Please help I’ll mark you as brainliest if correct!

Step-by-step explanation:

x = number of quarters.

y = number of dimes.

z = number of pennies.

0.25x + 0.1y + 0.01× = 1.05

but it is not possible to find a combination of a subset of the coins to create exactly 1 (= the change for $1).

like to have only 3 quarters and 3 dimes (and no pennies). that makes $1.05, and no combination can create exactly $1.

as a consequence

x < 4 (because 4 quarters is $1, and more than 4 quarters is already more than $1.05).

z < 5 (because with 5 or more pennies, since the total sum is $1.05, if I simply remove 5 pennies, I get $1 with the other coins, no matter what combination they are).

with 1 or 2 or 3 or 4 pennies I cannot build a total sum of $1.05, as the other coins will can only build a sum that ends in 0 or in 5.

so, the sum of these other coins and 1, 2, 3, 4 pennies can never end in 5.

that means, we have 0 pennies.

that rules out to have 0 or 2 quarters, because then together with the dimes the sum can only end in 0 (and actually also give change for $1).

so, we can have only 1 or 3 quarters.

that means the solutions are

1 quarters and 8 dimes

or

3 quarters and 3 dimes.

1 quarter and 8 dimes (and 0 pennies) is the desired solution, because it contains more coins.

for the maximum amount of money built by coins not providing change for $1 we need to remember :

4 quarters are $1 (and would provide change for $1). so, we always need less than 4 quarters. but also at least 1 quarter to keep the sum from ending with a 0 (which would allow again to build $1).

10 dimes are $1 (and provide change for $1). we always need less than 10 dimes.

5 or more pennies would always allow to take away or fill up to create a sum that ends in 0 and therefore build $1. so, we always need less than 5 pennies.

that means again

1 or 3 quarters

max. 9 dimes

4 pennies.

if the the maximum possible sum would be higher than 1.19, then we could only increase in steps of 0.10 (dimes) : 1.29, 1.39, ...

if the sum is 1.29, I could remove 1 quarter and 4 pennies to make $1.

if it is 1.39, I could remove 1 quarter, 1 dime and 4 pennies to make $1.

and so on.

any sum >= 1 created incl. 4 or more quarters or 10 or more dimes or 5 and more pennies can always be reduced to a full $1.

$1.19 can only be built by 1 quarter and 9 dimes and 4 pennies, so that we cannot build $1 out of a subset, or by 3 quarters, 4 dimes and 4 pennies.

and 1 quarter, 9 dimes and 4 pennies has more coins.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

1st part is 64,000,000

2nd part 500,000

step-by-step explanation: