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saw5 [17]
3 years ago
8

What is 4 (x-y) - 3 (x-y) ?

Mathematics
2 answers:
Anettt [7]3 years ago
7 0

Answer: x+y

Step-by-step explanation: 4x-4y-3x-3y

4x-3x is x

4y-3y is y

almond37 [142]3 years ago
4 0

Answer:

x-y

Step-by-step explanation:

First you must distribute:  

4(x-y)= 4x-4y

-3(x-y)=-3x+3y

4x-4y-3x+3y

Then combine like terms:

(be careful of negatives)

4x-<em>4y</em>-3x+<em>3y</em>

x-y

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Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
ladessa [460]

Answer:

(-2, 4, -2)

x=-2, y=4, z=-2.

Step-by-step explanation:

So we have the three equations:

4x-y-2z=-8\\-2x+4z=-4\\x+2y=6

And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

-2x+4z=-4

First, divide everything by -2 to simplify things:

x-2z=2

Subtract x from both sides. The xs on the left cancel:

(x-2z)-x=2-x\\-2z=2-x

Now, divide everything by -2 to isolate the z:

z=-\frac{2-x}{2}

So we've isolated the z variable. Now, do the same to the y variable in the third equation:

x+2y=6

Subtract x from both sides:

2y=6-x

Divide both sides by 2:

y=\frac{6-x}{2}

Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:

4x-y-2z=-8\\4x-(\frac{6-x}{2})-2(-\frac{2-x}{2})=-8

Distribute the third term. The -2s cancel out:

4x-(\frac{6-x}{2})+(2-x)=-8

Since there is still a fraction, multiply everything by 2 to remove it:

2(4x-(\frac{6-x}{2})+(2-x))=2(-8)

Distribute:

8x-(6-x)+2(2-x)=-16\\8x-6+x+4-2x=-16

Combine like terms:

8x+x-2x-6+4=-16\\7x-2=-16

Add 2 to both sides:

7x=-14

Divide both sides by 7:

(7x)/7=(-14)/7\\x=-2

Therefore, x is -2.

Now, plug this back into the second and third simplified equations to get the other values.

Second equation:

z=-\frac{2-x}{2}\\ z=-\frac{2-(-2)}{2}\\z=-\frac{4}{2}\\z=-2

Third equation:

y=\frac{6-x}{2}\\y=\frac{6-(-2)}{2}\\y=\frac{8}{2}\\y=4

Therefore, the solution is (-2, 4, -2)

3 0
3 years ago
Read 2 more answers
Find the area of the regular trapezoid. The figure is not drawn to scale. The top side is 4, the bottom side is 7, and both side
svp [43]
A regular trapezoid is shown in the picture attached.

We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5

Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:

AH = (AB - DC) ÷ 2
      = (7 - 5) ÷ 2
      = 2 ÷ 2
      = 1

Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²) 
      = √(5² - 1²)
      = √(25 - 1)
      = √24
      = 2√6

Last, we have all the information needed in order to calculate the area by the formula:

A =  \frac{(AB + CD)DH}{2}

A = (7 + 5) × 2√6 ÷ 2
   = 12√6

The area of the regular trapezoid is 12√6 square units.

7 0
3 years ago
Tabitha received $2,200 from her aunt as a birthday gift. She decided to put the money in an account to save for college. The ac
arsen [322]

3225.36

Step-by-step explanation:

8 0
3 years ago
Circle the difference 9 - 4=5
Igoryamba
5 is the difference.

Note: Minuend - Subtrahend = Difference
3 0
3 years ago
Read 2 more answers
Jim and Dianna want to save for their child’s college expenses. They find an annuity that pays 6% annual interest, compounded mo
lana66690 [7]

Answer:

future value = $49163.8

so required amount will be $491200 nearest $100

Step-by-step explanation:

given data

annual interest rate = 6 %

annuity = $300 per month

time period = 10 years

to find out

how much money will they have for the college expenses

solution

we know that effective rate will be

effective rate = \frac{0.06}{12}

effective rate = 5 × 10^{-3}

number of payment = 12 × 10 = 120

so future value will be express as

future value = annuity × \frac{(1+r)^t-1}{r}   .........1

future value = 300 × \frac{(1+5*10^{-3})^{120}-1}{5*10^{-3}}

future value = 300 × 163.8793  

future value = $49163.8

so required amount will be $491200 nearest $100

7 0
3 years ago
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