Given:
Two identical parallelograms total area = 9 1/3 yd²
Each parallelogram has height 1 1/3 yd
Area formula: area = base × height
Split the total area equally to find each parallelogram's area.
Convert 9 1/3: (9*3)+1 = 28/3
Divide by 2: 28/3 × 1/2 = 28/6 yd², which is 4 4/6 yd² → 4 2/3 yd²
So each parallelogram's area is 4 2/3 yd²
Set up base × 1 1/3 yd = 4 2/3 yd²
Convert and divide: 14/3 yd² ÷ 4/3 yd = base
Multiply: 14/3 × 3/4 = base
Compute: 14*3 / 3*4 = base
42 / 12 = base
Which simplifies to 3 6/12 yd = base
or 3 1/2 yd = base
a) Each parallelogram has a base of 3 1/2 yards
b) If the two parallelograms form a rectangle:
Rectangle area = length × width
Length = 3 1/2 yd × 2 = 7 yds
Width = 3 1/2 yds
Area = 7 yd × 3 1/2 yd
Area = 7 × 7/2 yd²
Area = 7*7 / 2 yd²
Area = 49 / 2 yd²
Area = 24 1/2 yd²
Answer:
We require a total of 144 birthday candles for the 12 parties.
Step-by-step explanation:
As a caterer focused on children’s birthday celebrations, you have 12 events to cater to in the upcoming week, each requiring 2 cakes. Each cake will be adorned with 6 candles.
Thus, for all 12 birthday gatherings, you need a total of =
= 24 cakes.
Further, since every cake holds 6 candles, the overall number of candles for the 24 cakes amounts to =
= 144 candles.
Therefore, you will need 144 birthday candles to accommodate the 12 celebrations.
Answer:
quadratic
Step-by-step explanation:
Given
x²y - 2xy - 24y ← extract y from each term
= y(x² - 2x - 24) ← factors in quadratic form
To factor the quadratic
Identify the factors of the constant term (-24) that add up to the coefficient of the x-term (-2)
The relevant factors are -6 and +4, since
-6 × 4 = -24 and -6 + 4 = -2, thus
x² - 2x - 24 = (x - 6)(x + 4) and
x²y - 2xy - 24y = y(x - 6)(x + 4) ← expressed in factored form
