Maths Trigonometry Question
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The length of the flagpole is x - 5 yards

The formula for calculating the area of the flagpole is expressed as:

A = L²

Given that;

A = x² - 10 + 25

Factorize

A = x² - 5x - 5x + 25

A =(x - 5) - 5(x - 5)

A = (x-5)²

Compare

L = x - 5 yards

Hence the length of the flagpole is x - 5 yards

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Answer:

620.14

Step-by-step explanation:

Original Equation:

[tex]\frac{4y}{1.025^4}+y-2y(1.05)^2=1500[/tex]

Calculate exponents

[tex]\frac{4y}{1.103812890625}+y-2y(1.1025)=1500\\[/tex]

Simplify:

[tex]3.6238025791990193084270042653997y + y - 2.205y = 1500[/tex]

Add like terms

[tex]2.4188025791990193084270042653997y \approx 1500[/tex]

Divide both sides by 7.012

[tex]y\approx 213.91[/tex][tex]y\approx620.14[/tex]

Answer:

y = $620.14 (nearest cent)

Step-by-step explanation:

Given equation:

[tex]\dfrac{4y}{1.025^4}+y-2y(1.05)^2=\$1,500[/tex]

Factor out y from the left side:

[tex]\implies y\left(\dfrac{4}{1.025^4}+1-2(1.05)^2\right)=\$1,500[/tex]

Carry out the arithmetic operations inside the parentheses by following the order of operations PEMDAS:

Calculate the exponents:

[tex]\implies y\left(\dfrac{4}{1.103812891...}+1-2(1.1025)\right)=\$1,500[/tex]

Carry out the multiplication and division from left to right:

[tex]\implies y\left(3.623802579...+1-2.205\right)=\$1,500[/tex]

Carry out the addition and subtraction from left to right:

[tex]\implies y\left(4.623802579...-2.205\right)=\$1,500[/tex]

[tex]\implies y\left(2.418802579...\right)=\$1,500[/tex]

Finally, divide both sides by the coefficient of y to isolate y:

[tex]\implies \dfrac{y\left(2.418802579...\right)}{2.418802579...}=\dfrac{\$1,500}{2.418802579...}[/tex]

[tex]\implies y=\$620.141558...[/tex]

Therefore, y = $620.14 (nearest cent)

Answer:

18

Step-by-step explanation:

So since the two lines are parallel, 3x is congruent to the angle to the left of 6x+18 and since the two angles together are a straight line it's equal to 180 degrees. So

6x + 18 + 3x = 180

9x + 18 = 180

9x = 162

x = 18

Answer:

m=2/3

Step-by-step explanation:

[tex]m=\dfrac{\delta y}{\delta x} \\\\=\dfrac{-5-(-3)}{(-2)-1}\\ \\\dfrac{2}{3}[/tex]

Answer:

Step-by-step explanation:

Comment

I would think Pakistan should be more than just 4 times as large as Kenya. However if you are given that Kenya is 50 000 000 then Pakistan will be 4 times the size of Kenya.

Pakistan = 4 * Kenya

Pakistan = 4 * 50 000 000

Pakistan = 200 000 000

Answer: Pakistan = 200 000 000

The value of the house in the year 2010 is 150056.47.

The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year)

Value

v(t) = V0 ( 1 + r)^t

let V0 =  106, v(20) = 146

So,

146 = 110(1 + r )^20

146/110 = (1 + r )^20

1.327 = (1 + r )^20

1+ r = 1.014

r= 0.014

So, annual growth rate is 1.4%.

In the year 2010

v(t) = 106(1.014)^25

v(t) = 106(1.014)^25

v(t) - 150056.47

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Answer:

Step-by-step explanation:

When ratios of quantities are given, it is often convenient to consider a group of objects in which the objects have that ratio.

Here, we have 2 dimes for each quarter, so a group of 2 dimes and 1 quarter is a useful group for this problem. Its value is 2×$0.10 +0.25 = $0.45.

The total value of all of the groups is $3.60, so there must be ...

  $3.60/($0.45/group) = 8 groups

The 8 groups of coins will have 16 dimes and 8 quarters.

