Graph the line with slope 1/3 and y-intercept −2.

The solution to the given system of equations is x = 14/3 and y = 10/3.

To eliminate the variable "y" in the given system of equations using the elimination method, we need to make the coefficients of "y" in both equations the same or multiples of each other. In this case, we can see that the coefficient of "y" in the second equation, x + y = 8, is already 1.

To make the coefficients of "y" the same or multiples of each other, we need to choose a number to multiply the second equation by. In this case, we want to eliminate "y," so we want the coefficient of "y" in the first equation, 5x + 2y = 30, to become the opposite of the coefficient in the second equation, which is -1.

To achieve this, we need to multiply the second equation by -2. Multiplying x + y = 8 by -2 yields -2x - 2y = -16. Now we have the equations:

5x + 2y = 30

-2x - 2y = -16

By adding these two equations together, the "y" terms will cancel out, allowing us to solve for "x":

(5x + 2y) + (-2x - 2y) = 30 + (-16)

3x = 14

Now we can solve for "x" by dividing both sides of the equation by 3:

3x/3 = 14/3

x = 14/3

Substituting the value of "x" back into one of the original equations, we can solve for "y." Let's use the second equation:

x + y = 8

14/3 + y = 8

Subtracting 14/3 from both sides:

y = 8 - 14/3

y = 24/3 - 14/3

y = 10/3

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The answer to your question is -2

I have done this quiz!

hope this helps :)

To find an equation for the temperature, D, in terms of t, we can use the properties of a sinusoidal function to model the temperature variation over the day.

Given:

High temperature: 80 degrees

Low temperature occurs at 5 AM (t = 5)

t is the number of hours since midnight

Let's assume a sinusoidal function of the form:

D = A * sin(B * t + C) + Dc

where:

A represents the amplitude (half the difference between the high and low temperatures)

B represents the frequency (how many cycles occur over a 24-hour period)

C represents the phase shift (how much the function is shifted horizontally)

Dc represents the vertical shift (the average temperature throughout the day)

We can determine the values of A, B, C, and Dc based on the given information.

Amplitude (A):

The amplitude is half the difference between the high and low temperatures:

A = (80 - 50) / 2

= 30 / 2

= 15 degrees

Frequency (B):

Since we want the temperature to complete one cycle over a 24-hour period, the frequency can be calculated as:

B = 2π / 24

Phase Shift (C):

Since the low temperature occurs at 5 AM (t = 5), the function should be shifted horizontally by 5 hours. To convert this to radians, we multiply by (2π / 24):

C = 5 * (2π / 24)

Vertical Shift (Dc):

The average temperature throughout the day is the midpoint between the high and low temperatures:

Dc = (80 + 50) / 2

= 130 / 2

= 65 degrees

Now we can put all the values together to obtain the equation for the temperature, D, in terms of t:

D = 15 * sin((2π / 24) * t + (5 * 2π / 24)) + 65

Simplifying further:

D = 15 * sin((π / 12) * t + (π / 12)) + 65

Therefore, the equation for the temperature, D, in terms of t is:

D = 15 * sin((π / 12) * t + (π / 12)) + 65.

Answer:

Step-by-step explanation: ong

The equation 4x² - 2y² = 9 is the equation of a hyperbola x²/(3/2)² - y²/(3/√2)² = 1 with vertices are (0, ±3/2) and co vertices (±3/√2, 0)

The equation of a hyperbola with vertices (0, ±a) and co vertices (±b, 0)and transverse axis x - axis is given by

x²/a² - y²/b² = 1 where

Given the equation 4x² - 2y² = 9,we want to determine which type of equation it is. We proceed as follows.

Since 4x² - 2y² = 9,

Dividing through by 9, we have that

4x²/9 - 2y²/9 = 9/9

4x²/9 - 2y²/9 = 9/9

x²/9/4 - y²/9/2 = 1

Comparing this equation with the equation of a hyperbola above we have that

So,

So, x²/(3/2)² - y²/(3/√2)² = 1

So, its vertices are (0, ±3/2) and co vertices (±3/√2, 0)

So, the equation is the equation of a hyperbola

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A sailor sails upstream in 2*1/2 hours and returns upstream in 3*3/4 hours. The bank velocity is 10 km/h, and the current velocity is 2 km/h.

