my teacher didn't explain fully​

The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

To find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:

Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.

Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.

Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.

Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.

Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).

Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

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The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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The domain of the function consists of all real numbers greater than 0.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Next, we would determine the function which models the amount of gas as follows:

Function, f(x) = rate × x

Function, f(x) = 2.25 × x

Function, f(x) = 2.25x

Based on the function above, we can reasonably and logically deduce that the amount of gas cannot be negative. Therefore, the domain of this function is given by:

Domain = [0, ∞]

In conclusion, the domain is equal to all real numbers that are greater than zero (0).

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Answer:

75 student tickets and 525 adult tickets

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

h(17) is falling under the top condition of:

So the answer is:

Answer:

a) For sketch see attached picture.

 \(y=-8cos(\pi t)+10\)

b) Mary will be able to enjoy the scenery for a total of 1.68 min or about 101 seconds.

Step-by-step explanation:

a) In order to find the algebraic representation of the problem, we must start by drawing a sketch of what the problem looks like (see attached picture). Next, we can analyze it to see what function better fits the situation. In this case, since the ride starts at the lowest point, then we are talking about a negative cos function. A cos function has the followng general form:

\( y= Acos(\omega t - \phi) + C\)

where:

A= amplitude

\(\omega\)=angular speed

t=time

\(\phi\)= phase shift

C= vertical shift.

In this case the amplitude will be the radius of the ferris wheel, so:

A=-8

it's negative because it starts at the lowest point.

the angular speed is the angle the ride will move in a given amount of time. In this case:

\(\omega=\frac{\pi rad}{1 min}\)

\(\omega=\pi rad/min\)

There will be no phase shift for this problem.

the vertical shift is the height of the platform, so:

C= 2

so the algebraic expression is:

\(y=-8cos(\pi t)+10\)

b) In order to find the total time for which she will enjoy the ride we must start by building an inequality:

\(-8cos(\pi t)+10>12\)

and solve it for t. We can start by turning it into an equation, solve it for t and find the answers that can be found into its domain, in this case D=[0,4]

so we get:

\(-8cos(\pi t)+10=12\)

we subtract a 10 from both sides so we get:

\(-8cos(\pi t)=2\)

and divide 8 to both sides so we get:

\(cos(\pi t)=-\frac{1}{4}\)

Next, we take the inverse cosine to both sides and get different answers:

\(\pi t = 1.823+2\pi n\)

and

\(\pi t=4.46 + 2\pi n\)

we take both equations and divide them into pi so we get:

\(t = 0.58+2 n\)

and

\(t=1.42 + 2n\)

so now we find the possible answers that are between 0 and 4 minutes, this is for n=0 and 1, so we get the following times:

t={0.58, 1.42, 2.58, 3.42} min

we can now build our possible intervals for which the ferris wheel is higher than 12 m so we get the following intervals:

(0, 0.58) (0.58, 1.42) (1.42, 2.58) (2.58, 3.42) and (2.58, 4)

so we pick a test value for each of the intervals and test it on our equation. If the equation gives us a number that is greater than 12, then we have a valid interval. If we get a value that is less than 12, then we just discard that interval.

for (0, 0.58) we use 0.5 and get an answer of 10. We discard this interval.

for (0.58, 1.42) we use 1 and get an answer of 18. This is a valid interval.

for (1.42, 2.58) we use a 2 and get an answer of 2. We discard this interval.

for (2.58, 3.42) we use a 3 and get an answer of 18. This is a valid interval.

and finally, for (2.58, 4) we use a 3.5 and get an answer of 10. We discard this interval

So we have two valid intervals now: (0.58, 1.42) and (1.42, 2.58). So now we can use them to find the time for which Mary will enjoy the scenery.

\(t_{1}=1.42min-0.58min=0.85min\)

\(t_{2}=2.58min-1.42min=0.85min\)

\(t_{total}=0.85min+0.85min\)

\(t_{total}=1.68min\)

so:

Mary will be able to enjoy the scenery for a total of 1.68 min or about 101 seconds.

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Answer:

q=40

Step-by-step explanation:

q/10+71=75

       -71.  -71

q/10=4

 x10 x10

q=40

hopes this helps

Answer:

What the guy above me says!

