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lakkis [162]
3 years ago
6

The sales tax for an item was $16.40 and it cost $410 before tax.

Mathematics
1 answer:
emmasim [6.3K]3 years ago
8 0

Answer:

4%

Step-by-step explanation:

410 plus 16.4 is 426.4 take away 16.4 then you got 410 it is 410+4%=426.4

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Solve the following System of Three Equations: x−3y+z=−15<br> 2x+y−z=−2<br> x+y+2z=1
jeyben [28]

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = -3 , y = 4 , z = 0

6 0
3 years ago
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
andrew-mc [135]

Answer:

f(x):

x =  - 4

g(x)

x = 1

Step-by-step explanation:

When a function is of the form:

f(x) = a {(x - h)}^{2}  + k

The equation of the axis of symmetry is

x = h

The given function is

f(x) = 3 {(x + 4)}^{2}  + 1

We can see that h=-4

Hence the equation of axis of symmetry is

x =  - 4

From the graph, the axis of symmetry of h(x) is the vertical line that divides the parabola into two congruent halves.

This line is

x = 1

4 0
3 years ago
0.000000205<br> In standard form
zalisa [80]

Answer:

2.05 × 10⁷

Step-by-step explanation:

0.000000205

We'll move the decimal point after the first non-zero digit (as per the scientific notation rules) and the standard form would be :

=> 2.05 × 10⁷

6 0
3 years ago
Read 2 more answers
An x-ray machine for animals cost $125,000. if the loan is for 10 years, and the interest paid is $65,625, what's the interest r
solong [7]
The answer is 59,375 there hope this helps
3 0
3 years ago
The redwood national park is home to some of the largest trees in the world. Hyperion is the tallest tree in the park, with a he
vladimir1956 [14]

Answer:

h= 126.33\ yd

Step-by-step explanation:

Let h be the height of the tree.

Given:

Height of the tree = 379 feet

We need to find the height of the tree in yards.

Solution:

From the given statement, Hyperion is the tallest tree in the park, with a height of approximately 379 feet,

We need to convert the height of the tree from feet to yard. So, We divide the height of the tree by three for yard.

For one feet

h = \frac{1}{3}\ yd

For 379 feet

h = \frac{379}{3}\ yd

h= 126.33\ yd

Therefore , height of the tree h= 126.33\ yd

3 0
3 years ago
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