The order pairs (1, 2), (2, 5), (3, 10), (4, 17), and (5, 26) represent a function. What is a rule that could represent this function?

A. y = x2 + 1
B. y = x2 − 1
C. y = x2
D. y = x + 1

Answer:

The length of the curtain is 10.625 feet

Step-by-step explanation:

The length of the curtain to cover one side of the room depends on the shape of the room

Given a room shape of a square, we have;

Perimeter = 4 × Side length of the room

Length of the curtain = Side length of the room

Therefore;

Perimeter = 4 × Length of the curtain

42.5 feet = 4 × Length of the curtain

Length of the curtain = (42.5 feet)/4 = 10.625 feet

The length of the curtain = 10.625 feet.

\((0,0) \longrightarrow \sf{part \: \: of \: \: the \: \: graph} \\ (1, - 3)\longrightarrow \sf{given \: \:coordinate \: \: point}\)

\(m = \frac{dy}{dx} = \frac{y_2-y_1}{x_2-x_1}\)

Substitute these coordinate values in.

\(m = \frac{0 - ( - 3)}{0 - 1} \\ m = \frac{3}{ - 1} \\ m = - 3\)

Hence, the slope is -3.

From the graph, the line passes through the origin point. Therefore, the y-intercept is (0,0).

\(y = mx + b \\ \begin{cases} \sf{m = slope} \\ \sf{b = y - intercept} \end{cases}\)

Substitute both m and b in the slope-intercept form.

\(y = - 3x + 0 \\ y = - 3x\)

Hence the answer is y = -3x.

\( \large \boxed{y = - 3x}\)

Answer:  The graph is shown below. It is nonlinear

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

Explanation:

I used GeoGebra to make the graph. Desmos is another option I recommend.

The equation we graph is y = (1/2)^x since we're splitting the paper in half each time. This is an exponential decay function. Note how the curve slopes downhill when moving to the right.

It appears the curve touches or crosses the x axis; which is misleading. Instead, the curve is getting closer and closer to this horizontal asymptote. It will never reach the x axis. Think of it like an electric fence.

As the graph indicates, we don't have a straight line. Therefore, the function isn't linear. It's a nonlinear curve.

Answer:

2,654$

Step-by-step explanation:

8a + 2c

8 x 238 = 1,904

2 x 375 =  750

750 + 1,904 = 2,654

2,654$

Hopefully this helps you

pls mark brainlest

answer:

R -> R' (2,1)

T -> T' (0,2)

I -> I' (4,4)

reflection across the x axis

Answer:

\( \sqrt{9 {}^{0} } \)=\( \sqrt{1} \)=±1 is your answer

Answer:

± 1

Step-by-step explanation:

Using the rule of exponents

\(a^{0}\) = 1 , then

\(\sqrt{9^{0} }\)

= \(\sqrt{1}\)

= ± 1

Answer:

81.5

Step-by-step explanation:

<G and <H are congruent

<F and <I are congruent

so the last two angles in both triangles must also be congruent

this means that <K and <J are congruent

so we can create this equation: <K = <J

substitute the angles with what we know: 4\(y^{2}\) = 6\(y^{2}\) - 40

add 40 to both sides and subtract 4\(y^{2}\) from both sides: 40 = 2\(y^{2}\)

you get: 20 = \(y^{2}\)

root square on both sides: \(\sqrt{20}\) = \(\sqrt{y^{2} }\)

you get: y ≈ 4.5

substitute this into one of the equations for a missing variable:

6\(y^{2}\) -----> 6 (4.5 x 4.5) - 40

6 ( 20.25) - 40

121.5 - 40

81.5

Answer:

x = -4

The solution is x = -4

Natiοnal Incοme statistics = Tοtal Rent + Tοtal Wages + Tοtal Interest + Tοtal Prοfit. gοοds and services prοduced in a cοuntry during a year is οbtained, which is called tοtal final prοduct. This represents Grοss Dοmestic Prοduct ( GDP ).

Natiοnal incοme is the tοtal incοme earned by all individuals and businesses in a cοuntry in a specific periοd οf time, usually a year. It includes all fοrms οf incοme such as wages, salaries, prοfits, rents, and interest earned. Natiοnal incοme is an impοrtant measure οf a cοuntry's ecοnοmic perfοrmance, as it reflects the tοtal οutput and incοme generated within the cοuntry's bοrders.

Natiοnal incοme statistics are calculated by measuring the tοtal value οf gοοds and services prοduced within a cοuntry during a given periοd οf time, typically οne year. The fοllοwing are sοme οf the key cοmpοnents οf natiοnal incοme statistics:

Grοss Dοmestic Prοduct (GDP): This is the tοtal value οf all gοοds and services prοduced within a cοuntry's bοrders in a given periοd οf time. It is calculated by adding up the value οf all final gοοds and services prοduced in a cοuntry during the year.

