HELP PLEASE!! A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will they have less than 100 boxes remaining. Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.

Answer: These three planes are consistent and independent.

Explanation:

Since,  if the system of planes has a solution then it is  called Consistent, While, if it does not have any solution then it is called inconsistent.

Further, If the consistent system has infinite solution then it is dependent but if it has only a unique solution then it is called independent.

Here, given equations of planes are

12x+5y-3z=36           -------(1 )

x-2y+4z=3                 -------(2)

9x-10y+5z=27          -------(3)

From equation (1), 3z=12x+5y-36⇒z=4x+5y/3-12   ------(4)

after putting this value in equation (2) and (3), we will get two equation in variables x and y

So, x-2y+4(4x+5y/3-12)=3 ⇒x-2y+16x+20y/3-48=3⇒3x-6y+48x+20y-144=9⇒51x+14y=153   --------(5)

And, 9x-10y+5(4x+5y/3-12)=27⇒ 9x-10y+20x+25y/3-60=27⇒ 27x-30y+60x+25y-180=81⇒87x-5y=261   --------(6)

after solving equation equation (5) and (6) we will get x=3 and y=0

substituting these values in equation (4) we will get z=0

Thus the solution of these three plane (1), (2) and (3) is x=3, y=0 and z=o

Which is the unique solution, Thus the given planes are consistent and independent.

The given system of equations is consistent and independent so, [tex]\fbox{\begin\\\ \bf option (3)\\\end{minispace}}[/tex] is correct.

Further explanation:

A system of equations is said to be a consistent system if the solution exists and if the solution does not exist then it is an inconsistent system.  

If a consistent system has a unique solution then it is an independent system of equations but if the number of solutions is infinite then it is a dependent system of equations.

Label the given equations as shown below:

[tex]\boxed{x-2y+4z=3}[/tex]               …… (1)

[tex]\boxed{12x+5y-3z=36}[/tex]         …… (2)

[tex]\boxed{9x-10y+5z=27}[/tex]         …… (3)

The augmented matrix for the above equations is, as follows:

[tex]\left[\begin{array}{ccc}1&-2&4\\12&5&-3\\9&-10&5\end{array}\Biggm\vert\begin{array}{c}3\\26\\27\end{array}\right][/tex]

Apply row transformation [tex]R_{2}\rightarrow R_{2}-12R_{1}[/tex] and [tex]R_{3}\rightarrow R_{3}-9R_{1}[/tex] as,

[tex]\left[\begin{array}{ccc}1&-2&4\\0&29&-51\\0&8&-31\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]  

Now, apply row transformation [tex]R_{2}\rightarrow R_{2}-4R_{3}[/tex] and [tex]R_{3}\rightarrow R_{3}-3R_{2}[/tex] as,

[tex]\left[\begin{array}{ccc}1&-2&4\\0&-3&73\\0&-1&188\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]  

Now, apply row transformations [tex]R_{2}\rightarrow -R_{2}+2R_{3}[/tex] and [tex]R_{3}\rightarrow R_{3}+R_{2}[/tex] as,

[tex]\left[\begin{array}{ccc}1&-2&4\\0&1&303\\0&0&491\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]  

The equations obtained from the above augmented matrix are,

[tex]\begin{aligned}x-2y+4z&=3\\y+303z&=0\\491z&=0\end{aligned}[/tex]  

The first equation is simplified to obtain the value of z as,

[tex]\begin{aligned}491z&=0\\z&=0\end{aligned}[/tex]  

Substitute [tex]0[/tex] for [tex]z[/tex] in the equation [tex]y+303z=0[/tex]  to obtain the value of [tex]y[/tex] as,

[tex]\begin{aligned}y+(303\cdot0)&=0\\y&=0\end{aligned}[/tex]

Now, substitute [tex]0[/tex] for [tex]z[/tex] and [tex]0[/tex] for [tex]y[/tex] in the equation [tex]x-2y+4z=3[/tex] to obtain the value of [tex]x[/tex] as,

[tex]\begin{aligned}x-(2\cdot0)+(4\cdot0)&=3\\x&=3\end{aligned}[/tex]  

Therefore, the value of [tex]x[/tex] is [tex]3[/tex], the value of [tex]y[/tex] is [tex]0[/tex] and the value of [tex]z[/tex] is [tex]0[/tex] and the system has a unique solution.

Thus, the given system of equations is consistent and independent.

Option (1)

Here, the first option is inconsistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (1) is incorrect.

Option (2)

Here, the second option is consistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (2) is incorrect.

Option (3)

Here, the third option is consistent and independent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (3) is correct.

Option (4)

Here, the fourth option is inconsistent and independent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (4) is incorrect.

Learn more:

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Answer details

Grade: High school

Subject: Mathematics

Chapter: System of linear equations

Keywords: Equations, unique solution, independent, dependent, consistent, inconsistent, infinite solutions, homogeneous equation, non- homogeneous equation, determinant.

