Find the asymptotes and intercept of the following rational function

Show your work for the intercepts!

a) These ramp dimensions do not meet the ADA guidelines.

b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.

The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:

The ratio between the vertical change to the horizontal change is of:

3/15 = 1/5.

Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.

If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:

As the ratio would be of:

3/39 = 1/13 < 1/12.

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Answer:

see explanation

Step-by-step explanation:

using the cofunction identities

cos x = sin(90 - x)

sin x = cos(90 - x)

then

cos76° = sin(90 - 76)° = sin14°

sin66° = cos(90 - 66)° = cos24°

sin53° = cos(90 - 53)° = cos37°

cos49° = sin(90 - 49)° = sin41°

The  Matched values are

cos(76) —> sin (14)

sin(66)—> cos (24)

sin(53)—> cos (37)

cos(49)—> sin (41)

One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.

For complementary angle,

a+ b= 90

So, sin (14)

= cos (90 - 76)

= cos 76

and, cos (37)

=sin (90 - 53)

= sin (53)

and, sin (49)

= cos (90- 41)

= cos 41

and, cos (66)

= sin (90 - 24)

= sin 24

Then, the Matched values are

cos(76) —> sin (14)

sin(66)—> cos (24)

sin(53)—> cos (37)

cos(49)—> sin (41)

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Answer:123

Step-by-step explanation:

7328x3424

Steven battling average for the whole season he played was 0.45

An equation is an expression showing the relationship between two or more numbers and variables.

Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season.

Hence:

Batting average = (total number of time he hit the ball in both season half) / (total number of balls thrown)

Therefore:

Battling average = (12 + 6)/ (26 + 14) = 18 / 40 = 0.45

Steven battling average was 0.45

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The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.

A function is simply a relationship that maps one input to one output. For relation to qualify as a function,  each x-value can only have one y-value.

Given the data in the question;

To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.

g( a ) = 3a + 2

g( -3 ) = 3( -3 ) + 2

Multiply 3 and -3

g( -3 ) = -9 + 2

Add -9 and 2

g( -3 ) = -7

Therefore, the output value is -7, this forms an ordered pair of (-3,-7).

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Answer:

L=66 degrees

KL=3.5

LM=8.7

Answer:

Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.

c + y = 2s ------ equation (1)

t + 4 = c ------ equation (2)

6t + 1 = y ------ equation (3)

Since Sofia is 38 years old, substitute s = 38 into equation (1):

c + y = 2(38)

        = 76 ------ equation (4)

Substitute equations (2) and (3) into equation (4):

t + 4 + 6t + 1 = 76

          7t + 5 = 76

                7t = 71

∴ t = 10 (to the nearest whole number)

∴Tony is 10 years old (to the nearest whole number).

There will be 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 when repeated digits are allowed by fundamental counting principle.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting simplifies the approach to selection by taking into account all of the possible choices and their combinations in order to calculate the Probability.

Here,

Since there are 6 digit given,

In first place, there are 6 ways to arrange the digits. In second place, there are 6 ways to arrange the digits. In third place, there are 6 ways to arrange the digits.

This way,

6×6×6=216 ways

When repeated digits are allowed by the fundamental counting principle, 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6.

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a.  I would rather compound annually at 5 % interest

b.  I would increase the simple interest rate if i were to change my answer

Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.

Since  you have $200 to invest for 10 years at  7% simple interest, using the simple interest formula for the amount, we have

A = P(1 + rt) where

Substituting the values of the variables into the equation, we have

A = P(1 + rt)

A = 200(1 + 0.07 × 10)

A = 200(1 + 0.7)

A = 200(1.7)

A = 340

Also, since  you have $200 to invest for 10 years at  5% interest compounded annually, using the compound interest formula for the amount, we have

A' = P(1 + r)ⁿ where

Substituting the values of the variables into the equation, we have

A' = P(1 + r)ⁿ

A' = 200(1 + 0.07)¹⁰

A' = 200(1.07)¹⁰

A' = 200(1.9672)

A' = 393.43

Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest

To change my answer, I would increase the simple interest rate if i were to change my answer

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Answer:

138° (nearest degree)

Step-by-step explanation:

Bearing:  The angle (in degrees) measured clockwise from north.

The given scenario can be modelled as a right triangle (see attachment).

Therefore, the bearing is 90° + θ (shown in green on the attached diagram).

To find angle θ, use the cosine trigonometric ratio:

[tex]\implies \cos{\theta}=\dfrac{A}{H}[/tex]

[tex]\implies \cos{\theta}=\dfrac{624}{927}[/tex]

[tex]\implies \theta=\cos^{-1}\left(\dfrac{624}{927}\right)[/tex]

[tex]\implies \theta=47.69018863...[/tex]

[tex]\implies \theta=48^{\circ}\; \; \sf (nearest\;degree)[/tex]

Therefore, the bearing of the drawbridge from the tower is:

[tex]\begin{aligned}\implies \sf Bearing&=90^{\circ}+\theta\\&=90^{\circ}+48^{\circ}\\&=138^{\circ} \end{aligned}[/tex]

Answer:

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

Add 90° to the angle measure we just found, since bearing is counted from the north direction:

Answer:

Carmen will have her loan paid back in 20 months

Answer:

-4x(x-3)

Step-by-step explanation:

-4x^2+12x

divide by -4x

-4x(x-3)

The solution of x ≤ 3 depicts that all the value of x is either less than 3 or equal to 3, so option C is correct.

In mathematics, numbers are shown visually as a straight line on a number line. The numerals on a number line are positioned in a specific order and spaced out equally throughout its length. Since it can go on forever in any direction, it is frequently presented horizontally.

The expression x ≤ 3 depicts that the value of x is less than 3 or equal to 3, this can be represented in the image attached below.

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Answer:600

Step-by-step explanation:

i think

The fraction of a mile that Evan has to hike and the fraction he has hiked, gives the completed statement as follows;

[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex]. So the difference is closest to [tex]\frac{1}{2}[/tex]

A fraction is a representation of the part of a whole of an item or collection of items. The distance Evan's hiking trail of [tex]\frac{5}{6}[/tex] miles is a fraction of a mile.

The length of the trail = [tex]\frac{5}{6}[/tex] mile

The distance Evan has hiked = [tex]\frac{2}{5}[/tex] mile

The distance Evan has left to hike is given by the difference between the length of the trail and the distance Evan has hiked as follows;

Distance remaining = [tex]\frac{5}{6} -\frac{2}{5} = \frac{13}{30}[/tex]

Representing the numbers in decimal form, we have;

[tex]\dfrac{5}{6} = 0.8\overline 3[/tex]

The value of [tex]\frac{5}{6}[/tex] is close to 1

[tex]\dfrac{2}{5} = 0.4[/tex]

The value of [tex]\frac{2}{5}[/tex] is closest to 0.5

[tex]\dfrac{13}{30} = 0.4\overline 3[/tex]

The difference between [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{5}[/tex], which is [tex]\frac{13}{30}[/tex] is therefore closest to [tex]\frac{1}{2}[/tex]

The completed statement is therefore;

[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex] so the difference is closest to [tex]\frac{1}{2}[/tex]

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Answer: [tex]\frac{17}{7}[/tex]

Step-by-step explanation:

7x - 3y = 23
3y = -2 × 3 = -6

7x + 6 = 23

7x = 23 - 6

7x = 17

x = [tex]\frac{17}{7}[/tex]

Answer:

115.226337449

Step-by-step explanation:

84/0.729= 115.226337449

And thank you and your welcome

Answer:  the quotient of 84/0.729 is 115.226337

Answer:

Step-by-step explanation:

-22.7

The sampling method used in this scenario is random Systematic random sampling

Systematic random sampling

Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.

If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.

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Answer:

x = [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]\frac{3}{2}[/tex] = 4x ( multiply both sides by 2 to clear the fraction )

3 = 8x ( divide both sides by 8 )

[tex]\frac{3}{8}[/tex] = x

the sum of two odd integers will always be resulted in an odd digit.

Odd numbers are entire numbers that can't be isolated precisely into matches. Odd numbers, when separated by 2, leave a rest of 1. , 3, 5, , 9, 11, , 15  are consecutive odd numbers.

These are added together to get n + n+1, or 2n+1. Since +1 make it odd, 2n is even. Any two successive integer sums are hence odd. According to the solution is "2n + (2n + 1) = 4n +1."

Even numbers result from the addition of two fractions, but still only digits result from the addition of one odd number with one even number. In order to only receive an odd number, add one odd as well as one even.

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The cost of the gas will be equal to £67.81 p.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that,

Initial gas reading = 8247

Final gas reading = 8631

The total consumed gas is given by,

Final gas reading - Initial gas reading  → 8631 - 8247 = 384

Since the cost of gas is 11p per unit we have, the total cost of the gas consumed is given by

Cost of consumed gas = Units of gas consumed × Unit cost of gas

= 384 × 11p = 4224 p

100 p ≡ £ 1

4224 p  = £42.24 p

The total cost of the gs is obtained by adding the fixed charge to the cost of gas consumed as follows,

£25.57 + £42.24 = £67.81 p

The cost of the gas = £67.81 p

The complete question is given below,

The gas meter readings at the beginning and end of a period were: 8247 = 8631 the cost of the gas is 11p for each unit. there is also a fixed charge of £25.57. calculate the cost of the gas. you must show your working

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Answer:

Step-by-step explanation:

5 dollars and 25 cents

Answer:

7xy(2x-3y+4xy)

Step-by-step explanation:

14÷7=2

21÷7=3

28÷7=4

they all have 7, x and y so that would be on the outside

The number of large boxes of porridge that William bought, using a system of equations, was of:

8.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem.

For this problem, the variables are defined as follows:

William buys 5 small boxes of oat porridge, hence:

x = 5.

The total weight of his purchase is of 6825 grams, hence, considering the weight of each box, the following equation is built:

325x + 650y = 6825.

It is already stated on the problem that x = 5, hence the value of y can be obtained as follows:

325(5) + 650y = 6825.

y = (6825 - 325(5))/650

y = 8 large boxes.

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The distance between two cyclists after 45 minutes as described in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.

It follows from the task content that the distance between the two cyclists after 45 minutes is to be determined from the given parameters.

Given; the speed of the first cyclist is; 12 miles per hour, while the speed of the second cyclist is b miles per hour greater than that of the first.

The speed of the second cyclist is therefore; (b + 12).

On this note, since the distance covered by each cyclist is given by;

Distance = Speed × Time where, Time = 45 minutes = 0.75 hours.

Therefore, the total distance between the two cyclists can be determined from the expression as follows;

7 + 0.75 (12) + 0.75 (b + 12).

Therefore, the distance between the two cyclists as required in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.

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If Helen wants to find the value. the upper bound for Helen's value of TC is 3.123 and lower bound is 3.092.

Upper bound

405 = 405.999

130 =130.99

Lower bound

405 = 405.001

130 =130.01

Now let find the upper and lower bound

Upper bound = 405.999/130.01

Upper bound =3.123

Lower bound = 405.001 /130.99

Lower bound = 3.092

Therefore the upper bound is 3.123.

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