Step-by-step explanation:

If  a player hits a ball while a bird is flying across the field. The intersection points of the equations represent: C the time when the height of the ball and the bird are the same.

Intersection points  can be defined as the points in which two parallel lines meet each other.

Given data:

Height of the baseball over time = h = –16t² + 65t

Height of a bird over time = h = 8t + 20

Where:

t = time in seconds

h = height in feet

–16t² + 65t =  8t + 20

-16t² +57t -20 =0

So,

t = -57 ±√57² -4×(-16) × (-20) / 2× (-16)

t = -57±√3249  -1280/ -32

t = -57 ±√1969 /-32

t = -57 + 44.373 / -32

t =  -12.627 /-32

t =.395

And

t = -57 - 44.373 / -32

t =  -101.373 /-32

t =3.168

Based on the above of the height of both the baseball and the bird, the time when the height of the ball and the bird are the same  are the points were the two lines intersect.

Therefore the correct option is C.

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Answer:

yes

Step-by-step explanation:

Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."

The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:

1 / 750 = 0.001333

This means that for every 750 Hispanic females, one is expected to have the disease.

To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:

0.001333 * 26,000 = 34.658

So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

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Any proper CDF \(F(x)\) has the properties

• \(\displaystyle \lim_{x\to-\infty} F(x) = 0\)

• \(\displaystyle \lim_{x\to+\infty} F(x) = 1\)

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

\(\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1\)

and so

\(\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0\)

\(\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1\)

Answer:x=6

Step-by-step explanation:g o h is a composition function

First we find g o h

g o h is g(h(x))

We plug in h(x) in g(x)

We replace x  with 2x-8 in g(x)

To find domain we look at the domain of h(x) first

Domain of h(x) is set of all real numbers

now we look at the domain of g(h(x))

Negative number inside the square root is imaginary. so we ignore negative number inside the square root

So to find domain we set 2x - 12 >=0   and solve for x

2x - 12 >=0

add both sides by 12

2x >= 12

divide both sides by 2

x > = 6

Answer:  x ≥ 6

Step-by-step explanation:

The notation shown in your question means "g of h of x"

So we are taking whatever output we get from function 'h' and then applying function 'g' to that output.

For example, suppose I have two functions, 'a' and 'b'. Further suppose a(x) = 2x and b(x) = x +5

If I want a°b, that is really a[b(x)] = a(x + 5) = 2(x+5) = 2x + 10

In your case, we want g[h(x)] = g(2x-8) = \(\sqrt{(2x - 8) - 4}\) = \(\sqrt{2x - 12}\)

Now, we know that in the set of Real numbers, we cannot take a square root of a negative number.

Therefore, (2x - 12) must be zero or greater.

So, our restriction is that 2x - 12 ≥ 0. But of course we must simplify.

    Add 12 to both sides  --->    2x  ≥ 12

    Divide both sides by 2 --->    x ≥ 6

That is the restriction for (g ° h)(x) --->  x ≥ 6

Hope this helps!

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Step-by-step explanation:

y=mx+c where m us the slope and c is the y intercept.

in this case m is given.

\( 8 = \frac{ - 2}{3} ( - 3) + c \\ 8 = \frac{6}{3} + c \\ 8 = 2 + c \\ c = 8 - 2 \\ c = 6\)

I did all that to find the value of c by plugging in the slope magnitude and the given points.

now that means

\(y = \frac{ - 2}{3} x + 6\)

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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Answer:

A line has a slope of 2/3 and y–intercept -2. The equation of the line is y = (2/3)x - 2.

Step-by-step explanation:

Hope this helps

Answer:

y = (2/3)x - 2

Step by step explanation:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

Given, slope of the line is 2/3

y-intercept is -2.

