Shawnee richards and her husband have decided to purchase a cabin in the county. they have applied for a mortgage loan of 80,000 at 6% for a period of 25 years. they will pay it off in equal monthly payments that include interest.

The equation for the trigonometric graph given above is:

y = 4sin(2x + (π/2))

y = 4 cos 2x

It is to be noted that the domain value of θ  is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.

Note that

y = A Sin (Bx - C) + D

The vertical shift → D

Horizontal [Phase] shift → C/B

Wavelength [Period] →  (2/B) π

Amplitude → | A |

Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)

Wavelength | Period | → (2/B)π → π → (2/2)π

Amplitude → 4

Hence, working the above further we get:

y = 4sin(2x + (π/2))

y = 4 cos 2x

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Answer(s):

[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

subtracting 6x from 8x. It's quite simple to deal with small two-part numbers like these. After subtracting 6x from 8x, you will get the answer 2x.

Quick Answer:

You simply 8x-6x by subtracting 6x from 8x, and then you will get the answer 2x

HAVE A NICE DAY

You did not provide any question. I will give general advice.

Pythagorean Theorem: a² + b² = c²

If you know two sides, you know ll three sides.

A house sits in the shade.

The house is 18 feet tall. The shadow is 24 feet long. What is the hypotenuse of this triangle?

We know a and b here! a=18, b=24.

18 * 18 = 324.

24 * 24 = 576.
324+576 = 900

The square root of 900 is what will be your answer:

18*18 + 24*24 = 30*30.

I hope this helps!

Answer:232 inch^2

Step-by-step explanation:to solve, add the surface area of each side. Remember, there are 3 pairs of sides and the pairs have equal area. Area =length x length. So we have 2x(8x2)+2x(2x10)+2x(10x8) in square inches.

x = 53/80 = 0.6625

​

if isn't right I have another equation

Answer:

13.25

Step-by-step explanation:

[tex]x - 7 \div 20 = 5 \div 16[/tex]

by cross multiplying

16(x-7)=5(20)

16x-112=100

16x=100+112

16x=212

x=212 /16

×=13.25

if the question is this

The height of the television given the length of its diagonal and its width is 55.6 inches

The  height of the television can be determined using Pythagoras Theorem.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

√95² - 77² = 55.6 inches

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Answer: 55.6

Step-by-step explanation: 55.6 that's what I put in and got it right

Answer: -13

Step-by-step explanation:

m = -5

-5 + (-5-3)

-5 -8

-13

Answer:

-13

Step-by-step explanation:

dado m= -5

m+(m-3) = -5+(-5-3) = -5 + (-8) = -5-8 = -13

Part A

The pattern of squares is 1, 4, 9, ... which is the set of perfect squares

and so on

The 7th figure will have 49 squares because 7^2 = 49

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

Part B

Each pattern has one circle per corner (4 circles so far). In addition, there's one circle per unit side to form the perimeter.

The nth term will have 4+4n circles. The first '4' is the number of circles at the corners. The 4n is the circles along the perimeter. If you wanted, 4+4n factors to 4(1+n).

Plug in n = 20 to find the 20th figure has 4+4n = 4+4(20) = 84 circles

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

Part C

This seems to suggest if the pattern number is odd, then we need an odd number of tiles (square + circular).

Let n be the pattern number. Pattern n needs n^2 square tiles and 4+4n = 4n+4 circular tiles. Overall, n^2+4n+4 tiles are needed.

It turns out that if n is odd, then n^2+4n+4 is always odd. The proof is shown below.

Side note: n^2+4n+4 factors to (n+2)^2

Answer:

Step-by-step explanation:

The probability that he will receive the job will be 1 / 6

The complete question is given below:-

A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

It is given that:

The chance of passing a qualifying examination is 2/3=P

and chance of being appointed, if he does pass, is 1/4=P'

Now, we are asked to find the probability that he will receive the job.

We are asked to find the probability that he will receive the job.

The probability is calculated as The probability that he qualify the exam×Probability that he is being appointed.

=P×P'

=(2/3)×(1/4)

=1/6

Therefore the probability that he will receive the job will be 1 / 6

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Answer: B- x/4

Step-by-step explanation:

The period is the horizontal distance needed for the values to repeat themselves.

