-x=225

<h2>Solve</h2>

5x=225-75=150

5x=150

x=30

75-30=45

So, we need 30 gallons of 6% milk, and 45 gallons of 1% milk.

8 0
3 years ago
Read 2 more answers
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