The equation of the line in slope-intercept form is given by

y = mx + c

Where, m is the slope

c is the y-intercept.

y = (2/3)x - 2

Answer:

\(2x - 1 > 4x + 6 \\ 2x - 2x - 1 > 4x - 2x + 6 \\ - 1 > 2x + 6 \\ - 6 - 1 > 2x \\ - 7 > 2x \\ \frac{ - 7}{2} > x \)

I hope I helped you^_^

1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)

2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)

3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)

4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)

5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)

6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)

7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)

8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)

9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)

10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)

11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)

12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)

13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)

14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)

Here are the journal entries for the given transactions:

1. Bricks and timber purchased for construction:

Debit: Bricks (Asset) - Rs 60,000

Debit: Timber (Asset) - Rs 35,000

Credit: Bank (Liability) - Rs 95,000

2. Transfer to fixed deposit account:

Debit: Fixed Deposit (Asset) - Rs 13,000

Credit: Current Account (Asset) - Rs 13,000

3. Appointment of Mr. S.N. Rao as Accountant:

Debit: Salary Expense (Expense) - Rs 300

Debit: Security Deposit (Asset) - Rs 1,000

Credit: Accountant (Liability) - Rs 300

4. Goods sold to Shruti:

Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000

Credit: Sales (Income) - Rs 80,000

5. Goods purchased from Richa:

Debit: Purchases (Expense) - Rs 60,000

Credit: Accounts Payable - Richa (Liability) - Rs 60,000

6. Goods sold to Shilpa:

Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000

Credit: Sales (Income) - Rs 50,000

7. Goods sold to Garima:

Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000

Credit: Sales (Income) - Rs 1,00,000

8.Purchase of land:

Debit: Land (Asset) - Rs 2,00,000

Debit: Brokerage Expense (Expense) - Rs 2,000

Debit: Registration Charges (Expense) - Rs 15,000

Credit: Bank (Liability) - Rs 2,17,000

9. Goods and cash taken away by proprietor:

Debit: Proprietor's Drawings (Equity) - Rs 65,000

Credit: Goods (Asset) - Rs 25,000

Credit: Cash (Asset) - Rs 40,000

10. Goods sold to Charu:

Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000

Credit: Sales (Income) - Rs 1,20,000

Credit: Cost of Goods Sold (Expense) - Rs 80,000

Credit: Profit on Sales (Income) - Rs 40,000

11. Rent paid for the building:

Debit: Rent Expense (Expense) - Rs 60,000

Credit: Bank (Liability) - Rs 60,000

12. Goods sold to Sunil:

Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000

Credit: Sales (Income) - Rs 24,000

Credit: Cost of Goods Sold (Expense) - Rs 20,000

Credit: Profit on Sales (Income) - Rs 4,000

13. Goods purchased from Nanda and supplied to Helen:

Debit: Purchases (Expense) - Rs 1,000

Debit: Accounts Payable - Nanda (Liability) - Rs 1,000

Credit: Accounts Receivable - Helen (Asset) - Rs 1,300

Credit: Sales (Income) - Rs 1,300

14. Goods received from Rohit and Sons and supplied to Madan:

Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)

Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700

Debit: Accounts Receivable - Madan (Asset) - Rs 3,000

Credit: Sales (Income) - Rs 3,000

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Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

When one and seventy one hundredth is written in decimal form, it would be 1. 71

A single part of something that has been evenly divided into one hundred parts is referred to as a hundredth in mathematics. The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal.

This means that when given the number one and seventy One Hundredths in words, then the number, " one " would be written before the decimal and the 71 would be 0. 71 as a hundredth figure.

When put together, this becomes:

= 1 + 0. 71

= 1. 71

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Answer:

17 ounce cereal

Step-by-step explanation:

It is only a 53. cent difference so the better option would be the 17 ounce bag

Answer:

A slope of the line over the interval of [-6, -1] is ⅕ as illustrated in the graph above

The answer you are looking for is -9/10, or -0.9.

Solution:

-1 3/10+4/10

-13/10+4/10

-9/10, or -0.9

Answer:

-0.9

Step-by-step explanation:

Answer:

See explanation below.

Step-by-step explanation:

Given transformed function:

\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)

The parent function of the given function is:  y = sin(x)

The five key points for graphing the parent function are:

(See attachment 1)

Standard form of a sine function:

\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)

where:

Therefore, for the given transformed function:

\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)

See attachment 2.