If a bird is flying at 30 meters above sea level and a fish is swimming 15 meters below sea, how many meters are between them? You can draw a vertical number line to help you.

After partial fraction decomposition the correct expression we get,

[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{6}{2x-3} - \frac{7}{(2x-3)^2}[/tex]

Hence option fourth is correct.

Partial fractions is a technique used in mathematics to decompose a rational function into simpler fractions.

It involves breaking down a rational function with a denominator of a higher degree into a sum of fractions with simpler denominators.

The given expression is,

[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{A}{2x-3} + \frac{B}{(2x-3)^2}[/tex]

[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{A(2x-3) + B}{4x^2 - 12 x + 9}[/tex]                      [since (a-b) = a² + b² -2ab]

Simplifying we get

⇒ 12x - 25 = A(2x - 3) + B

⇒ 12x - 25 = 2Ax + (B - 3A)

Comparing the coefficients we get

2A = 12

⇒ A = 6

And B - 3A = -25

Put the value of A we get

B =  -7

Hence,

After substituting the values of A and B in the given expression we get

[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{6}{2x-3} - \frac{7}{(2x-3)^2}[/tex].

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Answer:

Answers: (4. = 3) (5. = 9) (6. = 20)

Therefοre , the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be the average yearly rate οf decrease (in dοllars per year) is $100.

Explain functiοn.

Each tοpic, mathematics, variable design, which is and bοth actual and hypοthetical lοcatiοns will be cοvered in the midterm exam questiοns. a catalοg οf the cοnnectiοns between variοus cοmpοnents that wοrk tοgether tο prοduce the same οutcοme. A service is made up οf many unique parts that wοrk tοgether tο prοduce unique οutcοmes fοr each input.

Here,

[tex]= > V(t) = V(0) * e^{(-kt)[/tex]

By using the numbers at times t=1 and t=3, we can determine the decay cοnstant k:

[tex]= > V(1) = 400 = V(0) * e^{(-k1)[/tex]

[tex]= > V(3) = 100 = V(0) * e^{(-k3)[/tex]

[tex]= > 100/400 = e^{(-k3) / e^{(-k1)[/tex]

[tex]= > 1/4 = e^{(-2k)[/tex]

[tex]= > ln(1/4) = -2k[/tex]

[tex]= > k = ln(4)/2[/tex]

[tex]= > k ≈ 0.69315[/tex]

The value οf the cοmputer at times t=2 and t=4 can nοw be determined using the algοrithm fοr V(t):

[tex]= > V(2) = V(0) * e^{(-k2)[/tex]

[tex]= > V(4) = V(0) * e^{(-k4)[/tex]

[tex]= > V(4)/V(2) = e^{(-k4) / e^{(-k2)[/tex]

[tex]= > V(4)/V(2) = e^{(-2k)[/tex]

[tex]= > V(4)/V(2) = e^{(-0.69315*2)[/tex]

[tex]= > V(4)/V(2) =0.5[/tex]

Over this time periοd, the average yearly rate οf decline (in dοllars per year) is:

Ratiο οf decline equals value shift. (time interval)

=>  V(2) - V(4) = (rate οf decline) / (4 - 2)

=>  (amοunt οf reductiοn) is equal tο (V(2) * (1 - 0.5)) / 2.

=>  (amοunt οf decline) is equal tο (V(2) * 0.5) / 2.

=>  V(2) / 4 equals (rate οf decline)

=>  (rate οf reductiοn) equals 400 / 4

=> rate οf decline) = $100 annually

As a result, οver the twο-year periοd frοm t=2 tο r=4, the average yearly rate οf decrease (in dοllars per year) is $100.

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Answer: The answer is 13.5

Step-by-step explanation:

Answer:

f(x)=-4x+22

f(12)=-4×12+22=-48+22=-26 if your

Step-by-step explanation:

question is f(x)=-4x+22

Answer:

3/18 = 6/ DG

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angle of depression is the angle between the line of sight and a vertical line.

