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A single fraction will be;

⇒ 1/(y + 12)

And, Domain of this expression is,

⇒ Domain = (-∞, ∞) - { 12 }

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)

Now,

Since, The expression is,

⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)

Simplify the expression as;

⇒ 4 (y - 2) - 3 (y + 2) / (y-2) (y+2) + 12 / (y² - 4)

⇒ 4y - 8 - 3y - 6 / (y² - 4) + 12 / (y² - 4)

⇒ (y - 14) / (y² - 4) + 12 / (y² - 4)

⇒ (y - 14 + 12) / (y² - 4)

⇒ (y - 12) / (y- 12) (y + 12)

⇒ 1/(y + 12)

Hence, A single fraction will be;

⇒ 1/(y + 12)

And, Domain of this expression is,

⇒ Domain = (-∞, ∞) - { 12 }

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Answer:

Step-by-step explanation:

The expression you've provided is a combination of several fractions, but it's not clear how they are supposed to be combined. Without more information, it's impossible to know what the value of the expression is.

It would be helpful if you could provide more context or clarify how you want the fractions to be combined.

I can only tell you how the fraction works in mathematics and how you can evaluate the value of it if you have the complete information.

9514 1404 393

Answer:

  A (-2), A

Step-by-step explanation:

A function will have a point of discontinuity at a point where it is undefined. Rational functions will be undefined where the denominator is zero. This function will have denominator zeros at x = -2, so is discontinuous there.

__

As x approaches -2 from either direction, the value of y approaches positive infinity. The type of discontinuity can be described as an infinite discontinuity.

The solution is Option A. , Option C.

The equations which are also proportional is y = 3x and x = 2y

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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Answer: The solution is Option A. , Option C.

Step-by-step explanation:

The equations which are also proportional is y = 3x and x = 2y

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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Answer:

[tex]x=\frac{1}{5}[/tex]

[tex]y = -\frac{1}{15}[/tex]

Step-by-step explanation:

4x - 3y = 1

x + 3y = 0

Req To Solve With Elimination:

Make Them Equal:

-> 4x - 3y = 1

-> 4x + 4 . 3y = 0

Simplify:

->  4x - 3y = 1

-> 4x + 12y = 0

-> 4x - 4x - 3y - 12y = 1

-> -3y - 12y = 1

-> -15y = 1

-> [tex]y = -\frac{1}{15}[/tex]

-> [tex]x+3(-\frac{1}{15} )=0[/tex]

-> [tex]x -\frac{1}{5}=0\\[/tex]

-> [tex]x=\frac{1}{5}[/tex]

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Answer:

4x – 3y = 1

x + 3y =​

Adding the equations gives us:

5x =1

x = .2

since 4x - 3y = 1

then -3y -1 = -4x then we multiply by -1

3y +1 = 4x

3y = 4*.2 -1

3y = .8 -1

3y = -.2

y = -.2 / 3  = -0.066666666...

For a double check you can use Cramer's Rule

http://www.1728.org/cramer.htm

Step-by-step explanation:

Answer:

0

8

0

9

0

9

9

098098809667906432

Answer:

18.5 in=decimal feet,

Step-by-step explanation:

1)18.5/12=18.512

2)18.512=1.542 feet

Answer:

Total intake in ML = 414 ml (Approx.)

Step-by-step explanation:

Given:

Apple juice intake = 2 oz

Chicken broth intake = 4 oz

Gelatin dessert intake = 3 oz

Hot tea intake = 5 oz

Find:

Total intake in ML

Computation:

1 oz = 29.5735 ml

Apple juice intake in ml = 2 x 29.5735

Apple juice intake in ml = 59.147 ml

Chicken broth intake = 4 x 29.5735

Chicken broth intake = 118.294 ml

Gelatin dessert intake = 3 x 29.5735

Gelatin dessert intake = 88.7205ml

Hot tea intake = 5 x 29.5735

Hot tea intake = 147.8675 ml

Total intake in ML = 59.147 ml + 118.294 ml + 88.7205ml + 147.8675 ml

Total intake in ML = 414.029 ml

Total intake in ML = 414 ml (Approx.)