Grοss Natiοnal Prοduct (GNP): This is similar tο GDP, but alsο includes the value οf gοοds and services prοduced by a cοuntry's citizens and cοmpanies abrοad.

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The derivate of f(y) is -9y^6 - 33y^4 + 84y^2.

To differentiate the given function f(y), we will use the product rule and the chain rule of differentiation. Let's break down the function into two parts:

f(y) = (1 y^2 - 9 y^4) * (y + 3y^3)

Using the product rule, we can differentiate each part separately:

f'(y) = (1 y^2 - 9 y^4)' * (y + 3y^3) + (1 y^2 - 9 y^4) * (y + 3y^3)'

The derivative of the first part is:

(1 y^2 - 9 y^4)' = 2y - 36y^3

Now we need to differentiate the second part using the chain rule. Let's call the inner function u:

u = y + 3y^3

Using the power rule, the derivative of u with respect to y is:

u' = 1 + 9y^2

Now we can substitute these values back into our original equation:

f'(y) = (2y - 36y^3) * (y + 3y^3) + (1 y^2 - 9 y^4) * (1 + 9y^2)

Simplifying further:

f'(y) = 2y^2 + 6y^4 - 36y^4 - 108y^6 + y^2 + 9y^4 - 9y^6 + 81y^2

Combining like terms:

f'(y) = -9y^6 - 33y^4 + 84y^2

Therefore, the derivative of f(y) is -9y^6 - 33y^4 + 84y^2.

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the area will be fall in between 100≤ 20x ≤1000.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,A quadrilateral should be closed shape with 4 sides

All the internal angles of a quadrilateral sum up to 360°.

The area of a rectangle is A = a*b

Here in the figure the length is given 4x and the breadth is 5.

The area is given in between 100≤A≤1000

So this area will be A = 5x*4 = 20x

Now the area will be lie in between 100≤ 20x ≤1000

hence, the area will be fall in between 100≤ 20x ≤1000.

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The probability sum of the dice is 2/11.

Let A be the event that the sum of dots is 5, then

A={(1,4), (2,3), (3,2), (4,1)}

n(A)=4

And, B is the event that one die shows a "one"

B={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), (6,1)}

n(B)=11

The Event that some of the dots are five and one of the die shows "one".

A intersection B = {(1,4), (4,1)}

Since n(A) = 36 (thirty-six possible samples of two dice)

P(A)=4/36

P(B)=11/36

P(A intersection B)=2/36

So, the required probability is

P(A|B)=P(A intersection B)/P(B) =2/11

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Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

oof  we just went over that

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

diffusion is move from high to low

Answer:

36!

Step-by-step explanation:

There is 3 brands of clothing each brand has short and long sleeve, and both come in 6 different colors.

multiply 6*2 (because 6 different colors per long and short sleeve) get 12, then you multiply 12 times 3 because each one is from a different brand.

IT MAY BE A BI CONFUSING I SUCK AT EXPLAINING BUT

YEAHHH!

Answer:

18shirts

Step-by-step explanation:

3×6=18 shirts

Answer: 12 eggs

Step-by-step explanation:

12 eggs the anwser is 12 eggs

The code will execute the line totaldifference = -30. Otherwise, if the condition is False, the code will execute the line totaldifference = numdifference.

Here's the if-else statement you requested:

python

Copy code

if numdifference >= stringdifference:

   totaldifference = -30

else:

In this code, the condition numdifference >= string difference

   totaldifference = numdifference is checked. If this condition evaluates to True, meaning that numdifference is greater than or equal to stringdifference, the code will execute the line totaldifference = -30. Otherwise, if the condition is False, the code will execute the line totaldifference = numdifference.

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Answer:

the selling price of the product that will generate zero dollars in profit

Step-by-step explanation:

PLATO

The x-intercept of the given data represents the selling price of the product that will generate zero dollars in profit.

Thus, the x-intercept represents the selling price of the product that will generate zero dollars in profit.

Hence, option A is the correct answer.

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Answer:

Prime Factors of 72: 2, 3

Step-by-step explanation:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

The rectangular coordinates of the point are (6.9895, -0.3664, 0).

(a) The cylindrical coordinates of the given point are (8, 5, -2). The cylindrical coordinates system is one of the ways to represent a point in three-dimensional space. It defines the position of a point in terms of its distance from the origin, the angle made with the positive x-axis and the z-coordinate.

The rectangular coordinates of the point can be found using the following formula: x = r cos θy = r sin θz = zwhere r is the distance of the point from the origin, θ is the angle made by the projection of the point on the xy-plane with the positive x-axis and z is the z-coordinate.