Answer:

13

Step-by-step explanation:

[tex]Sin = \frac{opp}{hyp} \\cos= \frac{adj}{hyp} \\tan = \frac{opp}{adj}[/tex]

=> get the length of the diag on bottom

[tex]tan x = \frac{3}{4} x = 36.87[/tex] degree

[tex]sin(36.87)=\frac{3}{y}[/tex]

y is about 5

=> calculate max length of stick

[tex]tan\left(x\right)\:=\frac{5}{12}, x= 22.62degree[/tex]

[tex]sin\left(22.62\right)\:=\:\frac{5}{x}[/tex]

which is 13

A sample is one that is representative of the population, selected at random, and large enough to provide accurate data.

A sample is a smaller group that is representative of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

For example, if a researcher is studying the impact of inflation on US families. It is not feasible to reach the whole of the families in the US. So, the researcher would use a representative group of US families. This is known as a sample.

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Equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it define​s.

The quadratic expressions can be simplified as follows;

Equation C is simplified as follows;

y = 3(x - 1)² + 18

y = 3(x² - 2x + 1) + 18

y = 3x² - 6x + 3 + 18

y = 3x² - 6x + 21

Thus, equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it define​s.

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Answer:

2)  $40 per shirt

3)  80/9 m = 8.9 m (nearest tenth)

Step-by-step explanation:

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Question 2

Given information:

Let [tex]x[/tex] = number of $1 increases

Let [tex]y[/tex] = total revenue (in dollars)

From the given information:

Therefore, we can create a quadratic equation with the given information:

[tex]\implies y = (20+x)(300-5x)[/tex]

As we need to find the maximum amount of revenue, we need to find the vertex of [tex]y[/tex].  As the equation is already factored, the quickest way to do this is to the find the mid-point of the zeros (since a quadratic curve is symmetrical).

[tex]\begin{aligned}y & =0\\\implies (20+x)(300-5x) & =0\\\implies (20+x) & =0 \implies x=-20\\\implies (300-5x) & = 0 \implies x=60\end{aligned}[/tex]

[tex]\textsf{Midpoint}=\dfrac{-20+60}{2}=20[/tex]

Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:

[tex]\implies \$20 + 20 \times \$1 = \$40\: \sf per\:shirt[/tex]

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Question 3

Given information:

As the bridge is modeled as a parabola, and we have been given the width and height, we can create a quadratic equation using the vertex form.

Vertex form:  [tex]y=a(x-h)^2+k[/tex]

where:

Middle of the bridge = 30 m ÷ 2 = 15 m

Max height of the bridge = 10 m

Therefore, the vertex of the parabola is (15, 10)

[tex]\implies y=a(x-15)^2+10[/tex]

We know that when [tex]x = 0, y = 0[/tex].  Therefore, substitute these values into the equation and solve for a:

[tex]\implies 0=a(0-15)^2+10[/tex]

[tex]\implies 0=225a+10[/tex]

[tex]\implies 225a=-10[/tex]

[tex]\implies a=-\dfrac{10}{225}[/tex]

[tex]\implies a=-\dfrac{2}{45}[/tex]

Therefore, the equation of the parabola is:

[tex]\implies y=-\dfrac{2}{45}(x-15)^2+10 \quad \quad \textsf{for }0\leq x\leq 30[/tex]

The horizontal distance at 5 m right of the middle is:

[tex]\implies \dfrac{30}{2}+5=20\:\sf m[/tex]

Therefore, to find the height at this point, input [tex]x=20[/tex] into the equation and solve for y:

[tex]\implies -\dfrac{2}{45}(20-15)^2+10=\dfrac{80}{9}\:\sf m[/tex]

Therefore, the height of the bridge at 5 m to the right of the middle is:

[tex]\dfrac{80}{9}\:=8.9\: \sf m\:(nearest\:tenth)[/tex]

Answer:

A standard form of a linear equation would look like this Ax+ By = C A x + B y = C

Step-by-step explanation:

The quadrilaterals and their corresponding properties as shown in the given table are explained below.

Property 1; All sides are Congruent means all sides are equal and only Square and Rhombus have this property.

Property 2; All angles are congruent means all angles are equal. Only Rectangle and Square have this property.

Property 3; Diagonals are perpendicular to each other. Only Square and rhombus have this property.

