What is the best approximation for the relative minimum of the polynomial
function graphed below?
OA. (1.5,-1.8)
B. (0,-3)
C. (-3,0)
OD. (-1.5,-1.8)
G

Answer:

a=3√77=26.3 ( rounded to the nearest tenth)

Step-by-step explanation:

hyp.=37

base=26

a²+b²=c²

a²=c²-b²

a²=37²-26²

a²= 693

a=√693

a=3√77=26.3 ( rounded to the nearest tenth)

                                  Answer:       \(\huge\boxed{26.3}\)

Explanation...

Our hypotenuse =37

Our B = 26

___________________________________________________________

Rearrange Formula (A^2+B^2=C^2)...

A^2=C^2-B^2

A^2=37^2-26^2

37^2= 1396

26^2= 676

1396-676=√693

√693= 26.342

26.342=26.3

Answer:

$1,849

Step-by-step explanation:

7,396/4=1,849

Answer:

shading,

Step-by-step explanation:

do shading to the fraction supposed to be, eg: 1\4 here we have four parts divided and 1 is to be shaded as it gives 1 out of 4 okay? or 2\8 here in 8 divided parts only shade 2 as it's given. I hope it's right!!

Answer

-21x + 5y - 7

Did this help?

Step-by-step explanation:

The height of the flagpole is 20.3 feet.

A flagpole casts a 20-foot shadow at the same time Lexi casts a 5-foot shadow. If Lexi is 5'9", the height of the flagpole can be calculated as follows:

5 ft 9 inches = 5.075 feet's

Using proportion let's find the height of the flag,

let

height of flag = x

Therefore,

x / 20 = 5.075 / 5

cross multiply

5x = 20(5.075)

5x = 101.5

divide both sides by 5

x = 101.5 / 5

x = 20.3 feet

Hence,

height of the flagpole = 20.3 feet

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Answer:

23,370

Step-by-step explanation:

Because 18% of 28,500 is 5130 and 28500-5130=23370

Answer:

Not A Math Person

Step-by-step explanation:

Answer:

$11.50 per CD

Step-by-step explanation: u have to make 5 into 1, thats divinding. Then u divide $57.50 by 5, there's your unit price :)

So, here we are to factor the polynomials :

\(\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\\)

\( \longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\\)

\(\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\\)

\( \longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\\)

\(\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\\)

\(\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\\)

\(\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\\)

\( \longrightarrow \sf \qquad 16 {x}^{2} y(x^4 + y^3 + 2xy)\\ \\\)

Some points to know :

Step-by-step explanation:

\(h(x) = a.6 \div 3 \\ \)

i hope its good

Answer:

\(y = {(0.7634)}^{4} \\ log(y) = 4 log(0.7634) \\ log(y) = - 0.46899 \\ y = {10}^{ - 0.46899} \\ y = 0.3396\)

Performance measures dealing with the number of units in line and the time spent waiting are called D. operating characteristics.

Operating characteristics are performance measures that provide information about the operational behavior of a system. In the context of queuing theory, operating characteristics specifically refer to measures related to the number of units in line (queue length) and the time spent waiting (queueing time) within a system. These measures help assess the efficiency and effectiveness of the system in managing customer or job arrivals and processing.

The number of units in line is an important indicator of how congested a system is and reflects the amount of work waiting to be processed. By monitoring the queue length, managers can determine if additional resources or adjustments to the system are required to minimize customer wait times and enhance throughput.

Similarly, the time spent waiting, often referred to as queueing time, measures the average or maximum amount of time a customer or job must wait before being serviced. This measure is crucial in assessing customer satisfaction, as excessive wait times can lead to dissatisfaction and potential loss of business.

Operating characteristics provide quantitative insights into these key performance indicators, allowing organizations to make informed decisions regarding resource allocation, process improvements, and service level agreements.

