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anastassius [24]
2 years ago
5

Tyrone has $8.06.How many bagels can he buy if each bagel cost$0.65?

Mathematics
1 answer:
worty [1.4K]2 years ago
5 0
He can get 12 bagels
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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
Which ordered pair is generated from the equation shown below? y = 3x + 2 A. (3, 11) B. (3, 9) C. (5, 15) D. (2, 4)
borishaifa [10]

Answer:

y = 3x + 2

There slope is  3 and intercept is 2.

<u>First find what are the 2 pair that given by slope =3</u>

First consider A. (3, 11)  and B. (3, 9)

Tan α = \fraction(11-9)(3-3)

It is undefine.

Next consider A. (3, 11)  and BC (5,15)

Tan α = \fraction(15-11)(5-3)

=2

Next consider A. (3, 11)  and D. (2,4)

Tan α = \fraction(11-4)(3-2)

=7

Next consider B (3, 9)  and C. (5,15)

Tan α = \fraction(15-9)(5-3)

=3

So this is ordered pair is generated from slope =3

Step-by-step explanation:

8 0
2 years ago
point (4,4),(4,0), and (0,0) are the vertices of the triangle the enclosed whole squares and half squares on the grid. determine
Advocard [28]

Answer:

8

Step-by-step explanation:

finding the area is h x l x 1/2. The h is 4 and the l is also 4. That multiplied is 16. Multiply that by 1/2 and you get 8

6 0
2 years ago
In What quadrant is the point (-5, -5) located
sineoko [7]

Answer:

Since both values are negative, it can be found in the 3rd quadrant

<em>Feel free to mark this as brainliest :D</em>

4 0
3 years ago
4 in.<br> 7 in.<br> O 124 6 in<br> 87.9 in<br> O 97.5 in<br> O 78.9 in<br> 5<br> 6<br> 7
Dima020 [189]

Answer:

v=3.14 r 2 h

3.14 (2)(2)(7)= 87.9

5 0
2 years ago
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