Let's denote the speed of the sailor in still water as "s" km/h and the speed of the current as "c" km/h.

When the sailor is sailing upstream, they are moving against the current, so their effective speed is reduced. The time it takes to travel a certain distance is given by the formula:

Time = Distance / Speed

Given that the time to sail upstream is 21/2 hours (or 2.5 hours) and the time to sail downstream is 33/4 hours (or 3.75 hours), we can set up the following equations:

Distance Upstream / (s - c) = 2.5 (Equation 1)

Distance Downstream / (s + c) = 3.75 (Equation 2)

Since the distance traveled upstream is the same as the distance traveled downstream, we can set the left sides of both equations equal to each other:

Distance Upstream / (s - c) = Distance Downstream / (s + c)

Cross-multiplying, we get:

Distance Upstream * (s + c) = Distance Downstream * (s - c)

Since the distances are the same, we can simplify the equation to:

s + c = s - c

Simplifying further, we get:

2c = 0

This means that the current velocity is 0 km/h, which is not possible. Therefore, there must be an error in the problem statement. Please double-check the information provided to ensure accuracy.

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The value of p is 1 unit.

The distance between two points A( x₁, y₁) and B(x₂, y₂) is given by:

d= [tex]\sqrt{((y_{2}-y_{1})^{2}+({x_{2}-x_{1})^{2}) }[/tex]

Given that the distance between the origin and point P(-2, p-1) is 2p units.

i.e. 2p = [tex]\sqrt{(p-1-0)^2+(-2-0)^2}[/tex]

⇒  2p = [tex]\sqrt{(p-1)^{2} +(-2)^2}[/tex]

⇒ 2p = [tex]\sqrt{p^2 + 1- 2p +4}[/tex]

⇒ 2p = [tex]\sqrt{p^2 - 2p +5}[/tex]

Squaring both sides, we get:

4p² = p² - 2p + 5

⇒ 3p² + 2p - 5 = 0

⇒ 3p² + 5p - 3p - 5 = 0

⇒ p (3p + 5) - 1 (3p + 5) = 0

⇒ (3p + 5) (p-1) = 0

p = 1 unit

Note: p ≠ -5/3 since distance cannot be negative.

Hence p = 1 unit.

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The unlabeled side length is 10 units. We don't need to round to the nearest hundredth in this case.

To find the unlabeled side length, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the given diagram, we have a right triangle with side lengths of 8 and 6. Let's label the unlabeled side as x.

Using the Pythagorean theorem, we can write the equation:

x^2 = 8^2 + 6^2

Simplifying, we have:

[tex]x^2[/tex]= 64 + 36

x^2 = 100

To find the value of x, we take the square root of both sides:

x = √100

x = 10

Therefore, the unlabeled side length is 10.

It's important to note that since the given side lengths are whole numbers, the unlabeled side length is also a whole number. As a result, we don't need to round to the nearest hundredth in this case.

Hence, the unlabeled side length is 10 units.

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The probability that either event will occur is 0.33

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

[tex]m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)[/tex]

Plugging in the values from the table:

m =[tex](776,600 - (299)(12,400) / 6(18,109) - (299)^2)[/tex]

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

Step-by-step explanation:

The correct answer is C.

"Labor costs for a repair are less expensive as the number of hours increases."

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The total amount of Japanese Yen exchanged for the 5 days of use is approximately 758,476.44 (¥).

To calculate the total Japanese Yen exchanged for the 5 days of use, we need to consider the average amount spent per day and convert it to Japanese Yen using the exchange rate provided.

The average amount spent per day is given as R 4,042.19.

To calculate the total amount spent for 5 days, we multiply this amount by 5, which gives us R 20,210.95.

To convert this amount to Japanese Yen, we need to use the exchange rate of 1 South African Rand (ZAR) to Japanese Yen (¥) provided in the table, which is 37.51715.