The preparation of the income statement for Longhorn Corporation for the year ended December 31, 2021, is as follows:

Longhorn Corporation

For the year ended December 31, 2021

Service revenue                             $ 65,700

Cost of goods sold (food expense) 53,000

Gross profit                                      $12,700

Delivery expense     $2,200

Salaries expense        5,100            $7,300

Net Income                                     $5,400

The income statement also called income summary is a financial statement that shows the financial performance of a business for a defined financial period.

Thus, from the income statement, the net income and the gross profit, which represent the gains achieved by the entity, are derived.

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The ways that zero growth stock valuation can affect business operations is that:

The Constant  stock valuation  is known to be a kind of share evaluation as it states that the dividends paid by a firm will consistently increase at a constant growth rate.

This will help one to know especially investors on how to set or know the fair price that one needs to pay for a stock on daily basis today by due to future dividend payments.

The overall statement is that  stock value affect one's business operations as  the company's stock price is one that shows an investor perception of their capability to get profit and also if they can grow their profits in terms of future times.

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Answer:

I would say b since this defintally usally you aren't expeced to use math ouside of math class at school

Hope This Helps!!!

Answer:

The correct answer is C.

Step-by-step explanation:

The required range for the owner to win the participant's money is given by
g ≤ 76 inches.

In the game of the Height, there is a participant named bobby and the guess maker a booth owner, if the booth owner makes the right guess than  he will get the money of the participant who are participating in the game.

Range, it is the set of the values that come out to an outcome for certain mathematical operation.

As per the condition, the booth owner can guess the height of the participants more than 1 inches of the actual height.
so the range (g) ≤ 76, so the booth owener wins the money

Thus, the required inquility for the condition is given by (g) ≤ 76.

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The reduced form of the trig expression is 7/2sin²2a

Trigonometry identities are written in terms of sine, cosine and tangent. Given the trigonometry identity

14sin² acos² a

Since sin(a)cos(a) = sin2a/2, hence

14sin²acos²a = 14[sin(a)cos(a)]²

14sin²acos²a = 14(sin2a/2)²

14sin²acos²a = 14/4(sin²2a)

14sin²acos²a = 7/2sin²2a

Hence the reduced form of the trig expression is 7/2sin²2a

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TheThe best approximation for the perimeter of polygon ABCDE is: C. 24.3 units.

Coordinate:

A=(-2,3)

B=(0,6)

C=(5,4)

D=(4,-1)

E=(-1,-2)

Distance AB=√(0+2)²+(6-3)²

Distance AB=√4+9

Distance AB=√13

Distance BC=√(5-0)²+(4-6)²

Distance BC=√25+4

Distance BC=√29

Distance CD=√(4-5)²+(-1-4)²

Distance CD=√1+25

Distance CD=√26

Distance DE=√(-1-4)²+(-2+1)²

Distance DE=√25+1

Distance DE=√26

Distance EA=√(-2+1)²+(3+2)²

Distance EA=√1+25

Distance EA=√26

Perimeter of pathogen ABCDE

=AB+BC+CD+DE+EA

=√13+√29+√26+√26+√26

=√13+√29+3√26

=24.2877 units
= 24.3 units (Approximately)

Therefore the correct option is C.

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Step-by-step explanation:

The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented below in the form of table.

The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented as:

                                   Statement of stockholder's equity        

Particulars Common stock Retained earnings    Total stockholder  

                                                                                          Equity

Beginning

balance        $11,000                  $7,900                     $18,900

Add: Additional

common stock $7,700                                                   $7,700

Add: Net income                           $8,200                    $8,200  

Less - dividend                            -$2,900                    -$2,900

Ending balance  $17,000              $5,300                 $5,300

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The inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.

It should be noted that an inference simply means the conclusion that can be deduced based on the information given.

In this case, the inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.

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Answer: It The mixture has less than the intended volume and has more than the intended percent of butterfat.

Step-by-step explanation:

The price p based on the equation given is p = 3000 - 0.1x.

The equation given in the question is x = 3000 - 10p. The price(p) will be:

x = 3000 - 10p.

Make p the subject of the formula

x + 10p = 3000

10p = 3000 - x

p = (3000 - x)/10

p = 3000 - 0.1x

The revenue will be price multiplied by quantity. This will be:

= (3000 - 0.1x) × x

= 3000x - 0.1x²

The marginal revenue will be calculated after differentiating. This will be:

= 3000x - 0.1x²

= 3000 - 0.2x

The demand which is the quantity based on the information will be:

3000 - 0.2x = 0

0.2x = 3000

x = 1500

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Answer:

765314290

Step-by-step explanation:

doesn’t use 8

Not start with 8

Digits used only 1’cd

The graph of the parabola can be seen in the image below.

