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4 years ago

4 + 3r - 5r = -4r + 4

Mathematics

2 answers:

ioda4 years ago

7 0

Answer:

r= 0

Step-by-step explanation:

Cancel equal terms on both sides of the equation:

= 3r - 5r = -4r

collect like terms

= -2r = -4r

move variable to left and change its sign

= -2r + 4r = 0

collect like terms

= 2r = 0

divide both sides of the equation by 2

r=0

FinnZ [79.3K]4 years ago

5 0

Answer:

Step-by-step explanation:

$4 + 3r - 5r = -4r + 4\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\4+3r-5r-4=-4r+4-4\\\\Simplify\\3r-5r=-4r\\\\\mathrm{Add\:similar\:elements:}\:3r-5r=-2r\\-2r=-4r\\\\\mathrm{Add\:}4r\mathrm{\:to\:both\:sides}\\-2r+4r=-4r+4r\\\\Simplify\\2r=0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\frac{2r}{2}=\frac{0}{2}\\\\Simplify\\r=0$

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3 years ago

In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the function with its graph

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Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

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Step-by-step explanation:

We know that the function f(x) is:

$f(x)=(x-2)^{2}+1$

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

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$2(x-3)=0$

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Puting it on g(x) we will get y value.

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$y=g(3)=1$

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

$g(x)=f(x+2)$

$g(x)=((x+2)-2)^{2}+1$

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

$0=2x$

$x=0$

Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

$g(0)=1$

Then, the minimum point of this function is (0,1) and it corresponds to (C)

47)

Let's use the same method here.

$g(x)=f(x)+2$

$g(x)=(x-2)^{2}+1+2$

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

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$g(2)=(2-2)^{2}+3$

$g(2)=3$

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

$g(x)=f(x)-3$

$g(x)=(x-2)^{2}+1-3$

$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

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$g(2)=(2-2)^{2}-2$

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Then, the minimum point of this function is (2,-2) and it corresponds to (D)

I hope it helps you!

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