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xxTIMURxx [149]
3 years ago
5

The domain of a function is given by {-4,2,8}. If the function is defined by y= x +1 /3 ,then which of the following values is a

member of the range?
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
5 0

Answer:

{-1, 1, 3}

Step-by-step explanation:

Given the function

y = (x + 1)/3

The domain are the input value x while the range are the output values given the input value x;

Given the domain {-4, 2, 8}

when x = -4;

y = (-4+1)/3

y = -3/3

y = -1

when x = 2;

y = (2+1)/3

y = 3/3

y = 1

when x = 8;

y = (8+1)/3

y = 9/3

y = 3

Hence the member of the range are {-1, 1, 3}

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3t=−29

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VikaD [51]

Let's work to solve this system of equations:

y = 2x ~~~~~~~~\gray{\text{Equation 1}}y=2x        Equation 1

x + y = 24 ~~~~~~~~\gray{\text{Equation 2}}x+y=24        Equation 2

The tricky thing is that there are two variables, xx and yy. If only we could get rid of one of the variables...

Here's an idea! Equation 11 tells us that \goldD{2x}2x and \goldD yy are equal. So let's plug in \goldD{2x}2x for \goldD yy in Equation 22 to get rid of the yy variable in that equation:

\begin{aligned} x + \goldD y &= 24 &\gray{\text{Equation 2}} \\\\ x + \goldD{2x} &= 24 &\gray{\text{Substitute 2x for y}}\end{aligned}  

x+y

x+2x

​    

=24

=24

​    

Equation 2

Substitute 2x for y

​  

Brilliant! Now we have an equation with just the xx variable that we know how to solve:

x+2x3x 3x3x=24=24=243=8Divide each side by 3

Nice! So we know that xx equals 88. But remember that we are looking for an ordered pair. We need a yy value as well. Let's use the first equation to find yy when xx equals 88:

\begin{aligned} y &= 2\blueD x &\gray{\text{Equation 1}} \\\\ y &= 2(\blueD8) &\gray{\text{Substitute 8 for x}}\\\\ \greenD y &\greenD= \greenD{16}\end{aligned}  

y

y

y

​    

=2x

=2(8)

=16

​    

Equation 1

Substitute 8 for x

​  

Sweet! So the solution to the system of equations is (\blueD8, \greenD{16})(8,16). It's always a good idea to check the solution back in the original equations just to be sure.

Let's check the first equation:

\begin{aligned} y &= 2x \\\\ \greenD{16} &\stackrel?= 2(\blueD{8}) &\gray{\text{Plug in x = 8 and y = 16}}\\\\ 16 &= 16 &\gray{\text{Yes!}}\end{aligned}  

y

16

16

​    

=2x

=

?

2(8)

=16

​    

Plug in x = 8 and y = 16

Yes!

​  

Let's check the second equation:

\begin{aligned} x +y &= 24 \\\\ \blueD{8} + \greenD{16} &\stackrel?= 24 &\gray{\text{Plug in x = 8 and y = 16}}\\\\ 24 &= 24 &\gray{\text{Yes!}}\end{aligned}  

x+y

8+16

24

​    

=24

=

?

24

=24

​    

Plug in x = 8 and y = 16

Yes!

​  

Great! (\blueD8, \greenD{16})(8,16) is indeed a solution. We must not have made any mistakes.

Your turn to solve a system of equations using substitution.

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Volume is a three-dimensional scalar quantity. The cost of the glass is $1312.24.

<h3>What is volume?</h3>

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

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Given the cost of glass is $0.20 per square meter, therefore, the cost of the glass of the base will be,

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Hence, the cost of the glass is $1312.24.

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