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igomit [66]
3 years ago
6

An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 2 sm

all baskets and 4 large baskets, using a total of 60 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and 10 large baskets, using a total of 132 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
The small baskets each include______pieces and the large ones each include_____pieces.
Mathematics
1 answer:
Bingel [31]3 years ago
5 0

Let \: x,  y \: (x,y>0) \: be \: the \: number \: of \: fruits \: the \: small \: and \: large \: baskets \: hold \: respectively \\ We  \: have \:  a \:  system \:  of \:  equations:2x + 4y = 60 \: \wedge \: 2x + 10y = 132 \\ \Leftrightarrow x = 6 \: \wedge \: y = 12 \\ \Rightarrow The  \: small \:  baskets  \: each \:  include  \: 6  \: fruits \\ \Rightarrow The  \: large \: baskets \: each \: include \: 12 \: fruits

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Find the condition that one root of the quadratic equation may be 1 more than the other.
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3 years ago
F(x)=<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2-4%7D" id="TexFormula1" title="\sqrt{x^2-4}" alt="\sqrt{x^2-4}" align="abs
hammer [34]

Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :

√(<em>x</em> ² - 4) = 1

<em>x</em> ² - 4 = 1

<em>x</em> ² = 5

<em>x</em> = ±√5

We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.

This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.

Now apply the inverse function theorem:

If <em>f(a)</em> = <em>b</em>, then  (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.

We have

<em>f(x)</em> = √(<em>x</em> ² - 4)   →   <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)

So if <em>a</em> = -√5 and <em>b</em> = 1, we get

(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)

(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5

The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.

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3 years ago
I need emergency help I’ll mark you as brainlist
galben [10]

Answer:

352

Step-by-step explanation:

:)

:)

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4 0
3 years ago
Read 2 more answers
When you subtract one square number from another the answer is 3 what are the two square numbers
dimulka [17.4K]
The numbers are 1 and 2

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