Find the area of the regular polygons and degree of central angle when given either the apothem or side length.​

The graph of the function f(x)=−4.6|x+2|+7 is symmetric at x = -2

From the question, we have the following parameters that can be used in our computation:

The function f(x)=−4.6|x+2|+7.

The function f(x)=−4.6|x+2|+7 is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the line of symmetry is

x = h

Using the above as a guide, we have the following:

Line of symmetry: x = -2

Hence, the graph of the function is symmetric at x = -2

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Answer:

the price of each lemon bought by Encik Halim is RM1.45.

Step-by-step explanation:

Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.

Let's assume that the cost of each lemon bought by Encik Halim is x RM.

The total cost of 108 lemons would then be 108x RM.

Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.

We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:

Total cost = Total revenue - Profit

Total cost = RM244.80 - RM88.20

Total cost = RM156.60

We know that Encik Halim bought 108 lemons, so we can write:

Total cost = Number of lemons bought x Cost per lemon

RM156.60 = 108x

Therefore, the cost per lemon bought by Encik Halim is:

x = RM156.60/108

x = RM1.45

So the price of each lemon bought by Encik Halim is RM1.45.

In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug  can be expressed as 41%.

From the question, the total mass =400 g

The solvent mass = 236 g

Then the mass of the drug = 400-236

= 164

Then the mass percentage of the drug can be calculated as 164/400 * 100

= 41%

Therefore, the strenght of the drug can be expressed as  41%

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The balanced equation of the hanger is 3z = 45 and the solution is z = 15

From the question, we have the following parameters that can be used in our computation:

The hanger image

On the hanger image, we have the following

One side = z + z + z

The other side = 45

The expressions on either sides must be equal to have a balanced equation

So, we have

z + z + z = 45

Evaluate the like terms

3z = 45

Divide both sides of the equation by 3

z = 15

Hence, the balanced equation is 3z = 45 and the solution is z = 15

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The likelihood that the first question will be true is equally likely and unlikely.

From the question, we have the following parameters that can be used in our computation:

The teacher gave a true and false quiz where P(true) = 0.5 for each question.

This means that

P(true) = 0.5

As a percentage,, we have

P(true) = 50%

When the probability of an event is 50%, then the event is equally likely and unlikely.

Hence, the liikelihood is (c) qually likely and unlikely.

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Answer: We can start by simplifying the cube root of 8:

³√8 = 2

Next, we can rewrite 5^-2 as 1/5^2:

1/5^2 x 2 = 1/25 x 2 = 2/25

So the answer, as a decimal, is 0.08 (or 0.08 rounded to two decimal places).

Answer:

B) There is no absolute max for y=f(x)

Step-by-step explanation:

There is no absolute max as the function increases infinitely

However there is an absolute minimum at x=0

Answer:

6.92

Step-by-step explanation:

When ever there are also of decimal places you must at least write the first 2 only.

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The expressions are written as;

h(t)+k(t) = 10t - 1

h(t)−k(t) = -2t + 1

Note that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.

These expressions are made up of arithmetic operations, which includes;

From the information given, we have that;

h(t)=4t

k(t)=t+5t−1

To determine the value of h(t) + k(t), we have;

4t + t + 5t - 1

add the like terms, we get;

10t - 1

To determine h(t) = k(t)

4t- t - 5t + 1

add like terms

-2t + 1

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Applying the triangle sum theorem, the measure of angle x is calculated as: m<x = 72 degrees.

In a triangle, when all of its interior angles are added together, the triangle sum theorem states that we will get a sum of 180 degrees.

Therefore, we have:

m<AHI = 63 degrees [based on the corresponding angles theorem]

Considering triangle AHI, applying the triangle sum theorem, we will have the following:

m<x + m<AHI + m<A = 180°

Substitute:

m<x + 63 + 45 = 180°

m<x + 108 = 180°

m<x = 180 - 108 [subtraction property of equality]

m<x = 72 degrees.

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The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.

Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:

AC/CE = BC/CD

Given the following:

AC = 7.2 units

CE = 2.4 units

CD = 4.2 units

BC = ?

Plug in the values:

7.2/2.4 = BC/4.2

Cross multiply:

BC = 7.2 * 4.2 / 2.4

BC = 12.6 cm

Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.

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Answer:

t = time in years

p(t) = population at time t

[tex]p(t) = 500000( {1.043}^{t} )[/tex]

[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]

f(x) = the total cost for detailing the car. x = the number of minutes it takes to detail the car. m = The cost per minute for the detailing in car. b = the flat fee for detailing the car.

An algebraic equation is said to be linear if the maximum power of the variable is 1. In other words, it is an equation that, when plotted on a coordinate plane, defines a straight line. A linear equation with a single variable has the general form:

ax + b = 0, where a and b are constants and x is the variable. A single value of x that causes the equation to be true is the answer to this equation.

The given situation can be expressed in the form f(x) = mx + b.

Where,

f(x) = the total cost for detailing the car.

x = the number of minutes it takes to detail the car.

m = The cost per minute for the detailing in car.

b = the flat fee for detailing the car.

