MATHEMATICS MIDDLE SCHOOL

Jonathan is making his favorite pasta dish. He serves his mom 1/12 of the pot of pasta and his brother 1/6 of the pot. How much of the pot is left over?

Answers

Answer 1

Answer:

Answer: $(1)/(4)$ of the pot is left.

Step-by-step explanation:

Let x be the total amount of pasta in the pot .

Then the amount of pasta her mother got= $(1)/(12)x$

The amount of pasta her brother got= $(1)/(6)x$

The total amount of pasta he serve= $(1)/(12)x+(1)/(6)x$

First convert them in like fractions,then

The total amount of pasta he serve= $(1)/(12)x+(2)/(12)x=(x+2x)/(12)=(3x)/(12)=(1)/(4)x$

Hence, $(1)/(4)$ of the pot is left over.

Answer 2

Answer: 1/6 also is 2/12. So, there is 9/12 of the pasta left.

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The store paid $4.50 for a book and sold it for $7.65. What is the profit as a percent of the cost to the store?

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Answer:

3.00 i think

Step-by-step explanation:

Answer:

$4.00

Step-by-step explanation:

The point P(x,y) lies on the terminal side of an angle theata = -60 degrees in standard position. What are the signs of the values of x and y

Answers

Answer:

Step-by-step explanation:

andre has 4 times as many model cars as Peter , and Peter has one-third as many model cars as jade . andre has 36 model cars . a: write and solve an equation to find how many model cars Peter has . b: using your answer fir part a ,write and solve an equation to find how many model cars jade has.

Answers

Answer:

a: 9

b: 27

Step-by-step explanation:

Let's define

P = amount of model cars that Peter has

J =amount of model cars that Jade has

A = amount of model cars that Andre has

a: We need to find out how many model cars does Peter have, i.e. we need to find out P.

We know that Andre has 36 model cars and he has 4 times as many model cars as Peter. If we write that as an equation, we have

A = 4*P = 36

Now we just have to divide by 4:

4*P/4 = 36/4

P = 9

Peter has 9 model cars.

b: Now we need to find out how many model cars does Jade have, i.e. we need to find out J.

We will resolve it as in part a:

Peter has 9 model cars and he has one-third as many model cars as Jade, that is

P = 1/3*J = 9

We multiply by 3 and we have:

1/3*J*3 = 9*3

J = 27

Jade has 27 model cars.

p = how many cars Peter has
j = how many cars Jade has
a = how many cars Andre has
p x 4 = how many cars Andre has (36 model cars)
>>>TO FIND HOW MANY MODEL CARS PETER HAS:
p x 4 = 36
36 / 4 = 9
your equation to find how many model cars Peter has is:
36 / 4 = 9
So, Peter has 9 model cars.
>>>TO FIND HOW MANY MODEL CARS JADE HAS:
36 / 4 = how many cars Peter has (9)
Now, you are given the info that Jade has THREE TIMES (3x) as many cars as Peter already.
So, your equation for this one is:
9 x 3 = 27
So Jade has 27 model cars.

---- Jade has 27 model cars.
---- Andre has 36 model cars.
---- Peter has 9 model cars.

equation for a. 36 / 4 = p
equation for b. 9 x 3 = j

Solve the linear system1).5x + 4y = 16
y = -16

2). 3x + 6y = 15
-2x + 3y = -3

3). 7y = -14x + 42
7y = 14 x + 14

Answers

1.5x+4y=16
5x+4(-16)=16
5x-64=16
5x=80
x=16

2.3x+6y=15
-2x+3y=-3

Multiply the 2nd equation by 2

3x+6y=15
-4x+6y=-6
7x=9
x=9/7

3x+6y=15
3(9/7)+6y=15
27/7+6y=15
6y=78/7
y=78/42 or 39/21 or 13/7

3.7y = -14x + 42
7y = 14 x + 14

-14x+42=14x+14
-28x=-28
x=1

$1)\n \n\begin{cases} 5x + 4y = 16 \n y=-16\end{cases} \n \n \begin{cases} 5x + 4*(-16) = 16 \n y=-16\end{cases} \n \n \begin{cases} 5x -64 = 16 \n y=-16\end{cases}$

$\begin{cases} 5x = 16 +64\n y=-16\end{cases} \n \n \begin{cases} 5x =80/:5 \ \n y=-16\end{cases} \n \n \begin{cases} 5x = 16 +64\n y=-16\end{cases} \n \n \begin{cases} x =16\n y=-16\end{cases}$

$2)\n \n\begin{cases} 3x+6y=15 \n -2x + 3y = -3 \end{cases} \n \n\begin{cases} 3x = 15-6y \ /:3 \n -2x + 3y = -3 \end{cases} \n \n \begin{cases} x = 5-2y \n -2*(5-2y) + 3y = -3 \end{cases} \n \n\begin{cases} x = 5-2y \n -10+4y + 3y = -3 \end{cases} \n \n$

$\begin{cases} x = 5-2y \n 7y = -3+10 \end{cases} \n \n \begin{cases} x = 5-2y \n 7y = 7 \ /:7\end{cases} \n \n \begin{cases} x = 5-2 *1 \n y =1 \end{cases} \n \n \begin{cases} x = 3 \n y = 1 \end{cases} \n \n$

$3)\n \n\begin{cases} 7y = -14x + 42 \n 7y = 14 x + 14 /:7 \end{cases} \n \n\begin{cases} 7*(2x+2) = -14x + 42 \n y = 2 x + 2 \end{cases} \n \n \begin{cases} 14x+14 = -14x + 42 \n y = 2 x + 2\end{cases} \n \n \begin{cases} 14x+ 14x = 42 -14 \n y = 2 x + 2 \end{cases}$

$\begin{cases} 28x = 28 \ /:28 \n y = 2 x + 2 \end{cases}\n \n\begin{cases} x = 1 \n y = 2 *1+ 2\end{cases}\n \n\begin{cases} x = 1 \n y = 4 \end{cases}$

14+x=46;x=32

whats the answer im so stuck

Answers

The solution to your problem would be that x = 32; or just 32. You did all the heavy lifting!

so it say that x is equal to 32 so you equation must look like this
14+32=45

Is this correct. if it is how do I put 2 10/25 as minutes and if wrong tell me how to do it

Answers

yes that is the answer

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