The price of an item was increased twice by the same percent. by what percent was the second increase if the item became 1.44 times more expensive?

20%

Step-by-step explanation:

Lets start solving the problem step by step,

here in this problem it is asked that the price of an item was increased twice by the same percent. by what percent was the second increase if the item became 1.44 times more expensive.

the best way of solving such kind of problems is to consider the number as 100 because it will be more easier to calculate its percent e.g. if you want to calculate 30% of 100 then it will be 30/100*100=30% and like that.

now further it is mentioned that the item was increased twice by the same percent means both time the same percentage increase was there.

it will make easy to guess it now ,

just start taking guesses fro  minimum to max percent values.

take 10% now if first time there is 10% increase then the value will become 110 as the item was increased twice by the same percent so 10% of 110 will become 11 adding it to 110 will be 121 i.e w can say that the item value 100 will become 1.21 time that of original value 100.

now we get an idea that the percent of increase should be more than 10 percent as for 10% the item is getting only 1.21& expensive but we will need a percent increase for which item value must become 1.44 percent of its original value.

so now consider 20% as the increase in the item value each time.

for the first increase 20% of 100=20 and it becomes 120 after first increase.

now again we have to increase it by 20% for the second time as it is mentioned in the question.

Now 20% of 120 will give 24 and it becomes 144 after second increase.

so we can say that the number is increased by 1.44 percent of itself.

thus the percent by which the second increase should be done to make it 1.44 time more expensive is 20%

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: