I need help for the Wednesday one

Rewrite the function as

[tex]f(x) = \dfrac{\tan(\left(\frac{\pi x}4\right)}{x^2 - 8x + 15} = \dfrac{\sin\left(\frac{\pi x}4\right)}{\cos\left(\frac{\pi x}4\right) (x-3) (x-5)}[/tex]

Vertical asymptotes occur wherever the denominator is zero (but not necessarily when the numerator is also zero).

We have

[tex]\cos\left(\dfrac{\pi x}4\right) (x-3) (x-5) = 0[/tex]

[tex]\implies \cos\left(\dfrac{\pi x}4\right) = 0 \text{ or } x - 3 = 0 \text{ or } x - 5 = 0[/tex]

In the first case, we have

[tex]\cos\left(\dfrac{\pi x}4\right) = 0 \implies \dfrac{\pi x}4 = \pm\dfrac\pi2 + 2n\pi \implies x = \pm 2 + 8n[/tex]

where [tex]n[/tex] is an integer. That is, any of [tex]x\in\{\ldots,-10,-2,\boxed{6},14,\ldots\}[/tex] and [tex]x\in\{\ldots,-6,\boxed{2},10,18,\ldots\}[/tex] are asymptotes.

In the latter two cases, we get [tex]x=\boxed{3}[/tex] or [tex]x=\boxed{5}[/tex]. The numerator is finite at these values [tex]\left(\sin\left(\frac{3\pi}4\right)=\frac1{\sqrt2}\text{ and } \sin\left(\frac{5\pi}4\right)=-\frac1{\sqrt2}\right)[/tex].

This means [tex]x=4[/tex] is not an asymptote. (C)

Answer:

y = 1x + 5

Step-by-step explanation:

First, lets calculate the equation of the line passing through (5, 7) and (1, 3) in slope-intercept form

The general equation of a line in slope-intercept form is
y = mx + b

where m = slope and b = y-intercept is rise over run =

[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]

where (x₁, y₁) and (x₂, y₂) are any two points on the line

For the line passing through (5, 7) and (1, 3) , the slope
[tex]m = \dfrac{3 - 7}{1 - 5}[/tex]

[tex]m = \dfrac{-4}{-4}[/tex]

[tex]m = 1[/tex]

To compute the y-intercept, plug in any of the two points x and y values and solve for b

Take point 5, 7 ==> when x = 5, y must be 7

We get
7 = 1 x 5 + b
7 = 5 + b
2 = b                (subtract 5 from both sides)
b = 2

So the equation of the line is
y = 1x + 2  

A line parallel to another line will have the same slope and a different y-intercept

Therefore a parallel line will also have slope 1 and its equation will be of the form
y = 1x + b

To calculate this b, plug in the point (4, 9) into the equation and solve for b
9 = 1 x 4 + b
9 = 4 + b
b = 5

So the equation is
y = 1x + 5

Graph attached shows the real picture

The each bottle of juice cost $ 7.55  before tax .

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Grayson bought  bag of popcorn (P)= $3.50

Five pack of juice bottles.

The total cost before tax was $11.05.

According to given question we have

Let the cost of the juice bottles be x.

P+ x= $11.05.

$3.50+x=$11.05

x=$11.05-$3.50

x=$ 7.55

Therefore, the each bottle of juice cost $ 7.55  before tax .

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Answer:

$29.865

Step-by-step explanation:

Because 3.75/2 =1.875 so $1.875 plus $15 Plus the flat $12.99

Using a linear function, it is found that he spent $29.865 for the 4.5 hours he was on the river.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the cost of x hours is given by:

C(x) = 12.99 + 3.75x.

For 4.5 hours, the cost is given as follows:

C(4.5) = 12.99 + 3.75(4.5) = $29.865.

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Answer:

500

Step-by-step explanation:

3+6=9
10-9=1

They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left

Answer: 500 balloons

Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000

plss give your self a answer

Answer:

  1:30 pm

Step-by-step explanation:

You want the time when Sahil catches up to Joaquin, who left at 8 am riding 50 mph when Sahil left at 8:30 am, riding at 55 mph.

The relation between time, speed, and distance is ...

  distance = speed × time

  time = distance / speed

Joaquin has a head start of 0.5 hours (30 minutes), during which time he traveled ...

  head start distance = (50 mi/h) × (0.5 h) = 25 mi

Sahil is traveling 55 - 50 = 5 mph faster than Joaquin, so closes that gap at the rate of 5 mi/h. The time it takes to close the gap entirely is ...

  time = distance / speed = 25 mi / (5 mi/h) = 5 h

So, 5 hours after Sahil starts at 8:30, the two riders will be at the same place.

Sahil catches Joaquin at 1:30 pm.

__

Additional comment

By the time the gap is closed at 1:30 pm, both riders will have traveled a distance of ...

  distance = speed × time = 50 mi/h × 5.5 h = 55 mi/h × 5 h = 275 mi

In the attached graph, we have written equations for the total distance traveled by each motorcycle. The x-value used is the clock time on a 24-hour clock. That is, their meeting time of 13.5 hours corresponds to 13:30 hours or 1:30 p.m. on a 12-hour clock.

Answer:

She will need to rise 55.4 feet.

Step-by-step explanation:

-27.2 feet + 2.1 feet = -25.1

-25.1 + -19.6 = 44.6

100- 44.6 = 55.4 feet

((9×7)÷9−6)+13

(63÷9−6)+13

(7−6)+13

1+13

14

Answer:

9 X 7 / 9 - 6 + 13

we can cut 9

=7-6 + 13

=1+13

=14

we end up paying 41.25 % of the original price after the addition sale on the clearance.

Let the original price of the good be x

Now, there is a sale of 25 %.

So the price will become

Price = x - 25 % of x

Price = x - 25 / 100 x

Price = x - 0.25 x

Price = 0.75 x

Now, there is an addition 45 % sale on the price.

so the price become:

New price = P = 0.75 x - 45 % of 0.75 x

P = 0.75 x - 45 / 100 (0.75 x)

P = 0.75 x - 0.45( 0.75 x)

P = 0.75 x - 0.3375 x

P = 0.4125 x

percentage of original price is:

P = 41.25 % of x

Therefore, we get that, we end up paying 41.25 % of the original price after the addition sale on the clearance.

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Answer:

3×a-3×2=3a-6

3a-6=3a-6 proved

Answer:

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r ( t ) = 0.6 t r(t) = 0.6t r(t)=0.6t, where t is the time in seconds after the pebble strikes the water.

Step-by-step explanation:

Answer:

well dude it's because of the law of gravity

a)  cost C of manufacturing 1000 bicycle is $170

b) cost C of manufacturing 7000 bicycle is $110

c)  As more bicycle is manufactured the cost of manufacturing decreases

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

given expression of cost of bicycle C in terms of number of number of bicycles x is :  

C = (100x + 70,000)/ x

a)  Now, to get the cost C of manufacturing 1000 bicycle substitute  x as 1000 in above expression :

C = (100x + 70,000)/ x

C = 100 + (70,000/ x)

C = 100 + 70,000/1000

C = 100 + 70

C = 170 bicycle's

b)  Now, to get the cost C for 7000 bicycle substitute  x as 7000 in above expression :

C = (100x + 70,000)/ x

C = 100 + (70,000/ x)

C = 100 + 70,000/7000

C = 100 + 10

C = 110 bicycle's

c) As it is observed from the above analysis as more bicycle is manufactured the cost of manufacturing decreases.

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The term containing b^6 is -210 a^6 b^6

The given expansion can be solved by using the Binomial expansion

The binomial expansion for two terms (a + b)  raised to the power n is given by

(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!

To find term contain b^6 we use the formula

Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]

Putting n=10,

we get 10-r=6

             r=4

Therefore,

it is the fourth term ,

T = (-1)^3  10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]

   = -1  x   10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]

Hence the term containing b^6 is -210 a^6 b^6

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3(n-10)=-7

Solve the equation in 2 step equation.

n=18.5

Given that 3(n-10)=7

step1: multiplication

Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.

3n-30=7

step2: adding 30 on both sides of the equation.

When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.

2n-30+30=7+30

2n=37

step3: divide the equation by 2.

Basically, dividing is the act of dividing anything into equal sections or groups.

[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]

Therefore, n=18.5

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The cardinal number of (2, 4, 6, ..., 106) is 53.

The cardinal number of a set is the number of elements in the particular set.

We are given the set (2, 4, 6, ..., 106). As we can can clearly see, it is forming an Arithmetic Progression (AP).

Hence, let the number of elements or the cardinal number of the set be n.

Hence, according to the formula of AP, we can write,

2 + (n-1)(2) = 106

2(n-1) = 106 - 2

2(n-1) = 104

n - 1 = 104/2

n - 1 = 52

n = 52 + 1

n = 53

Hence, the cardinal number of the set is 53.

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Answer:

Step-by-step explanation:

You want the speed and speed multiplier for Jet B given that it makes a journey in 5 minutes that takes Jet A 2 hours for half the journey.

For the same distance, speed is inversely proportional to time.

  speed multiplier = (speed B)/(speed A) = (time A)/(time B)

  speed multiplier = ((2 h)/(1/2))/(5 min)

  speed multiplier = (240 min)/(5 min) = 48

The speed of Jet B is 48 times that of Jet A:

  48(417 mph) = 20016 mph . . . . speed of Jet B

__

Additional comment

The time for the full trip by Jet A can be found using the proportion ...

  partial time/partial distance = total time/total distance

If the total distance is "1 unit", then this proportion is ...

  (2 h)/(1/2) = t/1 . . . . . where t/1 = t is the time for the full trip by Jet A

You will recognize the value (2 h)/(1/2) as the time value we used for Jet A in the above solution.

Answer:

One could be: 8*8 times 4*4

Another could be: 8 to the second power times 4 to the second power

A third way to write this could also be: 8*4*8*4

Step-by-step explanation:

Hope its helpful

The shorter section is x inches length, or 44.

What constitutes a length?

A line segment can be drawn on paper and has a set length. the measurement of the separation between the longest or longer side of an object's ends. 2: an exact distance The three miles of the road. 3: How much time something requires The movie lasts for two hours. 4: a lengthy fragment of something She purchased a length of pipe in

accordance with the instruction;

the shorter portion should be x.

It is 4x because the longer portion is 4 times as long as the other.

4x + x = 55

5x = 55

4x = 44

x = 11

The length of the shorter piece is x, which is 44

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Answer:

Hello,

Step-by-step explanation:

a)

[tex]x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\[/tex]

b)

[tex]x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\[/tex]

As Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).

As given,

Regular working hours =40 hours

Overtime at the rate of (1.5 of regular hours) = 6 hours

Gross pay =$650

Let 'h' be the hourly rate

Required equation

40h + 6(1.5h) =650

⇒ 40h +9h=650

⇒49h=650

⇒h=$13.27(approximately)

Therefore, as Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).

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Answer: Joe's book has 1248 Pages.

Step-by-step explanation:

468 * 2 2/3

Multiply 2 and 3 to get 6.

468×( 6+2/3)

Add 6 and 2 to get 8.

468x(8/3)

Express 468×(8/3) as a single fraction

468x8/3

Multiply 468 and 8 to get 3744.

3722/3

Divide 3744 by 3 to get 1248.

1248

So Joe's Book has 1248 pages

a dot plot can easily show all the data.

Step-by-step explanation:

In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.

Answer:it's the second option

Step-by-step explanation:

-x is already -1 so why would factoring it make it -1 again

From the given scatter plot, finding a line of best fit, the estimate of the amount of prize money in year 10 of the contest is of $11,790.

To find the equation of the line of best fit, we need to insert the points (x,y) from the scatter plot in the calculator.

From the scatter plot, the points are given as follows:

(1, 9.5), (2,9), (3,7), (4,10), (5,11), (6, 10), (7, 10.5).

Inserting these points into a calculator, the line of best fit for the prize in year x is given as follows:

P(x) = 0.32143x + 8.28571

For year 10, we have that x = 10, hence:

P(10) = 0.32143(10) + 8.28571 = $11,500.

The closest option is $11,790, and the difference is due to rounding of coefficients or points in the table.

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The number of oranges that will fit in the box is 235 oranges.

The dimensions of the box are 13 inches by 16 inches by 13 inches.

Therefore,

volume of the box = lwh

where

Hence,

volume of the box = 13 × 16 × 13

volume of the box = 2704 inches³

volume of the spherical orange = 4 / 3 πr³

where

volume of the spherical orange = 4 / 3 × 3.14 × 1.4³

volume of the spherical orange = 34.46464 / 3

volume of the spherical orange = 11.4882133333 inches cube = 11.5 inches³

number of oranges in the box = 2704  / 11.5

number of oranges in the box = 235.130434783

number of oranges in the box = 235 oranges

Therefore, the number of oranges that will fit in the box is 235 oranges.

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Answers:

Length = 45 feet

Width = 9 feet

=========================================================

Work Shown:

x = width

5x = five times the width = length

P = perimeter of the rectangle

P = 2*(length + width)

P = 2*(5x+x)

P = 2*(6x)

P = 12x

Set this equal to the stated perimeter (108) and solve for x.

12x = 108

x = 108/12

x = 9 feet is the width

5x = 5*9 = 45 feet is the length

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

Check:

P = 2*(9+45) = 108

or you could add up the four sides like this

P = 9+45+9+45 = 108

Either way the answers are confirmed.