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3 years ago

4. The celluloid bakery sells two types of cinnamon buns. They must sell at least 35 and not more than 95 cinnamon

Mathematics

1 answer:

Sauron [17]3 years ago

6 0

Answer: 35≤ x ≤95

x ≤ 2y

y≤125

Step-by-step explanation:

In an optimization problem, a constraint is a condition with variables that the solution must meet.

Let x = Number of cinnamon strawberry raisin buns.

y = Number of cinnamon chocolate mango buns baked.

"at least 35 and not more than 95 cinnamon strawberry raisin buns per day."

⇒ 35≤ x ≤95

"cinnamon strawberry raisin buns cannot exceed twice the number of cinnamon chocolate mango buns baked."

⇒ x ≤ 2y

" cinnamon strawberry raisin buns cannot exceed 125 per day"

⇒ y≤125

Hence, the constraints are:

35≤ x ≤95

x ≤ 2y

y≤125

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The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

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Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

$A=b^{2}$

where b is the length side of the square

we have

$A=49\ units^2$

substitute

$49=b^{2}$

$b=7\ units$

therefore

$AB=BE=ED=AD=7\ units$

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

$A=(AC)(AG)$

substitute the given values

$A=(9)(10)=90\ units^2$

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

$A=(DE)(DG)$

we have $DE=7\ units$

$DG=AG-AD=9-7=2\ units$

substitute $A=(7)(2)=14\ units^2$

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

$A=(EF)(CF)$

we have

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

substitute

$A=(3)(7)=21\ units^2$

step 5

sum the shaded areas

$14+21=35\ units^2$

step 6

Divide the area of of the shaded region by the area of ACIG

$\frac{35}{90}$

Simplify

Divide by 5 both numerator and denominator

$\frac{7}{18}$

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

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