3x + 6y = 10 is the equation to determine of an apple x and the price of an orange y
<em><u>Solution:</u></em>
Let the price of each apple = $ x
Let the price of each orange = $ y
Martha bought 3 apples and 6 oranges
She had $10 in her wallet which was enough money for the purchase
Thus the equation is:
Total amount = 3 apples(price of each apple) + 6 oranges(price of each orange)
Thus we get,
Thus the equation is found
Answer:
For least material to be used lengths of square base and sides = 10 units.
Step-by-step explanation:
Let the lengths of the square base and the sides = x feet, x feet and y feet
Area of the square base = x² feet
Volume of the rectangular prism = Area of the square base × Height
= x²y cubic feet
1000 = x²y
y = -------(1)
Material used in the prism = Surface area of the rectangular prism
= 2(lb + bh + hl)
Here, h = height of the prism
l = length of the base
w = Width of the base
Material to be used (S) = 2(xy + x² + xy) - Area of lid
S = 2(x² + 2xy) - x²
S = x² + 2xy
Now by substituting the value of y from equation (1),
S = x² +
= x² +
For least amount of material used,
We will find the derivative of the given function and equate it to zero.
S' = 2x -
2x - = 0
2x³ = 2000
x³ = 1000
x = 10 feet
From equation (1),
y =
y = 10 feet
Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.
Answer:
20/7
Step-by-step explanation:
Check the picture
Answer:
89.0°
Step-by-step explanation:
The measure of arc CD is the same degree measure as the central angle.
To find the central angle use the right triangle.
The segment from the centre to the chord is a perpendicular bisector, thus
the third side of the triangle = 12.7 ÷ 2 = 6.35
Calculate one half of the central angle using the sine ratio and multiply by 2 for the whole central angle
sin( one- half ) = =
, hence
central angle = 2 × (
) ≈ 89.0°
Hence measure of CD ≈ 89.0°