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pishuonlain [190]
3 years ago
6

Johnny bought an oil painting originally priced at $80 but on sale for for 50% off. After 10% sales tax, what was the total cost

?
Mathematics
1 answer:
Alecsey [184]3 years ago
5 0

Answer:

$44

Step-by-step explanation:

Original price = $80

Discount on sale = 50%

Discounted price = (1 - 50%) * original price

Discounted price = 0.5 * $80 = $40

Sales tax = 10%

Sales tax amount = 0.1 * $40 = $4

Total cost = discounted price + sales tax amount

Total cost = $40 + $4 = $44

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an initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. how long will it take to double t
tino4ka555 [31]

Answer:

20 years

Step-by-step explanation:

9000/ 100= 900 = 10%

900/2= 450

450 x 2= 900

900 x 10= 9000

Now we multiply 10 by 2 because we doubled the value of our 450 into a 900 and now we get 20.

8 0
3 years ago
In a class of 20 students,12 were girls and the rest were boys
Ira Lisetskai [31]
It’s definitely A (:
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2 years ago
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Which points on the curve of x^2 - xy - y^2 = 5 have vertical tangent lines?
algol [13]

We need to differentiate this with respect to x to see if we can find an expression for the derivative of y at various points.  That will be the slope of the tangent to the curve.  Then we want to see where that derivative might be infinite -- i.e., where the tangent is vertical.

 

It's not written as a function, but it can still be differentiated using the chain rule:

 

x2 + xy + y2 = 3

(2x) + (x dy/dx + y dx/dx) + (2y dy/dx) = 0

 

(I used parentheses to show the differentiation of each term in the original equation.)

 

2x + x dy/dx + y + 2y dy/dx = 0

2x + y = -x dy/dx - 2y dy/dx

2x + y = dy/dx (-x -2y)

-(2x + y)/(x + 2y) = dy/dx

 

We have the derivative of y, but it's defined partly in terms of y itself.  That's OK.  Let's go on...

 

So where would the slope be infinite?  That would happen when x + 2y = 0, or y = -x/2

 

Let's plug that in for y in the original equation to find points where that's the case.

 

x2 + xy + y2 = 3

x2 + x(-x/2) + (-x/2)2 = 3

x2 - x2/2 + x2/4 = 3

3x2 / 4 = 3

x2 = 4

x = ±2

 

So we have two x values where the tangent might be vertical.  Let's plug them into the equation and see what the y values are.  First x = 2...

 

x2 + xy + y2 = 3

4 + 2y + y2 = 3

y2 + 2y + 1 = 0

(y + 1)2 = 0

y = -1

 

So at the point (2, -1) the tangent is vertical.

 

Now try x = -2...

 

x2 + xy + y2 = 3

4 - 2y + y2 = 3

y2 - 2y + 1 =0

(y - 1)2 = 0

y = 1

 

So at the point (-2, 1) the tangent is vertical.

8 0
2 years ago
Amy is helping plan her school's new basketball court. The west edge of the basketball court is located on the line y = 5x + 2.
Oksanka [162]

Answer:

5x-y=50

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

In this problem

The west edge of the basketball court is located on the line

y = 5x + 2 -----> the slope of this line is m=5

If the east edge cannot intersect with the west edge

then

east edge and west edge must be parallel

so

The east edge could be

5x-y=50

because

y=5x-50 ----> the slope of this line is m=5

5 0
3 years ago
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allsm [11]

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3 years ago
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