. If (5, 7) and (-3, 0) lie on the line ax - by = -20.

i) Find the value of a & b. [IM]
ii) Write the equation of the line in standard form.
iii) Find the coordinate of the point of intersections of the given line with x-axis and y-axis respectively.
iv) Find two more solutions of the given line. ​

The first ordered pair is (850, 162.65), indicating that at a price of $162.65 per ounce, the daily demand of Virbog is 850 ounces. The second ordered pair is (1450, 132.05), indicating that at a price of $132.05 per ounce, the daily demand of Virbog is 1450 ounces.

These ordered pairs represent the relationship between the quantity demanded and the price per ounce of Virbog. It shows how the demand for Virbog changes with respect to its price.

The first ordered pair indicates that as the price per ounce increases to $162.65, the quantity demanded decreases to 850 ounces. The second ordered pair indicates that as the price per ounce decreases to $132.05, the quantity demanded increases to 1450 ounces. This information can be used to analyze the demand curve for Virbog and study its price elasticity.


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Possessive adjectives and possessive pronouns are used to indicate ownership or possession. Here's a more detailed explanation for each sentence:

I am wearing my raincoat.

In this sentence, "my" is a possessive adjective that shows ownership. It indicates that the raincoat belongs to the speaker.

He is wearing his t-shirt.

In this sentence, "his" is a possessive adjective that indicates ownership. It shows that the t-shirt belongs to the person being referred to as "he."

She is wearing her skirt.

In this sentence, "her" is a possessive adjective indicating that the skirt belongs to the person being referred to as "she."

We are wearing our shorts.

In this sentence, "our" is a possessive adjective indicating that the shorts belong to the group of people being referred to as "we."

They are wearing their socks.

In this sentence, "their" is a possessive adjective showing that the socks belong to the group of people being referred to as "they."

You are wearing your pants.

In this sentence, "your" is a possessive adjective indicating that the pants belong to the person or people being referred to as "you."

These shorts are mine. (i)

In this sentence, "mine" is a possessive pronoun that replaces the need for a noun and possessive adjective. It indicates that the shorts belong to the speaker.

This tie is his. (he)

In this sentence, "his" is a possessive pronoun that replaces the need for a noun and possessive adjective. It indicates that the tie belongs to the person being referred to as "he."

This belt is hers. (she)

In this sentence, "hers" is a possessive pronoun indicating that the belt belongs to the person being referred to as "she."

These sneakers are ours. (we)

In this sentence, "ours" is a possessive pronoun showing that the sneakers belong to the group of people being referred to as "we."

These dresses are theirs. (they)

In this sentence, "theirs" is a possessive pronoun indicating that the dresses belong to the group of people being referred to as "they."

In summary, possessive adjectives are used before a noun to show ownership, while possessive pronouns can stand alone to indicate ownership without the need for a noun.

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The area of the triangle is  10.825 square feet.

The area of a triangle is the measure of the region enclosed by the three sides of the triangle. It is expressed in square units and can be calculated using various formulas, such as the formula for the area of a triangle using its base and height (A = (1/2)bh),

To find the area of the triangle, we can use Heron's formula, which states that the area of a triangle with sides of length a, b, and c is given by:

A = √(s(s-a)(s-b)(s-c))

where s is the semi perimeter of the triangle, given by:

s = (a + b + c)/2

Here, the sides of the triangle are 4 ft, 3 ft, and 2/3 ft. Therefore, the semi perimeter is:

s = (4 + 3 + 2/3)/2 = 3 2/3 ft

Using Heron's formula, the area of the triangle is:

A = √(3 2/3(3 2/3 - 4)(3 2/3 - 3)(3 2/3 - 2/3))

A = √(3 2/3(2/3)(9/3)(9/3 - 2/3))

A = √(3 2/3(2/3)(9/3)(8 1/3))

A = √(3 2/3(2/3)(3)(25/3))

A = √(323×25)/3

A = √(450)/3

A ≈ 10.825 ft²

Therefore, the area of the triangle is approximately 10.825 square feet.