Answer:

Looking at this, slope seems to be 2 for the graph

So, looking at your options, -4 is less than 2, therefore, the answer is

D, with slope -4

Answer:

D

Step-by-step explanation:

The graphed function rises 2 in y for each run of 1 in x

Therefor the slope is 2/1 = 2

-------------------------

A) goes up 6 for each run of 3

slope = 6/3 = 2

B) goes up 15 for each run of 3

slope = 15/3 = 5

C) this is in slope intercept for of y = mx + b

m is the slope = 6

D) this is in slope intercept for of y = mx + b

m is the slope = -4

-------------------------------------

only D has a slope less than 2

Answer:

y=2x+2

Step-by-step explanation:

Just look at the bottom dot which is 0,2 and y=2x+2 is the only one that works:

2=(2×0)+2

2=2

but the other is:

2=(3×0)

2=3

which isn't true,

therefore it must be the first one.

Answer:

$18

Step-by-step explanation:

Answer:

[tex]6\frac{14}{100}[/tex]

Step-by-step explanation:

First, you make fourteen a fraction.

[tex]\frac{14}{100}[/tex]

Then, make it a mixed fraction by adding a six.

[tex]6\frac{14}{100}[/tex]

Lastly, have a great day! :)

Answer:

24 may be

Step-by-step explanation:

coz i dont kmow waiii i dont know

m soo sry to disturb u

may god find ur answer

god bless u

be happy alys

Answer:

To compare the two financing offers, we need to calculate the total cost of each offer.

Part A: What is the total cost of offer 1?

To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2490/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,534.89.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.

Therefore, the total cost of offer 1 is $4,509.89.

Part B: What is the total cost of offer 2?

To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,

To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,405.70.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.

Therefore, the total cost of offer 2 is $4,381.70.

Part C: Which financing offer should the new homeowner choose?

Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.

Step-by-step explanation:

Answer:

Step-by-step explanation:

soulution:

        given,              2x +2x = 16 - 2x + 3y = 14

                                 2x + 2x = -2y +3y = 14 -16

                                       4x = y = -2

                                         y = 4x = -2

                                          y = x =  4/-2

                                         x = y = -2 ans

Answer:

3

Step-by-step explanation:

Answer:

The other pairs are:

[tex](a)\ (2, \frac{5\pi}{6}) \to[/tex]  [tex](2, \frac{17\pi}{6})[/tex] and [tex](-2, \frac{23\pi}{6})[/tex]

[tex](b)\ (1, -\frac{2\pi}{3}) \to[/tex] [tex](1, \frac{4\pi}{3})[/tex] and [tex](-1, \frac{7\pi}{3})[/tex]

[tex](c)\ (-1, \frac{5\pi}{4}) \to[/tex] [tex](-1, \frac{3\pi}{4} )[/tex] and [tex](1, \frac{7\pi}{4})[/tex]

See attachment for plots

Step-by-step explanation:

Given

[tex](a)\ (2, \frac{5\pi}{6})[/tex]

[tex](b)\ (1, -\frac{2\pi}{3})[/tex]

[tex](c)\ (-1, \frac{5\pi}{4})[/tex]

Solving (a): Plot a, b and c

See attachment for plots

Solving (b): Find other pairs for [tex]r > 0[/tex] and [tex]r < 0[/tex]

The general rule is that:

The other points can be derived using

[tex](r, \theta) = (r, \theta + 2n\pi)[/tex]

and

[tex](r, \theta) = (-r, \theta + (2n + 1)\pi)[/tex]

Let [tex]n =1[/tex] ---- You can assume any value of n

So, we have:

[tex](r, \theta) = (r, \theta + 2n\pi)[/tex]

[tex](r, \theta) = (r, \theta + 2*1*\pi)[/tex]

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](r, \theta) = (-r, \theta + (2n + 1)\pi)[/tex]

[tex](r, \theta) = (-r, \theta + (2*1 + 1)\pi)[/tex]

