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laiz [17]
4 years ago
9

a local hamburger shop sold a combined total of 456 hamburgers and cheeseburgers. The number of cheeseburgers sold was three tim

es the number of hamburgers sold. How many hamburgers were sold
Mathematics
1 answer:
Ganezh [65]4 years ago
4 0
H + c = 456
c = 3h

h + 3h = 456
4h = 456
h = 456/4
h = 114 <=== hamburgers sold

c = 3h
c = 3(114)
c = 342......cheeseburgers sold
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Add or Subtract to simplify
Drupady [299]

Answer:

3. - 8n² -8n + 3

Step-by-step explanation:

(4n^4 - 8n +4) - (8n² + 4n^4 +1)

Firstly, open the brackets.

= 4n^4 - 8n +4 - 8n² -  4n^4 - 1

Now, group like terms.

= 4n^4 - 4n^4 - 8n² -8n - 1 + 4

4n^4 - 4n^4 cancel out with each other since one is negative and the other is positive. So we're left with - 8n² -8n - 1 + 4

= - 8n² -8n - 1 + 4

= - 8n² -8n + 3

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3 years ago
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ell
Volgvan

Answer:

The answer is below

Step-by-step explanation:

Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16

Solution:

Given that the ellipse has the equation: 4x² + 16y² = 16

let us make x the subject of the formula, hence:

4x² + 16y² = 16

4x² = 16 - 16y²

Dividing through by 4:

x² = (16 - 16y²)/4

x² = 4 - 4y²

Taking square root of both sides:

x=\sqrt{4-4y^2 }\\

The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4xy

A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4}  \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\  \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}

Therefore the length = 2x = 2√2, the width = 2y = 2/√2

7 0
3 years ago
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Ira Lisetskai [31]

Answer:

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Step-by-step explanation:

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scalar multiplication, now, add them up
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Answer:

\boxed{\mathrm{view \ explanation}}

Step-by-step explanation:

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3/14 × 5

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15/14

3 0
3 years ago
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