Multiplying the total amount spent in Rand (R 20,210.95) by the exchange rate (37.51715), we get:

20,210.95 (R) [tex]\times[/tex] 37.51715 (¥/R) = 758,476.44 (¥)

Therefore, the total amount of Japanese Yen exchanged for the 5 days of use is approximately 758,476.44 (¥).

Note: The given exchange rate and currency data are based on the specified date and are subject to change.

It is advisable to refer to the most recent exchange rates for accurate calculations.

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Given: Deposit = $120, Annual Interest = 7%, Compounded Annually, No additional deposits or withdrawals. After 8 years we need to calculate the balance of this account. To solve this question, we use the formula for compound interest. So, the balance of the account after 8 years will be $219.11.

Compound Interest FormulaThe compound interest formula is given as follows; A = P (1 + r/n)nt, Where, A is the amount earned after time t, P is the principal amount,n is the number of times interest is compounded every year,r is the annual interest rate,t is the time the money is invested in years.

Substituting the values in the given formula; P = $120, r = 7%, n = 1 (compounded Annually), t = 8 years

A = 120(1 + 0.07/1)^(1×8)A = $219.11. Therefore, the balance of the account after 8 years will be $219.11.

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The integration of the given expression 32[tex]sinx^{2}[/tex]cosx can be done by applying the formula: ∫sin²x dx = (1/2)(x - sinx cosx)which we can derive from the double-angle formula for sin 2x, as shown below:

Sin 2x = 2 sin x cos x2 sin²x = 1 - cos 2x1/2(1 - cos 2x) = sin²xIf we let u = sin x², then du/dx = 2 sin x cos x.

This is the same as the integrand, except for the factor of 32. So we have: ∫32 sin x² cos x dx= 16 ∫ 2 sin x cos x sin x² dx= 16 ∫ 2 u du= 16u² + C= 16(sin x²)² + CNote that C is the constant of integration and could be any constant.

The solution for the integral of 32[tex]sinx^{2}[/tex]cosx with respect to x is given as: 16(sin x²)² + C.The steps for the above solution are:

Let u = sin x², then du/dx = 2 sin x cos xThe integral becomes 16 ∫ 2 u du16u² + C16(sin x²)² + C where C is the constant of integration.

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A ferris wheel is 10 meters in diameter and boarded from a platform that is 2 meters above the ground. The equation for the height above the ground, h = f(t), is:

f(t) = 5 sin[(π/2) t]

The ferris wheel completes one full revolution in 2 minutes, which means it takes 2 minutes for the wheel to go from its starting position to the same position again. Since a full revolution covers 360 degrees, we can say that in 2 minutes, the angle covered by the wheel is 360 degrees.

To find the equation for the height above the ground, we can use the sine function, as the height of a point on the wheel can be represented by the vertical component of the radius.

Let's consider the position at the six o'clock as the starting point, where the height above the ground is 2 meters. At this position, the angle is 0 degrees or 0 radians.

Now, as the wheel turns, the angle increases. We can relate the angle to time by assuming a constant angular velocity since the wheel completes one revolution in 2 minutes. Therefore, the angular velocity is (360 degrees / 2 minutes) = 180 degrees per minute.

Using radians, the angular velocity is (π radians / 2 minutes) = (π/2) radians per minute.

Thus, the equation for the height above the ground, h = f(t), is given by:

h = 5 sin[(π/2) t].

In this equation, t represents time in minutes, and h represents the height above the ground. The amplitude of the sine function is 5 since the radius of the ferris wheel is 5 meters (half of the diameter). The sine function generates values between -1 and 1, so multiplying by 5 ensures that the height varies between -5 and 5, relative to the starting position at 2 meters above the ground.

Therefore, the equation for the height above the ground is f(t) = 5 sin[(π/2) t].

