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1 year ago

Jack is 27 years older than Susan. In 5 years he will be 4 times as old as she is. Find the present ages of jack and Susan

1 answer:

riadik2000 [5.3K]1 year ago

5 0

X - Jack's age
y - Susan's age

Jack is 27 years older than Susan.
$x=y+27$

In 5 years he will be 4 times as old as she is.
$x+5=4(y+5)$

The system of equations:
$x=y+27 \\ x+5=4(y+5) \\ \\ \hbox{substitute y+27 for x in the 2nd equation:} \\ y+27+5=4(y+5) \\ y+32=4y+20 \\ y-4y=20-32 \\ -3y=-12 \\ y=\frac{-12}{-3} \\ y=4 \\ \\ x=y+27=4+27=31$

Jack is 31 years old and Susan is 4 years old.

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1 year ago

Given ED, DB which statements about the figure are true? Check all that apply.

Klio2033 [76]

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EB is a segment bisector

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Step-by-step explanation:

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1 year ago

The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars

stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

= $253x-2x^2$

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

= 3*x

= 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= $253x-2x^2 - (3x + 6972)$

= $253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\$

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

$-2x^2+250x-6972=0\\$

now we have to solve the above equation for x

Dividing both sides by -2 we get

$x^2-125x+3486=0$

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

$x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\$

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

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2 years ago

A metal disc of 12cm in diameter and 5cm thick is melted down and cast into a cylindrical bar of diameter 5cm .How long is the b

Trava [24]

Answer:

d bar

Step-by-step explanation:

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1 year ago