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Sonja [21]
3 years ago
11

There are currently 20 members in the school's Ski Club and the dues are $10 per member. To encourage the recruiting of new memb

ers, the club treasurer suggests that for each new member recruited, the dues for all members will be reduced by 10 cents. Write an equation in standard form to represent this situation.
Mathematics
1 answer:
guajiro [1.7K]3 years ago
8 0

Answer:

f(n)=-0.10n^2+8n+200

Step-by-step explanation:

Let n represent number of new members and f(n) represent membership money.

We have been given that there are currently 20 members in the school's Ski Club. So when n new members join, the total number of members would be 20+n.

Since for each new member recruited the dues for all members will be reduced by 10 cents, so new dues would be 10-0.10n.

The membership money would be number of total members times dues as:

f(n)=(20+n)(10-0.10n)

Since we need our equation in standard form, so we will use FOIL to expand our equation as:

f(n)=20(10)-20(0.10n)+n(10)-n(0.10n)

f(n)=200-2n+10n-0.10n^2

f(n)=200+8n-0.10n^2

f(n)=-0.10n^2+8n+200

Therefore, our required equation would be f(n)=-0.10n^2+8n+200.

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Answer:

The rectangle has a width of 18 inches and a height length of 8 inches.

Step-by-step explanation:

The perimeter of a rectangle is described by the equation:

p = 2w + 2l

where <em>l</em> is width, <em>h</em> is height, and <em>p</em> is perimeter.

We're also told that the total perimeter is 52 inches.

We're also told that the length is six inches less than three times the width.  We can express that as w = 3l - 6.

We can plug that definition of w into the perimeter equation to find the length:

p = 2w + 2l\\52 = 2(3l - 6) + 2 * l\\52 = 6l - 12 + 2l\\52 + 12 = 8l\\8l = 64\\l = 64/8\\l = 8

Now we can take that and the given perimeter, and substitute those into the perimeter equation to find the width:

p = 2w + 2l\\52 = 2w + 2(8)\\52 = 2w + 16\\36 = 2w\\w = 36 / 2\\w = 18

So the width is 18

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