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Answer:

[tex]\huge\boxed{\sf 44\ boys}[/tex]

Step-by-step explanation:

= Length × Width

Length = 32 m

Width = 11 m

Area of school room:

= Length × Width

= 32 × 11

= 352 m²

= 352 / 8

[tex]\rule[225]{225}{2}[/tex]

Answer:

CD: 8.5

m<D: 20.6°

m<C: 69.4°

Step-by-step explanation:

CD:

The first thing it wants us to do is find the length of CD. Since the triangle shown is a right triangle, we can use Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex])  to solve for the missing length. It's important to remember that when using the Pythagorean theorem, c is the hypotenuse.

[tex]a^{2}+b^{2}=c^{2}\\3^{2}+8^{2}=c^{2}\\9 + 64 = c^{2}\\73 = c^{2}\\\sqrt{73} =c[/tex]

Since our answer is no an integer, we must turn it into a decimal.

[tex]\sqrt{73}[/tex] ≈ 8.544003745 ≈ 8.5

m<D:

Now, they want us to find the measure of <D. To do this, we will need to use trig functions (sine, cosine, tangent). To help us determine which trig function to use, we can remember the acronym SOH CAH TOA. This acronym tells us that sine is equal to opposite divided by hypotenuse, cosine is equal to adjacent divided by hypotenuse, and tangent is equal to opposite divided by adjacent. Since we do the hypotenuse and sides adjacent and opposite of <D, we can choose whichever trig function we want. For this problem, we will use tangent, so we can avoid using a rounded number, 8.5, as one of our sides.

Tan(D) = opposite / adjacent

Tan(D) = 3 / 8     [Take the tan inverse of both sides}

[tex]Tan^{-1}(Tan(D))=Tan^{-1}(3/8)[/tex]     [Simplify]

[tex]D=Tan^{-1}(3/8)[/tex]     [Solve]

D ≈ 20.55604522

D ≈ 20.6°

m<C:

Lastly, we must find the last unknown angle on the triangle. Since all angles on a triangle total 180°, if know that <C+<D+<E=180°. Let's solve this equation.

<C+<D+<E=180°

<C + 20.6 + 90 = 180     [Add]

<C + 110.6 = 180     [Subtract]

<C = 180 - 110.6     [Solve]

<C = 69.4°

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The slope of line e is -8/7, which represents a proper fraction

The slope of line e, which is perpendicular to line d, can be determined using the concept that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's find the slope of line d using the given points (10, 8) and (2, 1). The slope (m) is calculated using the formula:

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

Plugging in the values, we have:

m = (1 - 8) / (2 - 10)

= (-7) / (-8)

= 7/8

Since line e is perpendicular to line d, its slope will be the negative reciprocal of 7/8. The negative reciprocal is obtained by flipping the fraction and changing its sign. Therefore, the slope of line e is -8/7.

Hence, the slope of line e is -8/7, which represents a proper fraction.

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Answer:

X=68m

Step-by-step explanation:

X²=40²+55²

X²=1600+3025

X²=4625

X=(4625)½

X=68m.

The coordinate of points on the graph indicates that the n-shaped graph which is below the x-axis, has no zeros, the correct option is therefore;

A. The graph has no zeros.

The zeros of a graph are the points at which the graph intersects the x-axis.

The graph in the question is n shaped and the peak point (the point with the highest y-value), which is a max point on the graph is located 2 units below the x-axis, therefore, the graph does not intersect the x-axis, and the graph therefore has no zeros. The correct option is therefore option A; The graph has no zeros

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Answer: the answer is 1:16

Step-by-step explanation:

To find the perimeter of a triangle, we need to add the lengths of all three sides. Let's calculate the perimeter using the given side lengths:

Side 1: -2x + 3

Side 2: 9x

Side 3: -2(3x - 2)

Perimeter = Side 1 + Side 2 + Side 3

Substituting the given expressions for each side:

Perimeter = (-2x + 3) + (9x) + [-2(3x - 2)]

Simplifying the expression within the square brackets:

Perimeter = -2x + 3 + 9x - 2(3x - 2)

Using the distributive property:

Perimeter = -2x + 3 + 9x - 6x + 4

Combining like terms:

Perimeter = x + 7

Therefore, the perimeter of the triangle is x + 7.

