Find the slope Y intercept in the equation for the data in the table and in the graph

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer:

This reservoir, will store drinking water for the town. Which of the following could cause contamination of the water and lead to human health-related problems and loss of native species? ... Air pollution can affect human health and the health of other living things.

Step-by-step explanation:

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Using the laws of exponents, we can simplify the given expression as:

-(¹/₂₇)(1/x¹²)y²¹

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

The expression is given as:

(-3x⁴y⁻⁷)⁻³

Using the power to power rule of exponents, we have:

-3⁻³x⁻¹²y²¹

Using the reciprocal law of exponents, we have:

(-1/3³)(1/x¹²)y²¹

= -(¹/₂₇)(1/x¹²)y²¹

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Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts.

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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sec(theta) = 1/cos(theta)

I believe that is your option D

As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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Given:

a.) You deposit $4000 in an account earning 8% interest compounded monthly.

Question: How much will you have in the account in 15 years?

We will be using the following formula:

Where,

A=final amount

P=initial principal balance = $ 4,000

r=interest rate = 8% = 8/100 = 0.08

n=number of times interest applied per time period = monthly = 12

t=number of time periods elapsed = 15 years

We get,

Therefore, in 15 years, you will have $13,235.57 in your account.

Answer:

The 3.907 is approximate.

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

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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

Extra info:

Answer:

B. 1,440

Step-by-step explanation:

Answer:

Step-by-step explanation:

think about it how many groups can see the movie in 12 hours. that would be 4, now multiply 360 people by 4. if you do it right you answer should be 1440.(hope this helps :)   )

Step-by-step explanation:

Volume = lwh

V = 23 x 24 x 8

V = 4416ft^3

Ft - Yd:

4416ft^3 = 163.5556^3 yd

(I'm not actually sure about this as I don't use the imperial system)

Lucia's sister has n - 10 dollars.

We can create an equation to depict the relationship between Lucia's and her sister's financial situations if Lucia has n–10 dollars and her sister has $10.00 more.

Assume that Lucia's sister has $x. We can write the equation using the information provided:

n - 10 = x

According to this formula, Lucia's wealth (n-10) is equivalent to her sister's wealth (x). We may find the quantity for Lucia's sister by rearranging the equation as follows:

x = n - 10

Therefore, Lucia's sister has n - 10 dollars.

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Answer:

Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.

For the larger box:

Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²

Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)

For the smaller box:

Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²

Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.

Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)

The difference in cost between the larger and smaller boxes is:

20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)

The percentage savings can be calculated as follows:

Percentage savings = (difference in cost / cost of larger box) * 100%

= (5.33718 / 20.55986) * 100%

= 25.98%

Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.

Answer:

33

Step-by-step explanation:

From what we know in April and May combined Joe has collected 61 stamps (27+34=61). To then work out how many Joe collected in June you would take the 61 we know he has already got away from the grand total of 94 (94-61=33) this means in June he collects 33 stamps. Hope this helps :)

Step-by-step explanation:

the simplest approach is a linear equation (a line), since we only got 2 data points.

and as we know, any set of 2 points creates a line.

so

y = ax + b

due to y = 0 for x = -2

0 = -2a + b

2a = b

and from

y = -25 for x = 8 (and the first equation) we get

-25 = 8a + 2a = 10a

a = -25/10 = -2.5

our equation is

y = -2.5x + 2(-2.5) = -2.5x - 5

Answer:

The correct answer is: 3, 4, 5, 6.

Step-by-step explanation:

The correct answer is: 3, 4, 5, 6.

To check, we can substitute each number into the inequality:

When x = 3: 9 - 2(3) ≥ 3, which simplifies to 3 ≥ 3 (true)

When x = 4: 9 - 2(4) ≥ 3, which simplifies to 1 ≥ 3 (false)

When x = 5: 9 - 2(5) ≥ 3, which simplifies to -1 ≥ 3 (false)

When x = 6: 9 - 2(6) ≥ 3, which simplifies to -3 ≥ 3 (false)

Therefore, only the numbers in the set {3, 4, 5, 6} satisfy the inequality.

Answer:

Explained below.

Step-by-step explanation:

A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.

While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.

A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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If f(n) = f(n - 1) + 4, then

f(n - 1) = f(n - 2) + 4

and substituting this into the first equation gives

f(n) = f(n - 2) + 2•4

Similarly,

f(n - 2) = f(n - 3) + 4

so that

f(n) = f(n - 3) + 3•4

and so on.

Note the pattern:

f(n) = f(n - k) + k•4

so that when k = n - 1, we have

f(n) = f(n - (n - 1)) + (n - 1)•4

or

f(n) = f(1) + 4 (n - 1)

so that

[D] f(n) = -2 + 4 (n - 1)

The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

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