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vitfil [10]
3 years ago
13

Kate has two lengths of ribbon. the pink ribbon is 4 6/12 feet long, and the purple ribbon is 2 4/12 feet long. how much ribbon

does kate have in all?
Mathematics
1 answer:
Vlad1618 [11]3 years ago
4 0
Data:
<span>Kate has two lengths of ribbon
pink ribbon = </span>4 \frac{6}{12} \;feet
purple ribbon = 2 \frac{4}{12} \;feet

<span>How much ribbon does kate have in all?
pink ribbon + purple ribbon

Solving:
</span>4\frac{6}{12} + 2\frac{4}{12} =  \frac{12*4+6}{12} + \frac{12*2+4}{12} =  \frac{48+6}{12} + \frac{24+4}{12} =  \frac{54}{12} + \frac{28}{12} =  \frac{82}{12} =
\frac{82}{12} \:simplify\: \frac{\div2}{\div2} =  \boxed{\boxed{\frac{41}{6} \:or\:6 \frac{5}{6} }}\end{array}}\qquad\quad\checkmark
<span>
Answer:
</span><span>Kate has it all </span>6 \frac{5}{6} of ribbons
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3 years ago
Express into partial fractions 3x³ - 5x² - 3x - 40/( x² + 4)(x - 3)​
Fudgin [204]

First simplify the rational expression by dividing. The degree in the numerator has to be at least 1 less than the degree in the denominator before you can decompose into partial fractions.

(3<em>x</em>³ - 5<em>x</em>² - 3<em>x</em> - 40) / ((<em>x</em>² + 4) (<em>x</em> - 3)) = 3 + (4<em>x</em>² - 15<em>x</em> - 4) / ((<em>x</em>² + 4) (<em>x</em> - 3))

Now decompose the remainder term into partial fractions:

(4<em>x</em>² - 15<em>x</em> - 4) / ((<em>x</em>² + 4) (<em>x</em> - 3)) = (<em>ax</em> + <em>b</em>) / (<em>x</em>² + 4) + <em>c</em> / (<em>x</em> - 3)

Multiply both sides by the denominator on the left:

4<em>x</em>² - 15<em>x</em> - 4 = (<em>ax</em> + <em>b</em>) (<em>x</em> - 3) + <em>c</em> (<em>x</em>² + 4)

Expand the right side:

4<em>x</em>² - 15<em>x</em> - 4 = <em>ax</em>² + (<em>b</em> - 3<em>a</em>) <em>x</em> - 3<em>b</em> + <em>cx</em>² + 4<em>c</em>

4<em>x</em>² - 15<em>x</em> - 4 = (<em>a</em> + <em>c</em>) <em>x</em>² + (<em>b</em> - 3<em>a</em>) <em>x</em> - 3<em>b</em> + 4<em>c</em>

Then

<em>a</em> + <em>c</em> = 4

<em>b</em> - 3<em>a</em> = -15

-3<em>b</em> + 4<em>c</em> = -4

Solve this system to get

<em>a</em> = 5, <em>b</em> = 0, <em>c</em> = -1

We end up with

(4<em>x</em>² - 15<em>x</em> - 4) / ((<em>x</em>² + 4) (<em>x</em> - 3)) = 5<em>x</em> / (<em>x</em>² + 4) - 1 / (<em>x</em> - 3)

and so

(3<em>x</em>³ - 5<em>x</em>² - 3<em>x</em> - 40) / ((<em>x</em>² + 4) (<em>x</em> - 3))

= 3 + 5<em>x</em> / (<em>x</em>² + 4) - 1 / (<em>x</em> - 3)

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ivann1987 [24]

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Step-by-step explanation:

Complementary angles are 2 angles which add up to 90.

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dexar [7]

Answer:

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Step by step explanation:

A= ½×4cm×4cm

A= ½×16cm²

A= 8cm²

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