Answer:

The perimeter is: x + 7

Step-by-step explanation:

A perimeter of a polygon is the sum of all of the sides. For the triangle's perimeter, we must find the sum of the sides.

(-2x+3) + (9x) + -2(3x-2)

-2x+3 + 9x - 6x + 4

9x - 8x + 7

x + 7

Answer:

introduction of a business invironment

Answer: Its going down by odd numbers

Step-by-step explanation:

5-2=3, 2-(-3)= 5, then it would go on 7, 9, 11, 13...

Answer:

The difference between the numbers does not follow a common pattern; hence, the sequence is not arithmetic.

Step-by-step explanation:

Let's take the 1st two digits, 5 and 2

The difference between the numbers, 5-2 = 3

Following this pattern,

2-(-3) = 5

-3-(-10) = 7 and,

-10-(-19) = 9.

We can see that the differences are 3, 5, 7 and 9 and therefore we can prove that there is no common difference between the numbers.

Hence the sequence does not follow an arithmetic pattern as there is no common difference

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The balance in the Inventory account at January 31 was $158,000.The correct answer is option C.

To determine the balance in the Inventory account at January 31, we need to consider the purchases and sales made during the period.

At the end of last year, the company had merchandise costing $140,000 in inventory. In January of the current year, they purchased merchandise costing $102,000. This means the total cost of available inventory at the beginning of January was $140,000 + $102,000 = $242,000.

During January, the company sold merchandise that it had purchased at a total cost of $84,000. Since Games-2-Use uses a perpetual inventory system, the cost of goods sold is immediately recorded, and the inventory balance is adjusted accordingly.

Therefore, to find the balance in the Inventory account at January 31, we subtract the cost of goods sold from the available inventory at the beginning of January: $242,000 - $84,000 = $158,000.

Hence, the correct answer is option c. $158,000. This represents the balance in the Inventory account at January 31, considering the purchases and sales made during the month.

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The probable question may be:

At the end of last year, Games-2-Use had merchandise costing $140,000 in inventory. During January of the current year, the company purchased merchandise costing $102,000, and sold merchandise that it had purchased at a total cost of $84,000. Games-2-Use uses a perpetual inventory system.

The balance in the Inventory account at January 31 was:

Select one:

a. $84,000.

b. $140,000.

c. $158,000.

d. $242,000

Answer:

54 m²

Step-by-step explanation:

i.

xy = 24

y = 24/x

ii.

A = (x + 2)(y + 3)

A = xy + 3x + 2y + 6

A = x(24/x) + 3x + 2(24/x) + 6

A = 24 + 3x + 48/x + 6

A = 3x + 48/x + 30

iii.

A = 3x + 48x^-1 + 30

dA/dx = 3 + (-1)(48)x^-2

dA/dx = 3 - 48/x²

3 - 48/x² = 0

48/x² = 3

x² = 16

x = 4 or x = -4

We discard the negative answer.

x = 4

y = 24/x

y = 24/4

y = 6

A = xy

A = (x + 2)(y + 3)

A = (4 + 2)(6 + 3)

A = 6(9)

A = 54

Lo siento, pero como modelo de lenguaje, no tengo la capacidad de verificar el contenido original de una pregunta. Por favor, proporciona las sucesiones específicas para que pueda ayudarte a determinar si son progresiones.

Lo siento, pero como modelo de lenguaje, no tengo la capacidad de verificar el contenido original de una pregunta. Sin embargo, puedo ayudarte a comprender qué es una progresión y darte algunos ejemplos comunes de progresiones para que puedas verificar si las sucesiones que mencionas cumplen con las características.

Una progresión es una secuencia de números en la que cada término se obtiene sumando o multiplicando un número constante al término anterior. Algunos ejemplos de progresiones son:

Progresión aritmética: 2, 5, 8, 11, 14... (se suma 3 a cada término para obtener el siguiente).

Progresión geométrica: 3, 6, 12, 24, 48... (se multiplica por 2 cada término para obtener el siguiente).

Si tienes las sucesiones específicas, por favor proporciona los números para que pueda ayudarte a determinar si son progresiones y qué tipo de progresiones son.

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