So, we have: r = 8θ = 5z = -2

Substituting these values in the formula above, we get: x = 8 cos 5 = 8(-0.9599) = -7.6798y = 8 sin 5 = 8(0.2808) = 2.2464z = -2 Therefore, the rectangular coordinates of the point are (-7.6798, 2.2464, -2).

(b) The cylindrical coordinates of the given point are (7, -3). This means that the distance of the point from the origin is 7 and the angle made by the projection of the point on the xy-plane with the positive x-axis is -3 (measured in radians). The z-coordinate is not given, so we assume it to be 0 (since the point is in the xy-plane).

The rectangular coordinates of the point can be found using the following formula: x = r cos θy = r sin θz = z where r is the distance of the point from the origin, θ is the angle made by the projection of the point on the xy-plane with the positive x-axis and z is the z-coordinate.

So, we have: r = 7θ = -3z = 0

Substituting these values in the formula above, we get: x = 7 cos (-3) = 7(0.9986) = 6.9895y = 7 sin (-3) = 7(-0.0523) = -0.3664z = 0

Therefore, the rectangular coordinates of the point are (6.9895, -0.3664, 0).

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Answer:

1281

Step-by-step explanation:

15% of 8540=1281

Answer:48

Step-by-step explanation:

In the given system of linear inequalities,

Solutions: (1, 0), (-2, 5)

Non-solutions: (2, 0), (0, 1)

To graph the system of linear inequalities, we will plot the boundary lines for each inequality and shade the appropriate regions based on the given inequalities.

1. Graphing the inequality y < −x + 3:

To graph y < −x + 3, we first draw the line y = −x + 3. This line has a slope of -1 and a y-intercept of 3. We can plot two points on this line, for example, (0, 3) and (3, 0), and draw a dashed line passing through these points. Since y is less than −x + 3, we shade the region below the line.

2. Graphing the inequality y ≥ 2x − 1:

To graph y ≥ 2x − 1, we first draw the line y = 2x − 1. This line has a slope of 2 and a y-intercept of -1. We can plot two points on this line, for example, (0, -1) and (1, 1), and draw a solid line passing through these points. Since y is greater than or equal to 2x − 1, we shade the region above the line.

Now let's find two ordered pairs that are solutions and two that are not solutions.

Ordered pairs that are solutions:

- (1, 0): This point satisfies both inequalities. Plugging in the values, we get y = -1 and y ≥ 1, which are both true.

- (-2, 5): This point satisfies both inequalities. Plugging in the values, we get y = 7 and y ≥ 3, which are both true.

Ordered pairs that are not solutions:

- (2, 0): This point does not satisfy the first inequality y < −x + 3 since 0 is not less than -2 + 3.

- (0, 1): This point does not satisfy the second inequality y ≥ 2x − 1 since 1 is not greater than or equal to -1.

By graphing the system of linear inequalities and examining the solutions and non-solutions, we have:

Solutions: (1, 0), (-2, 5)

Non-solutions: (2, 0), (0, 1)

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 Total volume of the salt shaker is 56.52+706.5=763.02 cm³

The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.

Given here: The volume of a salt shaker  

The radius of the salt shaker which is 5 cm

Thus the volume of the cylinderical salt shaker is = π×3²×5²

                                                                                  =706.5 cm³

and the volume of the hemisphere at the top is=  (2/3)πr³

                                                                               =56.52 cm³

Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³

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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm

Answer:

Step-by-step explanation:

x^2 -4x - 9 = 29

x^2 - 4x = 37

x = 2 ±\(\sqrt{42}\)

Answer:

x = 2 ± \(\sqrt{42}\)

Step-by-step explanation:

x^2 -4x - 9 = 29

x^2 - 4x = 37

x = 2 ± \(\sqrt{42}\)

The value of b²- 4ac for the quadratic equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²,

b is the coefficient of x,

c is a constant term.

The nature of roots is based on the value of the discriminant:

D > 0; the quadratic equation has real and distinct roots

D = 0; the quadratic equation has real and equal roots

D < 0; the quadratic equation has complex roots  

We have given,

The quadratic equation : x² + 5x + 4 = 0

For the quadratic equation of the form ax² + bx + c, the value of the discriminant is given by

D = b² – 4ac

For the given Quadratic equation,

a = 1

b = 5

c = 4

Discriminant, D = (5)² – 4(1)(4)

D = 25 - 16

D = 9

D > 0,

so, the quadratic equation has real and distinct roots

Hence, the value of b²- 4ac for the quadratic equation x² + 5x + 4 = 0 is 9.

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

x=-8-15

x=-23 ...........

Answer:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10".