Two angles are a linear pair. The measure of one angle is 5 more than 2/3 of the other. find the measure of both angles

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:

y=-1.7x+8

Step-by-step explanation:

An equation of a line is y=mx+c

m is the gradient and c is the y intercept, which is where the line intercepts y.

you work out m getting two points and then subtracting y - y ÷ x - x

So in this graph, if we chose points (6,-2) and (3,3) then we would do this equation.

[tex] \frac{3 - - 2}{3 - 6} = \frac{5}{ - 3} = - 1.7[/tex]

So m = -1.7

c = 8 because it goes through 8 in y.

So the equation is y=-1.7x+8

Answer:

3/18 = 6/ DG

Step-by-step explanation:

Answer:

1800

Step-by-step explanation:

Answer:

1800 pounds

Step-by-step explanation:

1st year: 2 rabbits

2nd year: 6 rabbits

3rd year: 18 rabbits

18 x 100 = 1800

hope this helps :)

Answer:

whats the question?

Step-by-step explanation:

Answer:

y approaches negative infinty

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

Answer:

120ft

Step-by-step explanation:

8 x 3 x 5

Answer:

6 in.

Step-by-step explanation:

Rectangular prism

V = lwh       l = 8   W = 3    h = 9

  = 8(3)(9)

  = 216

Cube

[tex]V = s^{3}[/tex]   where s = length of side

216 = [tex]s^{3}[/tex]

[tex]s = \sqrt[3]{216}[/tex]  = 6

9514 1404 393

Answer:

  3.16 or -3.16

Step-by-step explanation:

Add 10 and take the square root.

  x^2 = 10

  x = ±√10 ≈ ±3.16

x is 3.16 or -3.16

Answer:

5

Step-by-step explanation:

5/6 x 6 = 30/6

Basically just multiply the numerator and whole number to get the new numerator. Put that on top of the denominator and then convert it to the simplest fraction (if necessary).

Answer:

c = 10

Step-by-step explanation:

8² + 6² = c²

64 + 36 = c

64 + 36 = 100

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

Hope this helps :)

Just trying to win the CONTEST BUT GOOOOD LUCK

Answer:

56 units, 84 units, 56 units, 140 units

Step-by-step explanation:

Since you have the ratios, you can multiply each by x, because you do not know the actual values.

2x+3x+2x+5x=336

12x=336

÷12  ÷12

x=28

Then, plug in the values of x.

So 2*28= 56

3*28=84

2*28=56

5*28=140

Answer:

36% or  9/25

Step-by-step explanation:

35+36+29=100 so 100-35-29=64 and 36 are left so you divide 9/25 and you get 0.36 and you put it into a percentage and the answer is 36% or  9/25.

The probability it will be a student who prefers chicken is, 36/100.

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

He surveys 100 students,

29 students select sub sandwiches,

35 select steak and gravy,

and 36 select fried chicken

The probability of selecting a student who prefers fried chicken can be found by dividing the number of students who prefer chicken by the total number of students surveyed:

36/100 = 36%.

This can also be expressed as a decimal or a percentage:

0.36 or 36%.

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Answer:

I cant really help with the diagram but the equation is

$44.95 divided by 5 = $8.99

Answer: The equation is 5c = 44.95

Step-by-step explanation:

The equation is 5c = 44.95, when c is the price of each calculator.

Answer:

d = 6.3 units

Step-by-step explanation:

Distance formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

Your ordered pairs (-8, 6) and (-6, 0)

d=√((-6-(-8))²+(0-6)²)

d=√((-6+8))²+(-6))²)

d=√((2)²+ 36)

d = √40

d = 6.32...

d = 6.3

Answer:

2

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

2(2) + 15(2)+ 9 = 43

Answer:

43

Step-by-step explanation:

2 x 2 = 4

4 + (15 x 2) = 34

34 + 9 = 43

Answer:

B, for every y there are 150 x's

Answer:

x=180-(67+52)

Step-by-step explanation:

a linear pair is 180

we are already have two angles add them together

subtract that from 180 and you will get the last angle

Answer:

if you can try to go on your phone and then theres a app that lets you take a picture then it will answe it

Step-by-step explanation:

Answer:

$25.50

Step-by-step explanation:

3 people including Audrey went on the lunch break. If each spent $8.50, the total bill can be calculated in two ways

Method 1

$8.50 x 3 = $25.50

Method 2

$8.50 + $8.50 + $8.50 = $25.50

Answer:

.

Step-by-step explanation:

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:

Step-by-step explanation:

The area of a trapezoid is the height times the average of its parallel bases.

A=h(b1+b2)/2, in this case

A=14(4.6+8.7)/2

A=7(4.6+8.7)

A=7(13.3)

A=93.1 km^2

Answer:

2

Step-by-step explanation:

Answer:

Only 2, the 0 is not needed so it should just be 8.9

Step-by-step explanation: