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GenaCL600 [577]
4 years ago
8

A baseball team fundraiser collected​ $2,400 from the sale of balloons and banners. The amounts earned from balloons and banners

were equal. Balloons sold for​ $3, and banners sold for​ $4. How many of each were​ sold?
Mathematics
2 answers:
dmitriy555 [2]4 years ago
4 0
400 balloons and 300 banners
kumpel [21]4 years ago
3 0

Answer:

  • 400 balloons
  • 300 banners

Step-by-step explanation:

If the amounts earned from the sale of each item were the same, then both amounts were $2400/2 = $1200.

The number of balloons sold at $3 each was $1200/$3 = 400.

The number of banners sold at $4 each was $1200/$4 = 300.

400 balloons and 300 banners were sold.

___

<em>Check</em>

Total sales was ...

  $3 × 400 + $4 ×300 = $1200 +1200 = $2400 . . . answer checks OK

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If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.
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There's no if about it, 

f(x)=x^3+3x^2-x-3&#10;

has a zero f(1)=0 so x-1 is a factor.   That's the special case of the Remainder Theorem; since f(1)=0 we'll get a remainder of zero when we divide f(x) by x-1.

At this point we can just divide or we can try more little numbers in the function.  It doesn't take too long to discover f(-1)=0 too, so  x+1 is a factor too by the remainder theorem.  I can find the third zero as well; but let's say that's out of range for most folks.

So far we have 

x^3+3x^2-x-3 = (x-1)(x+1)(x-r)

where r is the zero we haven't guessed yet.  Again we could divide f(x) by (x-1)(x+1)=x^2-1 but just looking at the constant term we must have

-3 = -1 (1)(-r) = r

so

x^3+3x^2-x-3 = (x-1)(x+1)(x+3)

We check f(-3)=(-3)^3+3(-3)^2 -(-3)-3 = 0 \quad\checkmark

We usually talk about the zeros of a function and the roots of an equation; here we have a function f(x) whose zeros are

x=1, x=-1, x=-3

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Answer:

B-D

Step-by-step explanation:

smart

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For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(7, 6) = 42. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 6 = 42. In the next intermediate step , cancel by a common factor of 2 gives 1121.  

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