Answer:

  (3, 4) and (5, 12)

Step-by-step explanation:

The points where the two curves intersect are the solutions to the system of equations:

  (3, 4) and (5, 12)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: 35+(5+4)=35+5+4=40+4=44

When she finished the work, the time was 6:10 p.m. In other words, 6 hours and 10 minutes.

It says that she took 45 minutes to complete the work.

We need to find the time when she started working on it.

Start Time = Finish Time - time taken to complete work.

Start Time = (6 hours and 10 minutes) - 45 minutes

(Hint:- 1 hour = 60 minutes)

Start Time = (5 hours and 70 minutes) - 45 minutes

Start Time = 5 hours and 25 minutes i.e. 5:25 p.m.

It means that she started the work at 5:25 p.m.

The correct answer is C. 39.375 square feet.

The student's question pertains to finding the area of the actual banner when a scale transformation is applied to a triangular design. To calculate the area of the actual banner, we need to scale the base and the height of the triangle from the drawing size to the actual size and then use the formula for the area of a triangle.

First, we convert the measurements of the base and the height from inches to feet using the given scale of 1 inch = 1.5 feet:

We then apply the area formula for a triangle which is Area = (base × height) / 2:

Area = (7.5 feet × 10.5 feet) / 2 = 39.375 square feet

Therefore, the correct answer is C. 39.375 square feet.

Answer:

45

Step-by-step explanation:

60 + 55 + x + 20 = 180

135 + x = 180

x = 180 - 135 = 45

Answer: 45

its actually 1.5 but ok

Answer:

The correct option is B.

Step-by-step explanation:

It is given that Milo wants to make a mixture that is 50% lemon juice and 50% lime juice.

Milo has a juice mixture that is 20% lemon juice and 80% lime juice. Milo add a 100% lemon juice.

Let the 100% lemon juice added by milo be x.

In 4 gallon of mixture contains 50% lemon juice and 50% lime juice. It means 2 gallon  lemon juice and 2 gallon lime juice.

If we add 100% lemon juice, then the quantity of lime juice will remains same.

80% of the fist mixture is 2 gallon.

20% of the first mixture is 0.5 gallon.

It means the first mature contains 2 gallon lime juice and 0.5 gallon lemon juice.

Milo will add 100% lemon juice

[tex]2-0.5=1.5[/tex]

Therefore option B is correct.

Given

∠MQL=180°

∠XQR=180°

Hence ∠MQL=∠XQR

(We know that ∠MQL is the sum of ∠MQR and ∠RQL

and ∠XQR is the sum of ∠XQM and ∠MQR)

lets plug in these in our equation

∠MQL=∠XQR

∠MQR + ∠RQL = ∠XQM + ∠MQR

We can cancel out ∠MQR

hence ∠RQL = ∠XQM

hence we can infer that the opposite angles of intersecting lines are equal

similarly

∠MQR = ∠XQL

which is

125-10b = -5b+115

Hence the right option is A)

Answer:

120 sedans are in the fleet.

Step-by-step explanation:

A fleet of vehicles is comprised of 60 vans, 20 limos and X sedans.

It is given that 10% of all vehicles are limos.

Let all vehicles be n

10% × n = 20

0.10n = 20

n = [tex]\frac{20}{0.10}[/tex]

n = 200

Now we have to calculate the number of sedans.

So  60 vans + 20 limos + x sedans = 200

80 + x = 200

x = 200 - 80

x = 120

Therefore, 120 sedans are in the fleet.

Final answer:

By knowing that 10% of the fleet are limos and that there are 20 limos, we determine that the fleet has 200 vehicles. Subtracting the known number of vans and limos from the total, we find there are 120 sedans in the fleet.

Explanation:

To solve the problem, we need to determine the total number of vehicles in the fleet and use the information that 10% of all vehicles are limos. We know there are 60 vans and 20 limos already, and we want to find the number of sedans, denoted as X.

Since 10% of the vehicles are limos and there are 20 limos, that means there must be 200 vehicles in total (because 20 is 10% of 200).

So the equation to find the total number of vehicles is: 60 vans + 20 limos + X sedans = 200 vehicles.  We already know that there are 60 vans and 20 limos, so we can say: 60 + 20 + X = 200. Solving for X, we subtract 60 and 20 from 200: X = 200 - 80 = 120.

Therefore, there are 120 sedans in the fleet.

t = (C - 3*A)/B + 3

i dont know if its correct but hope it helps!

Answer: 9m^3

Step-by-step explanation:= 81^(1/2) * (m^6)^(1/2)

= 9 * m^(6*1/2)

= 9m^3

Answer:

30.2 mph

Step-by-step explanation:

Hello, I think I can help you with this

the speed average is the  is the quotient of the distance traveled and the time used to do it,  mathematical speaking

[tex]Average\ speed =\frac{distance}{time}\\[/tex]

Step 1

Put the values into the equation

Let

Distance:302 miles

Time:10  hours

[tex]Average\ speed =\frac{distance}{time}\\\\Average\ speed =\frac{302\ miles}{10\ hours}\\Average\ speed =30.2 \frac{miles}{hour} \\[/tex]

Average speed=30.2 mph

Have a great day.