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r-ruslan [8.4K]
3 years ago
15

Assume federal exemption is, $3300.00, you earn. 37,500.00, the tax rate is 2 3/4%, calculate the tax.

Mathematics
1 answer:
Sauron [17]3 years ago
3 0
3300 exemption

37,500−3,300=34,200 taxable
Tax rate is
2+3/4=2.75% we don't multiply 2by 3/4
Now calculate the amount of tax
34,200×2.75%=940.5
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{4x-2y+5z=6 <br> {3x+3y+8z=4 <br> {x-5y-3z=5
lesya692 [45]

There are three possible outcomes that you may encounter when working with these system of equations:


  •    one solution
  •    no solution
  •    infinite solutions

We are going to try and find values of x, y, and z that will satisfy all three equations at the same time. The following are the equations:

  1. 4x-2y+5z = 6
  2. 3x+3y+8z = 4
  3. x-5y-3z = 5

We are going to use elimination(or addition) method

Step 1: Choose to eliminate any one of the variables from any pair of equations.

In this case it looks like if we multiply the third equation by 4 and  subtracting it from equation 1, it will be fairly simple to eliminate the x term from the first and third equation.

So multiplying Left Hand Side(L.H.S) and Right Hand Side(R.H.S) of 3rd equation with 4 gives us a new equation 4.:

4. 4x-20y-12z = 20      

Subtracting eq. 4 from Eq. 1:

(L.HS) : 4x-2y+5z-(4x-20y-12z) = 18y+17z

(R.H.S) : 20 - 6 = 14

5. 18y+17z=14

Step 2:  Eliminate the SAME variable chosen in step 2 from any other pair of equations, creating a system of two equations and 2 unknowns.

Similarly if we multiply 3rd equation with 3 and then subtract it from eq. 2 we get:

(L.HS) : 3x+3y+8z-(3x-15y-9z) = 18y+17z

(R.H.S) : 4 - 15 = -11

6. 18y+17z = -11

Step 3:  Solve the remaining system of equations 6 and 5 found in step 2 and 1.

Now if we try to solve equations 5 and 6 for the variables y and z. Subtracting eq 6 from eq. 5 we get:

(L.HS) : 18y+17z-(18y+17z) = 0

(R.HS) : 14-(-11) = 25

0 = 25

which is false, hence no solution exists



3 0
2 years ago
At a local store, kelly and martin bought some notebooks and pencils. Kelly bought 4 notebooks and 25 pencils for 16.71. Martin
Nat2105 [25]
Let n = cost of 1 notebook
Let p = cost of 1 pencil

Then,

3n + 4p = 8.5
5n + 8p = 14.5

You can solve for one variable in terms of the other and then substitute into the remaining equation.

3n + 4p = 8.5
+ 5n + 8p = 14.5

Multiply the top equation by -2 so that the p-containing terms cancel each other out:

-2(3n + 4p = 8.5)
+ 5n + 8p = 14.5
-n + 0 = -2.5

So after dividing both sides by -1, we see that n = $2.5. Plugging into the first equation gives p = $0.25.


3n + 4p = 8.5
5n + 8p = 14.5
6 0
3 years ago
A van travels at a constant speed of x km/hr over a distance of 45km/hr. If the van increases its speed by 4km/h, it will be abl
harkovskaia [24]
Speed = Distance/Time. Let speed be V, distance D and time T

a)Given: D₁ =45km, V₁=x km/h 
V₁=D₁/T
V₁=45/T OR T= 45/V₁

b) Given : D₂ =48 km and V₂ = V₁ + 4 km/h
V₂ = 48/T, but V₂ = V₁+4, then:

V₁+4 = 48/T OR  T=48/(V₁+4). Since Time is same, then we can write:
45/V₁ =48/(V₁+4), solve for V₁:
45V₁ + 180 = 48V₁

3V₁ =180 and V₁ = x = 60 km/h
8 0
3 years ago
The points scored on a test for a sample of
jasenka [17]

Answer:

The mean is 42.6

Step-by-step explanation:

6+90+16+80+15 + 70 + 4 + 60 = 341 \\ there \: are \: 8 \: numbers \: in \: total \: so \: you \: divide \: the \: sum \\ by \: 8. \\ 341 \div 8 = 42.625  \\ mean≈42.6

5 0
3 years ago
What is the vertical change from Point A to Point B? What is the horizontal change from Point A to Point B? 8 7 6 What is the ra
Yuri [45]

9514 1404 393

Answer:

  • vertical change: 1 unit
  • horizontal change: 2 units
  • rate of change: 0.5

Step-by-step explanation:

The marks on the graph show the vertical change is 1 unit, and the horizontal change is 2 units.

The "rate of change" is the ratio of vertical change to horizontal change:

  rate of change = slope = Δy/Δx = 1/2 = 0.5

Expressed as a decimal, the rate of change is 0.5.

7 0
2 years ago
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