[tex](r, \theta) = (-r, \theta + (2 + 1)\pi)[/tex]

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](a)\ (2, \frac{5\pi}{6})[/tex]

[tex]r = 2\ \ \ \ \theta = \frac{5\pi}{6}[/tex]      

So, the pairs are:

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](2, \frac{5\pi}{6}) = (2, \frac{5\pi}{6} + 2\pi)[/tex]

Take LCM

[tex](2, \frac{5\pi}{6}) = (2, \frac{5\pi+12\pi}{6})[/tex]

[tex](2, \frac{5\pi}{6}) = (2, \frac{17\pi}{6})[/tex]

And

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](2, \frac{5\pi}{6}) = (-2, \frac{5\pi}{6} + 3\pi)[/tex]

Take LCM

[tex](2, \frac{5\pi}{6}) = (-2, \frac{5\pi+18\pi}{6})[/tex]

[tex](2, \frac{5\pi}{6}) = (-2, \frac{23\pi}{6})[/tex]

The other pairs are:

[tex](2, \frac{17\pi}{6})[/tex] and [tex](-2, \frac{23\pi}{6})[/tex]

[tex](b)\ (1, -\frac{2\pi}{3})[/tex]

[tex]r = 1\ \ \ \theta = -\frac{2\pi}{3}[/tex]      

So, the pairs are:

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](1, -\frac{2\pi}{3}) = (1, -\frac{2\pi}{3} + 2\pi)[/tex]

Take LCM

[tex](1, -\frac{2\pi}{3}) = (1, \frac{-2\pi+6\pi}{3})[/tex]

[tex](1, -\frac{2\pi}{3}) = (1, \frac{4\pi}{3})[/tex]

And

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](1, -\frac{2\pi}{3}) = (-1, -\frac{2\pi}{3} + 3\pi)[/tex]

Take LCM

[tex](1, -\frac{2\pi}{3}) = (-1, \frac{-2\pi+9\pi}{3})[/tex]

[tex](1, -\frac{2\pi}{3}) = (-1, \frac{7\pi}{3})[/tex]

The other pairs are:

[tex](1, \frac{4\pi}{3})[/tex] and [tex](-1, \frac{7\pi}{3})[/tex]

[tex](c)\ (-1, \frac{5\pi}{4})[/tex]

[tex]r = -1 \ \ \ \ \theta = \frac{-5\pi}{4}[/tex]

So, the pairs are

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi}{4} + 2\pi)[/tex]

Take LCM

[tex](-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi+8\pi}{4} )[/tex]

[tex](-1, \frac{-5\pi}{4}) = (-1, \frac{3\pi}{4} )[/tex]

And

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](-1, \frac{-5\pi}{4}) = (-(-1), \frac{-5\pi}{4}+ 3\pi)[/tex]

Take LCM

[tex](-1, \frac{-5\pi}{4}) = (1, \frac{-5\pi+12\pi}{4})[/tex]

[tex](-1, \frac{-5\pi}{4}) = (1, \frac{7\pi}{4})[/tex]

So, the other pairs are:

[tex](-1, \frac{3\pi}{4} )[/tex] and [tex](1, \frac{7\pi}{4})[/tex]

Answer:

E = 30.37 J

Step-by-step explanation:

Given that,

The spring constant of the spring, k = 300 N/m

The spring is stretched by 0.45 m, x = 0.45 m

We need to find the elastic energy stored in the spring. The formula for the elastic energy is given by :

[tex]E=\dfrac{1}{2}kx^2\\\\=\dfrac{1}{2}\times 300\times (0.45)^2\\\\=30.37\ J[/tex]

So, the required elastic energy is equal to 30.37 J.

Answer:

  ∠HAF ≈ 64.90°

Step-by-step explanation:

You want the angle HAF, a base angle in the isosceles triangle formed by the face diagonals of the cuboid with dimensions 6 cm, 6 cm, and 8 cm.