The distance between the two skyscrapers is 1269ft

I've added as an attachment, a figure that illustrates the scenario

First, we calculate distance AB using the following tangent ratio

[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]

So, we have:

[tex]\mathbf{\tan(60) = \frac{AB}{1250}}[/tex]

Make AB the subject

[tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]

Next, we calculate distance AC using the following tangent ratio

[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]

So, we have:

[tex]\mathbf{\tan(60+10) = \frac{AB + BC}{1250}}[/tex]

[tex]\mathbf{\tan(70) = \frac{AB + BC}{1250}}[/tex]

Make AB + BC, the subject

[tex]\mathbf{AB + BC = 1250 \times \tan(70)}[/tex]

Make BC the subject

[tex]\mathbf{BC = 1250 \times \tan(70) - AB}[/tex]

Substitute [tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]

[tex]\mathbf{BC = 1250 \times \tan(70) - 1250 \times \tan(60)}[/tex]

[tex]\mathbf{BC = 1269}[/tex]

Hence, the distance between the two skyscrapers is 1269ft

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Answer: 56.25%

Step-by-step explanation: You would divide 18 over 32, which would get the decimal 0.5625. Then you would multiply this by 100/100 which would get 56.25/100. This would get you 56.25%.

I think the answer is for

1 book (x = 1)

1150+25(1)= 1175

For 2 books (x - 2)

1150+25(2) = 1200

Next, to find the change in total cost, subtract these 2 answers:

1200 - 1175 = 25

Answer:

2

Step-by-step explanation:

Answer:

(-2.5,2)

Step-by-step explanation:

Answer:

A,D,E,

Step-by-step explanation:

9514 1404 393

Answer:

  42 cm²

Step-by-step explanation:

The attachment shows a couple of ways the figure can be considered.

a) Left and Right rectangles that are 5 cm high and 3 cm wide, together with a central rectangle that is 3 cm high and 4 cm wide. Then the total area is ...

  5×3 + 3×4 + 5×3 = 15 + 12 + 15 = 42 . . . . cm²

__

b) An enclosing rectangle that is 5 cm high and 10 cm wide with a cut-out that is 2 cm high and 4 cm wide. Then the total area is ...

  5×10 -2×4 = 50 -8 = 42 . . . . cm²

__

The area of the irregular figure is 42 cm².

Answer:

no solution

Step-by-step explanation:

Answer:

4/5

sin A = perpendicular/hypotenuse

sinA = 28/35

sinA = 4/5

hope it helps

option B

Answer:

B. Sin A = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Sin A = opposite / hypotenuse

Sin A = 28 / 35

Divide both by 7

28 / 7 = 4

35 / 7 = 5

[tex]\frac{28}{35} = \frac{4}{5}[/tex]

Answer:

Step-by-step explanation:

Sum of angles inside triangle is 180

b + (a -3) + 90 =180

b + a - 3 + 90 = 180

b + a +  87 = 180

b + a +  87 -87 = 180-87

b + a  = 180-87

b + a  = 93

b = 93 -a

Answer:

dam nvm the dud give out the answers

Answer:

10

Step-by-step explanation:

12x-10+8x-10=180. All horizontal lines equal 180 degrees. 12x+8x=20x. -10-10=-20. 20+180=200 200 diveded by 20 is 10

Answer:

c = 10

Step-by-step explanation:

8² + 6² = c²

64 + 36 = c

64 + 36 = 100

[tex]\sqrt{100\\[/tex] = 10

Hope this helps :)

Answer:

B. 25

Step-by-step explanation:

30 + 35 + 10 = 75

100 - 75 = 25

Answer:

it's B (25%) players play the woodwinds.

Step-by-step explanation:

35% + 10% + 30%= 75%

100% - 75%= 25%

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

3 vegetarian pizzas cost 25.50. First we must find the cost of one vegetarian pizza.

25.5/3 = 8.5.

Each pizza costs $8.50. She bought 10 of them.

Now, we must multiply $8.50 by 10.

8.5x10 = 85.

$85 for all of the pizza.

Finally, subtract 85 from 100.

100-85=15.

You will receive $15 in change.

Answer:

Should be $15 change

Step-by-step explanation:

Since 3 pizzas cost 25.50 you times that by 3. Divide the 25.50 by 3 and add them two together. Take away that from the 100

Answer:

Susan has more books than Michael.

Step-by-step explanation:

If Susan has 50% more books and Michael has 40 books, that means Susan has 1.5 times 40 = 60

40 + 8 = 48

60 is more than 48, so Susan has more books than Michael

Answer: b=

10.873127c2hn11t

4l

Step-by-step explanation:

Answer:

0.75 lb cause proportions

Answer:

Step-by-step explanation:

im clueless

Answer:

Ans (change recieved) = $0.80

Step-by-step explanation:

because 1 cupcake cost $1.05, 4 of them cost $4.2 because you multiply 4 cupcakes by the cost ($1.05) to obtain the total cost of the four cupcakes.

in order to know the change she recieved . you subtract the $5 bill she paid with the total cost of the 4 cupcakes

$5.00 - $4.20 = $ 0.80