Here we have the function:

g(x) = (15x)^2

Notice that this is a contraction of scale factor 15 of the function f(x) = x^2

To graph this, we can just evaluate the function in 3 points, the vertex and two other ones.

for x = 0.

g(0) = (15*0)^2 = 0

So we have the point (0, 0).

Evaluating in x = 1 and x = -1 (give the same value) we get:

g(±1) = (±15)^2 = 225

So we have the points (1, 225) and (-1, 225).

Now we can just connect these 3 points with a parabola. The graph can be seen below.

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Answer:

simple interest of the given question is 495

Step-by-step explanation:

SIMPLE INTEREST=P*T*R/100

The distance of the entire trip is 15 minutes and  distance far away from the house to the pizza store is 9 blocks away.

a. The entire trip based on the given graph is 15 minutes.

b.  Distance:

Distance=10-1

Distance=9 block away

c.  Andrew stopped for 3 minutes for 1 minutes between third minutes and fourth minutes.

d. Distance:

Distance=10-2

Distance=8

Distance=15-8

Distance=7 minutes

Distance=5-1

Distance=4 minutes

Therefore the distance of the entire trip is 15 minutes and  distance far away from the house to the pizza store is 9 minutes.

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By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.

The volume of the composite figure is the sum of the volumes of the two figures: (i) a cone, (ii) a hemisphere. The volume formula of the figure is shown below:

[tex]V = \frac{2\pi}{3} \cdot r^{3} + \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]      

If we know that r = 5.3 cm and h = 8.4 cm, then the volume of the composite figure is:

V = (2π/3) · (5.3 cm)³ + (π/3) · (5.3 cm)² · (8.4 cm)

V ≈ 558.900 cm³

By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.

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Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"

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Answer:

It's D

Step-by-step explanation:

Got it right

Using the continuity concept, it is found that the function is continuous at x = -3.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, the function is continuous at x = -3, as:

At x = -1, we have that [tex]\lim_{x \rightarrow -1^-} f(x) = \infty[/tex], hence it is not continuous.

The function is not defined for x = 1, and at x = 3, the lateral limits are different.

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Answer:

x= what they raised last year

2x+20= what they raise this year or y

d

Hope This Helps!!!

Answer: b.not enough info

Step-by-step explanation:

Corresponding angles of congruent triangles are congruent, so [tex]\angle A =\angle P[/tex]

However, we don't have all 3 interior angles of either triangle, so we cannot conclude anything.

The number of hours that Jasmine can work so she can afford the new headphones x = 6 weeks.

let x represent the number of weeks it will take to save enough money.

If she saves $11 each week, then in x weeks she will save  11x dollars.

Add this to the 107 she has already saved, and at the end of 11 weeks she will have

  11x + 107 dollars.

We want the amount saved to be equal to the price of the bike, so our equation is

11x + 107 = 173

In a word problem, writing the equation is usually the hardest part. Now we solve the equation.

Subtract 107 from both sides to get

11x = 66

Divide both sides by 11 to get

x = 6 weeks.

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The area under the standard normal curve to the left of z = 2.63 is given by calculator will be 0.995.

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The area under the standard normal curve to the left of z = 2.63 is given by calculator will be

Area = 0.995

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Using the normal distribution, it is found that there is a 0.1029 = 10.29% probability that the sample mean is above 96.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching the problem on the internet, the parameters are given as follows:

[tex]\mu = 92, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623[/tex]

The probability that the sample mean is above 96 is one subtracted by the p-value of Z when X = 96, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{96 - 92}{3.1623}[/tex]

Z = 1.265

Z = 1.265 has a p-value of 0.8971.

1 - 0.8971 = 0.1029 = 10.29% probability that the sample mean is above 96.

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The amount of money he lose on the last tool set is: $30.60.

Using this formula

Amount lose=Original amount paid -Selling price

Where:

Original amount paid=$54.60

Selling price=$24.00

Let plug in the formula

Amount lose=$54.60-$24.00

Amount lose=$30.60

Therefore the amount of money he lose on the last tool set is: $30.60.

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