What is the angle of rotation of 9x^(2)+4xy+5y^(2)-40=0?

A store is having a 20 percent off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of h

ArbitrLikvidat [17]

Answer:

$65

Step-by-step explanation:

Given

Percentage discount = 20%

Equivalent amount saved = $13

Let the original price of the product be x

To get x;

20% of x = 13

0.2x = 13

0.2x = -13

0.2 = 13

x = 13/0.2

x = $65

Hence the original price of the product is $65

3 0

2 years ago

A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the boat in still water

Paha777 [63]

Answer:

Speed of the boat in still water = 6.125 miles/hour

Step-by-step explanation:

We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.

We are to find the speed of the boat in the still water.

Assuming $S_b$ to be the speed of the boat in still water and $S_w$ to be the speed of the water.

The speeds of the boat add up when the boat and water travel in the same direction.

$Speed = \frac{distance}{time}$

$S_b+S_w=\frac{d}{t_1}=\frac{33 miles}{4 hours}$

And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.

$S_b-S_w=\frac{d}{t_2}=\frac{33 miles}{7 hours}$

Adding the two equations to get:

$S_b+S_w=\frac{d}{t_1}$

+ $S_b-S_w=\frac{d}{t_2}$

___________________________

$2S_b=\frac{d}{t_1} +\frac{d}{t_2}$

Solving this equation for $S_b$ and substituting the given values for $d,t_1, t_2$ :

$S_b=\frac{(t_1+t_2)d}{2t_1t_2}$

$S_b=\frac{(4 hour + 7hour)33 mi}{2(4hour)(7hour)}$

$S_b=\frac{(11 hour)(33mi)}{56hour^2}$

$S_b=6.125 mi/hr$

Therefore, the speed of the boat in still water is 6.125 miles/hour.

6 0

3 years ago

Read 2 more answers

A right triangle has a hypotenuse of length 99 inches. if one angle is 34 degrees34°, find the length of each leg.

Andreyy89

Sine (34) = opposite / 99
opposite side = .55919 * 99
opposite side = 55.35981 

Adjacent side² = 99² - 55.35981²
Adjacent side² = 9,801 -3,064.7085632361 
Adjacent side² = 6,736.29 
Adjacent side = 82.0749

5 0

3 years ago

Assume that the pond contains 90 fish: 64 purple, 25 green, and 1 red. A contestant pays $0.55 to randomly catch one fish and re

Licemer1 [7]

Answer:

The carnival is losing (on average) $0.15 on each play

Step-by-step explanation:

To find out how much the carnival wins or looses in each play one subtract the expected value (EV) from each play from the amount charged by the carnival for each play ($0.55). If the expected value is higher than what the carnival charges, the carnival is losing money.

Expected is the sum of the payouts of each bet multiplied by its likelihood:

$EV= \frac{64*0.40+25*1.15+1*9.00}{90}\\EV= 0.70$