The product of two whole numbers is
416 and their sum is
42. What are the two numbers?

The two numbers are 16 and 26.

Step-by-step explanation:

We can solve this question using 2 simultaneous equations based on the given information from the question.

Let number 1 = x

Let number 2 = y

xy = 416 -> ( 1 )

x + y = 42 -> ( 2 )

We can use either substitution or elimination to solve simultaneous equations. For this question, we will use substitution as it is the easier and shorter option.

Make y the subject in ( 2 ):

x + y = 42 -> ( 2 )

y = 42 - x -> ( 3 )

Substitute ( 3 ) into ( 1 ):

xy = 416 -> ( 1 )

x ( 42 - x ) = 416

42x - x^2 = 416

-x^2 + 42x - 416 = 0

- [ x^2 - 42x + 416 ] = 0

- [ x^2 - 16x - 26x + 416 ] = 0

- [ x ( x - 16 ) - 26 ( x - 16 ) ] = 0

- ( x - 16 ) ( x - 26 ) = 0

x = 16 -> ( 4 ) , x = 26 -> ( 5 )

Substitute ( 4 ) into ( 3 ):

y = 42 - x -> ( 3 )

y = 42 - ( 16 )

y = 26

Substitute ( 5 ) into ( 3 ):

y = 42 - x -> ( 3 )

y = 42 - ( 26 )

y = 16

Therefore:

x = 16 , y = 26

x = 26 , y = 16

The two numbers are 16 and 26.

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.