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Answer:

Step-by-step explanation:

14% of 150 mg = 0.14* 150 = 21 mg

21 mg will be eliminated  from our body in an hour

150/21 = \(7\frac{3}{21}\)

  = 7 hours { rounding to the nearest}

Dilating the triangle ABC would create a triangle with a different side length from triangle ABC

From the diagram, we have the coordinates to be:

A = (2,-5)

B = (2,4)

C = (-4,3)

The dilation rule is given as:

(x,y) => (1.5x, 1.5y)

So, we have:

A' = (3,-7.5)

B' = (3,6)

C' = (-6,4.5)

See attachment for the image of the dilation

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The linear approximation of f(x) at a point a is given by the equation f(a) + f'(a)(x - a), where f'(a) is the derivative of f(x) at x = a. Using this formula with a = 5π/6 and f(x) = sin(x), we get sin(5π/6) + cos(5π/6)(147∘ - 5π/6) as the linear approximation of sin(147∘).

To approximate sin(147∘), we first need to find the linear approximation of f(x) = sin(x) at x = 5π/6. The linear approximation of f(x) at a point a is given by the equation:

f(a) + f'(a)(x - a)

where f'(a) is the derivative of f(x) at x = a. Since f(x) = sin(x), we have f'(x) = cos(x). Therefore, at x = 5π/6, we have:

f(5π/6) = sin(5π/6) = 1/2

f'(5π/6) = cos(5π/6) = √3/2

Plugging these values into the linear approximation formula, we get:

sin(5π/6) + cos(5π/6)(x - 5π/6)

Now we can use this formula to approximate sin(147∘). To do this, we convert 147∘ to radians by multiplying it by π/180. This gives us:

sin(147∘) ≈ sin(5π/6) + cos(5π/6)(147π/180 - 5π/6)

Simplifying this expression, we get:

sin(147∘) ≈ sin(5π/6) + cos(5π/6)(7π/12)

Evaluating sin(5π/6) and cos(5π/6), we get:

sin(147∘) ≈ 1/2 + √3/2 * (7π/12)

Simplifying this expression, we get:

sin(147∘) ≈ √3/4 + π/12

Finally, we can evaluate this expression to get our approximation:

sin(147∘) ≈ 0.866025 + 0.261799/4 ≈ 0.8660

Thus, we have approximated sin(147∘) to four decimal places using a linear approximation of f(x) = sin(x) at x = 5π/6.

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in conclusion the option is round(pi, 2)

Why it is and what does pi mean?

To round the number held in the variable pi to 3.14, we can use the round() function in Python and specify the number of decimal places we want to round to. So the correct answer is:

round(pi, 2)

This will round the number held in the variable pi to 2 decimal places, resulting in 3.14.

Pi (represented by the Greek letter "π") is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is a non-repeating, non-terminating decimal, meaning that it goes on forever without ever settling into a permanent pattern.

Pi is approximately equal to 3.14159, but it has been calculated to over 31 trillion decimal places with the help of supercomputers.

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Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.

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Answer:

a. 26

Step-by-step explanation:

The formula for depreciation is given as

y = a(1 - r)^t

a = Initial value = $15,500

y = Current value = 1/10 of Initial value = $1,550

r = depreciation rate = 8.5% = 0.085

t = time in years = ?

Hence,

1550 = 15500(1 - 0.085)^t

1550 = 15500(0.915)^t

Divide both sides by 15500

1550/15500 =(0.915)^t

0.1 = (0.915)^t

Take the Logarithm of both sides

log 0.1 = log(0.915)^t

log 0.1 = t log (0.915)

Divide both sides by log 0.915

t = log 0.1/log 0.915

t = 25.920900964 years

Approximately Time t = 26 years

Option a is correct

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

Step-by-step explanation:

Answer:

The picture has the answer

Step-by-step explanation:

First since the y-intercept is -2 you will draw a point on -2 on the y - axis.

Next you will do rise over run. Go up 3 from -2 then move to the right 2. Then draw another point. And draw a line through the two points.

I will do a pic for you!

Hope this helps ya!!

Starting with the first term οf the sequence, which is 13. As a result, the sequence's fοurth term is -2.

The given sequence starts with the first term, which is 13. The term-tο-term rule is 'take away 5', which means we need tο subtract 5 frοm the previοus term tο get the next term in the sequence.

Sο, tο find the secοnd term, we subtract 5 frοm the first term, which gives us 13 - 5 = 8.