Property 4; Diagonals are congruent. This means the diagonals are equal and only Square and Rectangle have this property.

Property 5; Exactly One pair of parallel sides is given by Only Trapezoid.

Property 6; Two pairs of opposite sides are congruent. Only Parallelogram, Rectangle, Rhombus and Square have this property.

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Answer:

x = 36; y = 9

Step-by-step explanation:

To solve this problem you need to set up two equations. The first equation comes from the first sentence "One number is 4 times another." This equation can be written as x = 4*y where x and y are the two numbers. The second equation comes from the second sentence "Their difference is 27." This equation can be written as x-y = 27. To find the numbers you need to rearrange one equation and plug it into the other.

Step 1: write equations

x = 4*y

x-y = 27

Step 2: rearrange

Not necessary here

Step 3: substitute in

x - y = 27

4y -y = 27

3y = 27

y = 9

Step 4: solve for x

x = 4*y

x = 4*9

x = 36

[tex]x[/tex] - one number

[tex]4x[/tex] - the other number

[tex]4x-x=27\\3x=27\\x=9\\\\4x=4\cdot9=36[/tex]

These numbers are 9 and 36.

Answer:d.33

Step-by-step explanation: To begin we convert his living room floor length and width to inches. 8 1 slash 3 feet = 100 inches
10feet= 120 inches

hence the area in square inches of the living room floor is 100 inches times120 inches = 12000 inches squared.

Each carpet tile has an area of 20 by 20 which = 400inches squared. dividing the area of the living room by 400inches of each carpet tile, would yield 30 carpet tiles needed to cover this area.

As per linear equation, the minimum number of carpet tiles that Aurelio must purchase to cover the area of his living room floor is 29.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

Given, the room has a length of 10 feet = 12 × 10 inches = 120 inches

The width of the room is = 8 feet = 12 × 8 inches = 96 inches

Therefore, the area of the room is

= 120 × 96 square inches

= 11520 square inches

Length of each carpet tile is 20 inches

Width of each carpet tile is 20 inches

Therefore, the area of each tile is

= (20)² square inches

= 400 square inches

The number of tiles require

= (11520/400)

= 28.8

≈ 29

Therefore, 29 tiles will be required.

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Answer:

Girls = 16

Total students = 40

Step-by-step explanation:

40% of the students are girls, this means 60% of the students are boys.

To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.

Also let's convert the percentages to decimals by moving the decimal two places left.

40% = 0.4 and 60% = 0.6

[tex]\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16[/tex]

Now let's find the total number of students by adding the number of girls to the number of boys.

16 + 24 = 40

Answer:

13

Step-by-step explanation:

144 = pie radio square

144 divided by pie = 45.83662361

45.83662361 square root = 6.770275003

6.770275003 multiply by 2 =  13.54055001

13.54055001 = diameter

Answer:

Slope = 5/3

Step-by-step explanation:

See attached image

Answer: 1.75•5%=0.0875

1.75+0.0875=$1.84

I’m pretty sure this is correct

Answer:

5% of 1.75 is 0.085.

So 1.75 + 0.085 is 1.8375.

Answer:

triangles A and B are similar

Step-by-step explanation:

Answer:

16in x 22in

Step-by-step explanation:
8in = 100%
x = 200%
(200*8) / 100 = 16

11in = 100%
X = 200%
(200*11) / 200 = 22

The trick is to cross multiply (without multiplying the X) and then divide by the number that was not multiplied :)

Answer:

  16 in by 22 in

Step-by-step explanation:

Each dimension is multiplied by the scale factor when a photo is enlarged or reduced.

__

The enlarged photo will have dimensions ...

  (200% × 8 in) by (200% × 11 in) = 16 in by 22 in

_____

Additional comment

The factor 200% is equal to 200/100 = 2. (% and /100 are interchangeable)

Answer:

147

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\\frac{f(5)-f(3)}{5-3}\\ \\\frac{(3(5)^3+2)-(3(3)^3+2)}{2}\\ \\\frac{(3(125)+2)-(3(27)+2)}{2}\\ \\\frac{(375+2)-(81+2)}{2}\\ \\\frac{377-83}{2}\\ \\\frac{294}{2}\\ \\147[/tex]

Recall that if a function [tex]f[/tex] is continuous over the interval [tex][a,b][/tex], then its average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex].