Arica planned to donate a total of $89 to four charities. She wanted to give twice as much to Charity A as she did to Charity B, but only one-fourth as much to Charity A as to Charity C. It worked out best if she gave $12 to Charity D. How much (in dollars) did she give to each of Charities A, B, and C
complete the steps to find the area of the trapezoid.
area of rectangle = 256 square units
area of triangle 1 = 24 square units
area of triangle 2 = 16 square units
area of triangle 3 = 96 square units
area of trapezoid = 120 square units
the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:
option a. true
comparing with the form a^2-2ab+b^2
solving for a: square root both sides of the equation:
solving for b: square root both sides of the equation:
to be a perfet square trinomial 2ab must be equal to 12x. let's check:
2ab = 2 (3x) (2)
2ab = 12x
your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.
suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?
what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:
here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.
we break up the number 652 into parts so that the leading digit stands on its own:
652 = 600 + 52
first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that
652 = 1*500 + 152
next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so
152 = 3*50 + 2
now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.
putting everything together, we found that
652 = 1*500 + 3*50 + 2
and we can rearrange this to write
652 = 5*100 + 5*30 + 2
652 = 5(100 + 30) + 2
652 = 5*130 + 2
so and .
you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.