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Verizon [17]
3 years ago
11

Which expression is shown using the model below? A model with 6 rows of 6 squares and 6 rows of 5 squares. 5 (6 + 6) 5 (6 + 5) 6

(6 + 5) 6 (6 + 10)
Mathematics
1 answer:
hram777 [196]3 years ago
7 0

Answer:

c

Step-by-step explanation:

i took a quiz and got it right

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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)

8 0
2 years ago
Find the area of the shape below please. (:
e-lub [12.9K]

Answer:

105

Step-by-step explanation:

15*6=90

6*5=30

30/2=15

90+15=105

8 0
3 years ago
Read 2 more answers
There are 25 kids in a class, and the number of boys is 2/3 of the number of girls. How many boys and how many girls are in this
Ksju [112]
25 kids in all
2xboys:3x girls
 
so the equation would be 
2x+3x=25
solve,
5x=25
/5           /5
x=5
2x=10
3x=15


10 boys and 15 girls



3 0
3 years ago
Use the graphing calculator to
Leviafan [203]

Answer:

Step-by-step explanation:

Answer is C: x-min = 0, x-max= 30, y-min = 0, y-max = 30

5 0
3 years ago
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Austin is building a miniature replica of the empire state building. the actual empire state building is 1,423 feet tall and 6,0
Fofino [41]

60/6000 = x/1423

100/1 = 1423/x

100x = 1423

x = 14.23 --> About 14 cm

6 0
3 years ago
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