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Answer:

0.09125%

Step-by-step explanation:

Divide 73 by 800 and you will get 0.09125

Answer:

It should be %9.75

it is true that for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value. We can find these values by analyzing the critical points and their corresponding second partial derivatives.

True, for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value.
A scalar-valued function f(x, y) is a function that takes two inputs (x and y) and outputs a single value. These types of functions are often used to represent the relationship between two variables, such as the height of a surface above a plane, temperature distribution, or profit of a business depending on two factors.
To find the maximum or minimum value of a scalar-valued function f(x, y), we need to examine its critical points. Critical points are the points where the gradient of the function is either zero or undefined. The gradient is a vector consisting of the partial derivatives of the function with respect to x and y. We can calculate the partial derivatives (∂f/∂x and ∂f/∂y) and then set them equal to zero to find the critical points.
Once we have found the critical points, we can determine whether they correspond to a maximum, minimum, or saddle point (neither a maximum nor a minimum) by examining the second partial derivatives. The second partial derivatives help us determine the curvature of the function around the critical point. We can use the second partial derivative test, which involves calculating the determinant of the Hessian matrix (composed of the second partial derivatives) to classify the critical points.
In conclusion, it is true that for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value. We can find these values by analyzing the critical points and their corresponding second partial derivatives.

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Answer:

35

Step-by-step explanation:

If two things are directly proportional it means that their ratio is costant:

K (proportionality costant) : y/x

we know that when x=5 y=12

so:

K=5/12 (2.4)

we know that when x has a certain value, y=84

so:

2.4 = 84/x

we find the x to be 35

Step-by-step explanation:

The amplitude is the value that the cosine is being multiplied by.

The general equation of a sinusoid is

\( a \cos(b(x + c) ) + d\)

where a is the amplitude

\( \frac{2\pi}{ |b| } \)

is the period

-c is the phase shift

d is the midline(vertical shift)

Here the amplitude is -1/2 so b is the correct answer.

Answer:

the amplitude of the function that is y= -1/2 cos x, is 1/2.

Step-by-step explanation:

The two possible values of x are 2cm and 12 cm.

By changing the order of vertices,

Using the similarity of triangles,

ΔABE ∼ ΔACD

ΔABE ∼ ΔADC

ΔAEB ∼ ΔACD

ΔAEB ∼ ΔADC

Now,

When ΔABE ∼ ΔADC and ΔAEB ∼ ΔACD,

Then,

By the property of similar triangles,

AB/AD = AE/AC

10/18 = 15 / (10 + x )

By cross multiplication,

10( 10 + x ) = 18 × 15

100 + 10x = 270

Subtracting 100 from each side,

100 + 10x - 100 = 270 - 100

10x = 170

Dividing each side by 10

x = 17

But, when ΔABE ∼ ΔACD or ΔAEB ∼ ΔADC

Using the property of similar angles,

AE/AD = AB/AC

15/18 = 10 / (10+x)

Using cross multiplication,

15( 10 + x ) = 18 × 10

150 + 15x = 180

Subtracting 150 from each side,

150 + 15x - 150 = 180 - 150

15x = 30

Dividing each side of the equation by 15,

x = 30 / 15

x = 2

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Answer:

24 mph

Step-by-step explanation:

The basis for the subspace of R⁴ consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2] is:
[1, 0, 0, -5]
[0, 1, 4, -7]
[0, -1, -9, 0]

To find a basis for the subspace of R⁴ consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2], we can express the given vector in terms of x1 and x2:
v = x1[1, -2, -9, -5] + x2[0, 1, 4, -7]
The basis of the subspace is the set of linearly independent vectors that can be used to generate all other vectors in the subspace. In this case, the basis is formed by the vectors:
{[1, -2, -9, -5], [0, 1, 4, -7]}
These two vectors are linearly independent and can be used to form any vector in the given subspace by adjusting the values of x1 and x2.

To find a basis of the subspace of R⁴  consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2], we first need to rewrite this vector in terms of the standard basis vectors of R⁴.
[x1, -2x1+x2, -9x1+4x2, -5x1-7x2] = x1[1, 0, 0, -5] + x2[0, 1, 4, -7] + (-2x1)[0, -1, -9, 0]
We can see that this vector is a linear combination of the following three vectors:
[1, 0, 0, -5]
[0, 1, 4, -7]
[0, -1, -9, 0]
We want to check if these three vectors are linearly independent. We can do this by setting up the following matrix and finding its rank:
[1 0 0]
[0 1 -1]
[0 4 -9]
[-5 -7 0]
Row reducing this matrix, we get:
[1 0 0]
[0 1 0]
[0 0 1]
[0 0 0]
Since the rank of this matrix is 3, we know that the three vectors are linearly independent and therefore form a basis for the subspace.
So, the basis for the subspace of R⁴ consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2] is:
[1, 0, 0, -5]
[0, 1, 4, -7]
[0, -1, -9, 0]

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Answer:

The answer is 12

Step-by-step explanation:

2/3·18/1=36/3

36÷3=12

Answer: 1 tablespoon

Step-by-step explanation:

Answer: Scientific notation is used in the real world to make writing very large numbers, like the distance of a star from Earth or the weight of our oceans, much simpler and easier, especially when writing them in things like reports or scientific papers.

Step-by-step explanation: For example, the distance of the Sun from Neptune is somewhere around 4,500,000,000km. Writing this number takes time, and when you have to write this over and over, it wastes time, so instead, you would write 4.5 × 10⁸, which is much shorter and saves time when writing it down in a scientific report/paper many times.


Sorry for the really long explanation, I'm pretty sure just the 'Answer' bit should be fine, but you can include the 'Step-by-step explanation' bit if you want.

Hope this helps!

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

A

Step-by-step explanation:

the ship is 472 m from the lighthouse

Step-by-step explanation:

from the question, we can know ∠OAS = 90°-23° =67° and AO = 200m

OS = A0 • tan 67°

= 200 m • 236°

= 472 m

Answer:D)AP is not congruent to PB

Answer:

4?

lol

Step-by-step explanation:

Answer:

The answer is "\(\bold{\cos 65}\)"

Step-by-step explanation:

Given:

\(\Rightarrow \bold{\sin 25}\\\)

\(\Rightarrow \sin 25\) can be written as \(\frac{\sin 25}{1}\)

\(\therefore \tan \theta = \frac{\sin \theta }{cos \theta}\)

\(\Rightarrow \sin 25\) can be written as \(\cos (90-65)\)

The answer is "\(\bold{\cos 65}\)".

Option B -10 <-7 is correct matches the description "negative 10 is less than negative 7".

what is negative number ?

A negative number is a real number that is less than zero. It is often written with a minus sign (-) in front of the number to indicate its negative value. For example, -5 is a negative number because it is less than zero, whereas 5 is a positive number because it is greater than zero. Negative numbers are used in many areas of mathematics, science

In the given question,

A negative number is a real number that is less than zero. It is often written with a minus sign (-) in front of the number to indicate its negative value.

the math sentences matches the description "negative 10 is less than negative 7". The correct math sentence is: -10 <-7.

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Answer:

Step-by-step explanation:

x=3,-1

Answer:

The equation would be y=2x-2 so slope would be 2

sorry if i'm wrong

Answer:

$43 + $6l

Step-by-step explanation:

Hello!

She spends $43 and bus several $6 laces.

We don't know how many she buys, but we know that we can represent that number using l.

That means she spends $43 + $6l.

The algebraic expression is $43 + $6l.

We can determine the price if we know the number of laces she buys. We can simply plug in the number of laces she bought, and we can plug it in for l in the equation.

Answer:

43= 6(x)

Explanation:

43 is the total,  and each of them are 6$ each. X is the variable that we don't know.

The expected population of citizens aged 45-64 years in 2013 is 58.62 millions.

Given that P(t) = 197.9/(1+3.274e^{-0.0361t})

Approximation for P(t) will be taken for 0 ≤ t ≤ 25 (years), where P(t) is measured in millions and t is measured in years and it corresponds to the beginning of 1990.

This is a demographic equation of the population of a specific age group.

Suppose people belonging to the age group 45-64 years sell annuities.

