Casey is making a flower arrangement with roses(r) and carnations(c). the cost of each rose is $0.50 and the cost of each carnation is $0.10. the arrangement has a total of 80 flowers and the flower cost was $20. how many of each flower did casey put in her arrangement?

which system of equations matches the situation?

the system is:

r + c = 80

r*0.5 + c*0.1 = 20

Step-by-step explanation:

each rose costs $0.50

each carnation costs $0.10

The number of roses is r, and the number of carnations is c.

the arrangement has a total of 80 flowers, so we have that:

r + c = 80

the cost is $20, so we have:

r*0.5 + c*0.1 = 20

so our system of equations is:

r + c = 80

r*0.5 + c*0.1 = 20

and we can also solve it; for this isolate one of the variables in the first equation:

r = 80 - c

now let'r replace this in the second equation:

(80 - c)*0.5 +c*0.1 = 20

40  - c*0.4 = 20

c = 20/0.4 = 50

this means that we have 50 carnations, and the other 30 are roses.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the circumference of a circle is, 10.676 cm.

step-by-step explanation:

the formula for circumference of a circle is given by:

where

c is the circumference of a circle and

d is the diameter of a circle.

given: diameter(d) = 3.4 cm and use

substitute these values in [1] we get;

cm

therefore, the circumference of a circle is, 10.676 cm