Tο find the third term, we subtract 5 frοm the secοnd term, which gives us 8 - 5 = 3.

Tο find the fοurth term, we subtract 5 frοm the third term, which gives us 3 - 5 = -2.

Hence, the sequence's fοurth term is -2.

Overall, we can use the given term-tο-term rule tο find any term in the sequence by applying it successively tο the previοus term.

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Answer:

180 pages

Step-by-step explanation:

Answer: 180 pages

Step-by-step explanation:

Let the equation be

x - 7/9x = 40

9x - 7x = 360

x = 360 / 2 = 180

The book has total 180 pages

Means he has read (180 - 40) = 140 pages

Answer:

y = -1/2(x + 4)² + 2 or y = -1/2x²- 4x - 6

Step-by-step explanation:

Given

Vertex = (-4, 2)

The graph passes through the point (-8, -6)

The function in vertex form is:

y = a(x + 4)² + 2

Substitute the coordinates of (-8, -6) and find the value of a:

-6 = a(-8 + 4)² + 2

-8 = 16a

a = -1/2

The function is:

y = -1/2(x + 4)² + 2

or in standard form:

y = -1/2(x² + 8x + 16) + 2 = -1/2x²- 4x - 6

Answer:

-30

Step-by-step explanation:

i am not sure just remember getting taught it.

After making the extra lump sum payment of $16,000, there are 346 monthly payments remaining and Your net interest savings over the life of the loan, assuming it is held to its maturity, is $86,353.39.

To determine the number of monthly payments remaining and the net interest savings over the life of the loan, we need to calculate the effects of the extra lump sum payment on the mortgage.

Given:

Loan amount (principal balance) = $250,000

Interest rate = 6.50%

Discount points = 2

Extra lump sum payment = $16,000

A. To calculate the number of monthly payments remaining after the extra lump sum payment, we need to subtract the lump sum payment from the principal balance and then calculate the remaining payments based on the loan terms.

Principal balance after the lump sum payment:

$250,000 - $16,000 = $234,000

Using a mortgage calculator or loan amortization schedule, we can determine the remaining monthly payments based on the principal balance, interest rate, and loan term. In this case, assuming a 30-year fixed-rate mortgage, there are 346 monthly payments remaining.

B. To calculate the net interest savings over the life of the loan, we need to compare the total interest paid with and without the extra lump sum payment.

Total interest paid without lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 360 - $250,000

Total interest paid with lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 346 - $234,000

Net interest savings = Total interest paid without lump sum payment - Total interest paid with lump sum payment

Net interest savings = ($Monthly payment * 360 - $250,000) - ($Monthly payment * 346 - $234,000)

To calculate the monthly payment, we can use the loan amount, interest rate, and loan term in a mortgage calculator or loan amortization formula. Let's assume the monthly payment is $1,580.17.

Net interest savings = ($1,580.17 * 360 - $250,000) - ($1,580.17 * 346 - $234,000)

Net interest savings = $86,353.39

Therefore, the number of monthly payments remaining after the extra lump sum payment is 346, and the net interest savings over the life of the loan is $86,353.39.

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The Remainder when dividing f(x) by x - 3 is 840

The remainder when dividing the polynomial f(x) = 3x^5 + 4x^3 + 3 by the binomial x - 3, we can use the polynomial remainder theorem. According to the theorem, if we substitute the divisor, x - 3, into the polynomial f(x) and evaluate it at x = 3, the resulting value will be the remainder.

Let's calculate the remainder using this approach:

Substituting x = 3 into the polynomial f(x), we have:

f(3) = 3(3)^5 + 4(3)^3 + 3

    = 3(243) + 4(27) + 3

    = 729 + 108 + 3

    = 840

Therefore, when f(x) = 3x^5 + 4x^3 + 3 is divided by x - 3, the remainder is 840.

In summary, the remainder when dividing f(x) by x - 3 is 840.

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Answer:

sorry

Step-by-step explanation:

polynomial is not given

question is incomplete

Answer:

x=-8

Step-by-step explanation:

try using this app called cymath it helps with questions like this