To calculate the expected population of the citizens belonging to this age group in 2010 and 2013 respectively is calculated using the above equation:

Expected population of citizens aged 45-64 years in 2010:

Substituting t = 20 (since it is the year 2010) in the given equation:

P(t) = 197.9/(1+3.274e^{-0.0361t})

= 197.9/(1+3.274e^{-0.0361*20})

= 197.9/(1+3.274e^{-0.722})

= 197.9/(1+2.087)

= 82.27 millions (rounded to 1 decimal place)

Therefore, the expected population of citizens aged 45-64 years in 2010 is 82.27 millions.

Expected population of citizens aged 45-64 years in 2013:

Substituting t = 23 (since it is the year 2013) in the given equation:

P(t) = 197.9/(1+3.274e^{-0.0361t})= 197.9/(1+3.274e^{-0.0361*23})= 197.9/(1+2.369)= 58.62 millions (rounded to 1 decimal place)

Therefore, the expected population of citizens aged 45-64 years in 2013 is 58.62 millions.

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The expected population of citizens aged 45-64 years in 2010 is 76.4 million.

The expected population of citizens aged 45-64 years in 2013 is 81.5 million.

Based on the information provided above, the number of citizens that are aged 45-64 years can be approximated by the following exponential function:

\(P(t)=\frac{197.9}{1\; +\;3.274e^{ -0.0361t}}\)         (0 ≤ t ≤ 25)

where:

For the expected population of the citizens (45-64 years) in 2010, we have the following:

Number of years, t = 2010 - 1990

Number of years, t = 20 years.

When t = 20 years, we have:

\(P(20)=\frac{197.9}{1\; +\;3.274e^{ -0.0361 \times 20}}\\\\P(20)=\frac{197.9}{1\; +\;3.274e^{-0.722}}\\\\P(20)=\frac{197.9}{1\; +\;3.274(0.4857797243)}}\)

P(20) = 197.9/2.5904428173582

P(20) = 76.4 million.

For the expected population of the citizens (45-64 years) in 2013, we have the following:

Number of years, t = 2013 - 1990

Number of years, t = 23 years.

When t = 23 years, we have:

\(P(23)=\frac{197.9}{1\; +\;3.274e^{ -0.0361 \times 23}}\\\\P(23)=\frac{197.9}{1\; +\;3.274e^{-0.8303}}\\\\P(23)=\frac{197.9}{1\; +\;3.274(0.43591849115)}}\)

P(23) = 197.9/2.4271971400251

P(23) = 81.5 million.

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Complete Question:

Demographics Suppose the number of citizens aged 45-64 years is approximated by

\(P(t)=\frac{197.9}{1\; +\;3.274e^{ -0.0361t}}\)         (0 ≤ t ≤ 25)

where P(t) is measured in millions and is measured in years, with to corresponding to the beginning of 1990. People belonging to this age group to sell them annuities.

What is the expected population of citizens aged 45-64 years in 2010? In 2013? (Round your answers to one decimal place)

Answer:

$64

Step-by-step explanation:

Since 20% is 0.20 and a whole is 1.00, to discount the price, we have to subtract the whole value by the discount value 1.00-0.20=0.80

Then we have to find 80% of 80

80%=0.80

0.80*80=64

The sale price is $64

The least-squares line is represented by the equation y = mx + b, where m is the slope and b is the y-intercept. It minimizes the sum of squared differences between the data points and the line.

The least-squares line that best fits the given data can be represented as y = mx + b, where m and b are the coefficients to be determined.

To obtain the least-squares line that best fits the data, we need to find the values of m and b that minimize the sum of the squared differences between the observed data points and the corresponding points on the line.

The equation for the least-squares line is y = mx + b, where m represents the slope of the line and b represents the y-intercept. By applying the method of least squares, we can determine the values of m and b that provide the best fit to the data.

To calculate the values of m and b, we need the specific data points. Without the data, it is not possible to provide the exact values for the coefficients.

Therefore, to complete the statement, we would need the actual data points to perform the calculations and determine the values of m and b for the least-squares line.

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