First, lets determine the regular price of his purchase :
16.99 (3) + 34.99 (3) + 52.99 (2) + 5.99 (5) = 50.97 + 104.97 + 105.98 + 29.95 = 291.87
Therefore, the regular price of his purchase is $291.87 before sales tax.
If he receives 25% off of his total purchase, then the price is now :
291.87 * .75 = $218.90
We multiply by 75% because we are only paying 75% of the total purchase price since we received a 25% discount.
The total savings is
291.87 - 218.90 = $72.97
If sales tax is 10%, the total purchase price after sales tax is :
218.90 * 1.10 = $240.79
The sales tax is $21.89 since
240.79 -218.90 = 21.89
If he pays with 3 $100 bills, we should receive :
300 - 240.79 = $59.21
in change.
The television set has a rectangular shape. The diagonal of this rectangle along with its width and length together form a right angular triangle.
This means that we can apply the Pythagorean theorem which states that:
(diagonal)^2 = (length)^2 + (width)^2
Let the width be w. We know that the length is 0.75 times the width, this means that: length = 0.75 w
Substitute in the above equation:
(20)^2 = (0.75w)^2 + (w)^2
400 = 0.5625 w^2 + w^2
400 = 1.5625 w^2
w^2 = 256
w = 16
This means that the width of the screen is 16 in.
Answer:
Step-by-step explanation:
To obtain all coordinates of points (x,y) on the curve y = [(x - 5 )^6]/(x - 6 )^8, we deduce the value of X for which y is undefined as thus,
(x - 6 )^8 = 0
: (x - 6 ) = 0 : X=6
Therefore, all x-coordinates of points (x,y) on the curve are values of X < 6
Function 1:
f(x) = -x² + 8(x-15)f(x) = -x² <span>+ 8x - 120
Function 2:
</span>f(x) = -x² + 4x+1
Taking derivative will find the highest point of the parabola, since the slope of the parabola at its maximum is 0, and the derivative will allow us to find that.
Function 1 derivative: -2x + 8 ⇒ -2x + 8 = 0 ⇒ - 2x = -8 ⇒ x = -8/-2 = 4
Function 2 derivative: -2x+4 ⇒ -2x + 4 = 0 ⇒ -2x = -4 ⇒ x = -4/-2 ⇒ x= 2
Function 1: f(x) = -x² <span>+ 8x - 120 ; x = 4
f(4) = -4</span>² + 8(4) - 120 = 16 + 32 - 120 = -72
<span>
Function 2: </span>f(x) = -x²<span> + 4x+1 ; x = 2
</span>f(2) = -2² + 4(2) + 1 = 4 + 8 + 1 = 13
Function 2 has the larger maximum.
Answer:
sqrt(2)/2
Step-by-step explanation:
Sin(135) = sin(180-135) = sin(45)
= 1/sqrt(2) or sqrt(2)/2
sqrt: square root
