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lidiya [134]
3 years ago
13

The quotient of n and 7 is 39

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
4 0

Let n = the unknown number.

Quotient tells you use division.

n/7 = 39

Multiply both sides by 7 to cancel out the number in the denominator and isolate the variable.

n = 39(7) = 273

n = 273

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100 Points PLEASE ANSWER ASP! Will Give BRAINLIST!
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.

Use substitution to solve the following system of equations.

4x + y = 284x+y=28

y = 3xy=3x

4 0
3 years ago
Read 2 more answers
A pair of numbers that has the sum of 12 and a difference of eight
anygoal [31]

Answer:

2 ; 10

Step-by-step explanation:

a + B = 12

a - B = 8

a = 12 - B

(12 - B) - B = 8

a = 12 - B

12 - 2B = 8

B = 2

A = 10

7 0
2 years ago
Work out the volume of a prism with an area of 10m squared and a length of 8m
Jobisdone [24]
Is it 80 m I think that’s the answer
4 0
3 years ago
Write the slope-intercept form of the equation of the line perpendicular to the
Anni [7]

Answer:

12x=4y........................................

6 0
2 years ago
. Could someone please explain this to me in detail. I am very confused. Thank you so much!. . A candle is 17 inches tall after
andrew-mc [135]

The generic equation of the line is:

H-H0 = m (T-T0)

Where,

m: slope of the line

(T0, H0): ordered pair belonging to the line.

The slope of the line is:

m =\frac{H2-H1}{T2-T1}

Substituting values we have:

m =\frac{15-17}{5-3}

Rewriting:

m =\frac{-2}{2}

m = -1

Then, choosing an ordered pair we have:

(T0, H0) :( 5, 15)

Substituting values we have:

H-15=-(T-5)

Rewriting the equation:

H-15=-T+5

H=-T+5+15

H=-T+20

Then, for 8 hours we have:

H=-8+20

H=12

Answer:

a linear equation to model the relationship between height H of the candle, and T time is:

H=-T+20

the candle will be 12 inches after burning 8 hours

7 0
2 years ago
Read 2 more answers
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