We can solve with a system of equations, and use c for the amount of cans of soup and f for the amount of frozen dinners.
The first equation will represent the amount of sodium. We know the (sodium in one can times the number of cans) plus (sodium in one frozen dinner times the number of dinners) is the expression for the total sodium. We also know the total sodium is 4450, so:
250c + 550f = 4450
The second equation is to find how many of each item are purchased:
c + f = 13
Solve for c in the second equation:
c = 13 - f
Plug this in for c in the first equation:
250(13-f) + 550f = 4450
3250 - 250f + 550f = 4450
300f = 1200
f = 4
Now plug the value for f into the second equation:
c + 4 = 13
c = 9
The answer is 9 cans of soups and 4 frozen dinners.
Answer: x=15
Step-by-step explanation: Since 3x+5 is equal to 50, you can write 3x+5=50, and 3x=45, x=15.
Answer:
The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.
Step-by-step explanation:
Volume of the Cylinder=400 cm³
Volume of a Cylinder=πr²h
Therefore: πr²h=400
Total Surface Area of a Cylinder=2πr²+2πrh
Cost of the materials for the Top and Bottom=0.06 cents per square centimeter
Cost of the materials for the sides=0.03 cents per square centimeter
Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)
C=0.12πr²+0.06πrh
Recall:
Therefore:
The minimum cost occurs when the derivative of the Cost =0.
r=3.17 cm
Recall that:
h=12.67cm
The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.
Answer:
Step-by-step explanation:
<h3>Solution 1</h3>
The figure (kite) is symmetric and covers half of the area of rectangle with sides 8 units aby 10 units
<u>The area of the rectangle:</u>
<u>The area of the kite:</u>
- A = 1/2*80 = 40 sq. units
<h3>Solution 2</h3>
Split the kite into two triangles and calculate their area and add up
<u>Triangle DCB has b = 8, h = 2 and has area:</u>
- A = 1/2*8*2 = 8 sq. units
<u>Triangle DAB has b = 8, h = 8 and has area:</u>
- A = 1/2*8*8 = 32 sq. units
<u>Total area:</u>
