Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation 0.10d+0.05n=22.25. Select the THREE values (d, n) that could be solutions to the equation. ( 0 , 445 ) ( 0.50 , 435 ) ( 233 , 21 ) ( 118 , 209 ) ( 172 , 101 )

Correct options are:

a) ( 0 , 445 )

d) ( 118 , 209 )

e) ( 172 , 101 )

Step-by-step explanation:

A nickel is worth 5 cents $0.05

A dime is worth 10 cents = $0.10

The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation 0.10d+0.05n=22.25. Select the THREE values (d,n) that could be solutions to the equation.

a) ( 0 , 445 )

b) ( 0.50 , 435 )

c) ( 233 , 21 )

d)( 118 , 209 )

e)( 172 , 101 )

Verifying the options

a) ( 0 , 445 )

0.10d+0.05n=22.25.

= 0.10(0) + 0.05(445) = 22.25

= 22.25 = 22.25

Options a) is correct

b) ( 0.50 , 435 )

0.10d+0.05n=22.25.

= 0.10(0.50) + 0.05(435) = 22.25

= 21.8 ≠ 22.25

Option b is incorrect

c) ( 233 , 21 )

0.10d+0.05n=22.25.

= 0.10(233) + 0.05(21) = 22.25

= 24.35 ≠22.25

Option c is incorrect

d) ( 118 , 209 )

0.10d+0.05n=22.25.

= 0.10(118) + 0.05(209) = 22.25

= 22.25 = 22.25

Option d) is correct

e) ( 172 , 101 )

0.10d+0.05n=22.25.

= 0.10(172) + 0.05(101) = 22.25

= 22.25 = 22.25

Option e) is correct

answer: 1, 3 and 5 are correct

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.