The lengths of the diagonals can be found using the Pythagorean theorem:

  HA² = HD² + DA²

  HA² = 6² +6² = 2·6²

  HA = 6√2 . . . cm

  FA² = FB² +BA²

  FA² = 6² +8² = 36 +64 = 100

  FA = 10 . . . cm

Diagonal FH is the diagonal of a rectangle with the same dimensions as the rectangle whose diagonal is FA:

  FH = FA = 10 . . . cm

The angle A can be found using the law of cosines:

  FH² = FA² +HA² -2·FA·HA·cos(A)

  A = arccos((FA² +HA² -FH²)/(2FA·HA))

  A = arccos((100 +72 -100)/(2·10·6√2)) = arccos(72/(120√2))

  A = arccos(0.3√2) ≈ 64.90°

Angle HAF is about 64.90°.

Answer:

Step-by-step explanation: Total Cost: TC = $126.07

Base fee: B = $16.95

Rate per mile: r = $0.88/mile

Distance (miles) : d -->this is what we need to find

The general formula is:

TC = B + r*d

In this problem:

$126.07 = $16.95 + ($0.88/mile)*d

126.07 - 16.95 = 0.88d    (I dropped the units starting here)

d = (126.07 - 16.95)/0.88 = 124 miles  (notice the parentheses. subtraction has a lower precedence than division.  If you omitted them when using a graphing calculator you would get an incorrect answer)

So the answer is 124 miles.

Answer:

The answer is 6.25%

Step-by-step explanation:

So,

(61 ÷ 976) × 100%

0.0625 × 100% = 6.25%

Thus, 6.25% of potatoes are rotten.

Step-by-step explanation:

% of potatoes rotten = 61/976 × 100

=> 6100/976

=> 6.25%

Answer:

Two angles are vertical angles if their sides form two pairs of opposite rays. 5 and 6 are a linear pair. Two adjacent angles are a linear pair if the form a straight line. Linear Angle Pairs add up to 180°.

Answer:

There are 96 girls taking classes at the music school, while the number of boys is 32.

Step-by-step explanation:

Since for every boy taking classes at the music school, there are 3 girls who are taking classes at the school, if there are 128 students taking classes, for write and solve a proportion to predict the number of girls taking classes at the school you must perform the following calculation:

1 + 3 = 4

128/4 x 3 = Girls

32 x 3 = Girls

96 = Girls

Therefore, there are 96 girls taking classes at the music school, while the number of boys is 32.

Answer:

72 .22 inches is the answer bro

Answer:

72.22 inches

Step-by-step explanation:

Formula for circumference given diameter is:

c = πd

If you use 3.14 for pi, you get 72.22 inches:

c = 3.14(23)

c = 72.22

Answer:

Null (H0) : Mean chips weight = 1.75 , Alternate (H1) :  Mean chips weight < 1.75

Step-by-step explanation:

Null Hypothesis states no deviation from considered population parameter.

Alternate Hypothesis states deviation from considered population parameter. If anticipated deviation may be more or less, its two tail test. If anticipated deviation is only more or less, its left or right tail test .

Null Hypothesis [H0] : Average chips weight = 1.75 ounce

Alternate Hypothesis [H1] : Average chips weight < 1.75 ounce {Left Tail Test}

Answer:

The tree is 44 feet

Step-by-step explanation:

[tex]\frac{8}{6}[/tex] is equivalent to [tex]\frac{4}{3}[/tex] (divide the numerator and denominator by 2)

[tex]\frac{4}{3}[/tex] = [tex]\frac{x}{33}[/tex]

3 x 1  = 33, so 4 x 11 = 44

Answer:

Rate of change= 1/3

Initial value = -4

Step-by-step explanation:

The rate of change is rise/run = 1/3.

the initial value is the y-intercept which is -4.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-6)}}} \implies \cfrac{-3 +6}{3 +6} \implies \cfrac{ 3 }{ 9 } \implies \cfrac{1 }{ 3 }[/tex]

now as far as the "initial value", dunno what that means.

The start of the line? well, the line by definition goes to infinity both ways.

the y-intercept? well, just look at the graph, the graph intercepts the y-axis when x = 0 and y = -4, so at (0 , -4).