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The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.

In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).

We have to find the equivalent-expression for (3x-1)-2(x+2);

⇒ (3x-1)-2(x+2),

⇒ (3x - 1) - 2x - 4,

Combing the like-terms together in the above expression,

We get,

⇒ 3x - 2x -1 - 4,

⇒ x - 5,

Therefore, the correct equivalent expression is Option (c).

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The given question is incomplete, the complete question is

Which of the following expression is equivalent to (3x-1)-2(x+2)?

(a) x+3

(b) x+1

(c) x-5

(d) x-3

Using mathematical operations, Cindy's answer would have been 15 if she had worked the problem correctly by following her teacher's instructions.

The correct value can be determined by reversing Cindy's calculations to find the certain number as follows:

(x - 9) ÷ 3 = 43

x = 43 x 3 + 9

x = 138

With the certain number, x = 138, the correct mathematical operations can be performed as follows:

(138 - 3) ÷ 9

135 ÷ 9

= 15

Thus, Cindy's correct answer would have been 15 if she had performed the correct mathematical operations, according to her teacher's instructions.

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Answer:

2:35

Step-by-step explanation:

it takes 2 hours to get to Muar so 9:45

he spends 1 hour 40 in muar so 11:35

he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35

Answer:

(x, -1/2x + 5/2) or infinitely many solutions

Step-by-step explanation:

We can solve the system of equations using substitution.  We can start by isolating x in the first equation.  Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:

Isolating:

x = -2y + 5

Plugging in and solving for y:

4(-2y + 5) + 8y = 20

-8y + 20 + 8y = 20

20 = 20

We see that we get a constant equal to another constant.  Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:

y = -1/2x + 5/2

Thus, the general rule for the solution to the system of equations is

(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions

You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation.  Let's try 4 for x and 0 for x:

4 for x in first equation:

4 + 2(-1/2(4) + 5/2) = 5

4 + 2(0.5) = 5

4 + 1 = 5

5 = 5

4 for x in the second equation

4(4) + 8(-1/2(4) + 5/2) = 20

16 + 8(0.5) = 20

16 +4 = 20

20 = 20

0 for x in the first equation:

0 + 2(-1/2(0) + 5/2) = 5

0 + 2(2.5) = 5

5 = 5

0 for x in the second equation:

4(0) + 8(-1/2(0) + 5/2) = 20

0 + 8(2.5) = 20

20 = 20

Based on the above, the width of the field is 62 meters.

Based on the question, Let's say that the width of the field is  denoted with 'w'.

Note that the formula for the perimeter (P) of a rectangle is:

P = 2(l + w)

where"

l = length

w =  width.

Fixing the values into the equation, it will be:

300 = 2(88 + w)

So, Divide both sides by 2:

150 = 88 + w

Subtract 88 from both sides:

w = 150 - 88

w = 62

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Se text below

The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?

The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

From the given information, the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

We are to carry out the operation

Add -4(row 1) to row 3

This means we should multiply row 1 by -4

-4 × [ 1     2    1   | -5

       -4   -8   -4  | 20

Now, we will add the result to row 3

4    -1     6  |  -8

-4   -8   -4  | 20

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

0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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Answer:

[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = -1\\\\[/tex]

[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)= 0\\\\[/tex]

[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = -\dfrac{1}{0}[/tex]   is not defined

[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) =-1\\\\[/tex]

[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac {1}{0}\\[/tex]  is not defined

[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) =\:0[/tex]

Step-by-step explanation:

[tex]\text{Values of trig functions for $-\dfrac{\pi}{2}$ are: }\\\\[/tex]

[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = - sin\left(\dfrac{\pi}{2}\right) = -1\\\\[/tex]

[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)=\cos \left(\dfrac{\pi }{2}\right) = 0\\\\[/tex]

[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = \dfrac{sin\left(-\dfrac{\pi}{2}\right)}{cos\left(-\dfrac{\pi}{2}\right) } = \dfrac{-1}{0}[/tex]
This is undefined since division by zero is undefined

[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{sin\left(-\dfrac{\pi }{2}\right)} = \dfrac{1}{-1} =-1\\\\[/tex]

[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{\cos\left(-\dfrac{\pi }{2}\right)} = \dfrac {1}{0}[/tex]
This is undefined

[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) = \dfrac{cos\left(-\dfrac{\pi }{2}\right)}{sin\left(-\dfrac{\pi }{2}\right)}\:=\:\dfrac{0}{-1\:}=\:0[/tex]

The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260

The profit function is P = 50x + 80y.

In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.

From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.

Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.

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Chebyshev's inequality is a statistical tool that provides a bound on the probability that a random variable deviates from its mean by a certain amount. It can be used to determine whether there is statistical evidence to support a hypothesis based on sample data.

Suppose we have a random variable D that represents the proportion of defective lightbulbs in a population. We want to test the hypothesis that the average proportion of defective lightbulbs in the population is greater than 0.10, i.e., H₀: D ≤ 0.10 vs H₁: D > 0.10. Let's assume that we have a sample of n lightbulbs and that the sample proportion of defective lightbulbs is W.

Chebyshev's inequality states that for any random variable X, the probability that X deviates from its mean by k standard deviations is at most 1/k². In other words,

P(|X - μ| ≥ kσ) ≤ 1/k²,

where μ and σ are the mean and standard deviation of X, respectively.

Now, let's apply Chebyshev's inequality to our sample proportion W. Since we don't know the true mean and standard deviation of D, we can use the sample mean and sample standard deviation as estimates. The sample mean is W/n and the sample standard deviation is √[W(1-W)/n]. We want to find the probability that D is greater than 0.10, which is equivalent to finding the probability that W/n is greater than 0.10.

Let k = (0.10 - W/n)/(√[W(1-W)/n]). Then,

P(D > 0.10) = P(W/n > 0.10) = P(W - 0.10n > 0) = P(W - μ ≥ (0.10 - μ)n) ≤ σ²/[(0.10 - μ)n]²,

where μ = E(W) = D and σ² = Var(W) = D(1-D)/n. Thus,

P(D > 0.10) ≤ D(1-D)/n[(0.10 - D)n]².

To decide whether there is statistical evidence to support the hypothesis H₁, we need to compare this upper bound on the probability of D being greater than 0.10 to the significance level α = 0.05. If the upper bound is less than α, then we reject the null hypothesis H₀ in favor of the alternative hypothesis H₁.

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Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.

Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).

Here,

When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).

Let x represent the desired shadow's length. Next, we have

=> tan 35° = 15/x

When we multiply both sides by x, we obtain:

=> x tan 35° = 15

By dividing both sides by 35° of tan, we obtain:

=> x = 15 / tan 35°

We may calculate the value of the tangent of 35 degrees using a calculator:

=> tan 35° ≈ 0.7002

Next, we have

=> 15x/0.702x=21.424 metres

Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.

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The unearned interest and the payoff amount is $11,022.12 and $18,784.87 respectively

Given data ,

Kelly bought a new SUV for $28,000. She made a down payment of $11,000 and has monthly payments of $332.63 for 5 years.

She is able to pay off her loan at the end of 36 months.

Now , Total interest = (monthly payment x number of months) - loan amount

Total interest = ($332.63 x 60) - $17,000

Total interest = $19,957.80

Next, we need to calculate the interest that has already been paid over the first 36 months of the loan. We can use the formula:

Interest paid = (monthly payment x number of months) - (loan amount - down payment)

Interest paid = ($332.63 x 36) - ($28,000 - $11,000)

Interest paid = $8,935.68

The unearned interest is the difference between the total interest and the interest paid so far:

Unearned interest = total interest - interest paid

Unearned interest = $19,957.80 - $8,935.68

Unearned interest = $11,022.12

To find the payoff amount, we need to add the remaining principal balance to the unearned interest:

Payoff amount = remaining balance + unearned interest

To calculate the remaining balance, we can use the formula for the present value of an annuity:

Remaining balance = monthly payment x (1 - (1 + r)^-n) / r

Where r is the monthly interest rate and n is the number of remaining months. We can solve for r by using the total interest calculated earlier:

r = (Total interest / loan amount) / 12

r = ($19,957.80 / $17,000) / 12

r = 0.0986%

Using this interest rate and n = 24 (the remaining 24 months of the loan), we can calculate the remaining balance:

Remaining balance = $332.63 x (1 - (1 + 0.0986%)^-24) / 0.0986%

Remaining balance = $7,762.75

Payoff amount = $7,762.75 + $11,022.12

Payoff amount = $18,784.87

Hence , the interest is solved

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Answer:

the number is even

Step-by-step explanation:

an even number plus an even number will aalways be even. adding 6 to an odd number will never be even. Therefore the number will be even

The median of this data set is equal to 9.

The mean of this data set is equal to 13.7.

The number of mode that this data set have is zero modes.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 26+ 0 -1 + 33 + 2 + 31 + 10 + 21 + 7 + 8

Total, F(x) = 137

Mean = 137/10

Mean = 13.7.

Median = (8 + 10)/2

Median = 18/2

Median = 9.

In conclusion, the mode of the data set is non-existent or zero modes because all of the number have the same frequency.

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Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

B = 1/4 * S

S = 2/3 * P

B + S + P = 23.75 - 4.50

Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.

Now we have the equation:

B + S + P = 19.25

Substitute the expressions from relationships 1 and 2 into the equation:

(1/4 * S) + S + (3/2 * S) = 19.25

Now combine the terms:

(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25

(11/4 * S) = 19.25

Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):

S = (4/11) * 19.25

S = 7

The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:

B = 1/4 * S = 1/4 * 7 = 1.75

P = 3/2 * S = 3/2 * 7 = 10.5

Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

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Complete question

Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item

The expanded form of log y^10 is either 10 log y or 10 ln y

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Since the base is not specified, we can use any base we like. For example, we can use base 10 or base e (natural logarithm).

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

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