-2x + 15y + z = 44
4x + 3y + 3z = 18
-3x+6y-z = 8

Answer/Step-by-step explanation:

\( \overline{AB} \parallel \overline{CD} \parallel \overline{EF} \) ----› Given

\( \angle 1 + \angle 2 = 180 \) ----› consecutive interior angles are supplementary

\( \angle 3 + \angle 4 = 180 \) ----› consecutive interior angles are supplementary

Therefore:

\( \angle 1 + \angle 2 + \angle 3 + \angle 4 = 360 \)

Answer:

80%

Step-by-step explanation:

no. of insects=4

total no. of species=5

percentage of the insects

=4/5*100

=4*20

=80%

According to the given data we have the following percentage 88%.

To convert 88% to a fraction we would make the following:

First we would convert the percent to a ratio by dividing by 100:

So, a%=a/100

Then we would simplilfy the expression above and we would get so the percentage as a

Answer:

Step-by-step explanation:

The type of relationship indicated in the scatterplot is a negative curvilinear relationship.

A scatterplot is a type of graph that is used to display the relationship between two variables. In a scatterplot, the values of one variable are plotted on the x-axis and the values of the other variable are plotted on the y-axis. The relationship between the two variables can be determined by observing the pattern of the points in the scatterplot.

A negative curvilinear relationship is indicated when the points in the scatterplot form a curve that slopes downward. This means that as the values of one variable increase, the values of the other variable decrease, but not in a straight line. Instead, the relationship follows a curved pattern.

In contrast, a positive linear or curvilinear relationship is indicated when the points in the scatterplot form a curve that slopes upward, a negative linear relationship is indicated when the points in the scatterplot form a straight line that slopes downward, and no relationship is indicated when the points in the scatterplot do not form any discernible pattern.

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the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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The total surface area of the triangular prism is: 111 ft²

To find the total surface area of the given triangular prism, we will find the area of all the surfaces and add it up.

Formula for the area of a rectangle is:

Area = Length * Width

Area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Total Surface area = 2(¹/₂ * 3 * 7) + (7 * 5) + (8 * 5) + (3 * 5)

Total Surface area = 21 + 35 + 40 + 15

Total Surface area = 111 ft²

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Answer:

Volume of the sphere = 902 cm³ (Approx.)

Step-by-step explanation:

Given:

Diameter of circle = 12 centimeter

Find:

Volume of the sphere

Computation:

Radius of circle = Diameter of circle / 2

Radius of circle = 12 / 2

Radius of circle = 6 centimeter

Volume of the sphere = [4/3]πr³

Volume of the sphere = [4/3][22/7][6]³

Volume of the sphere = [4/3][22/7][216]

Volume of the sphere = [1.33][3.14][216]

Volume of the sphere = [216][4.1762]

Volume of the sphere = 902.05

Volume of the sphere = 902 cm³ (Approx.)

The residues of the function at these singular points are given by: Residue at z = -4: Residue at z = 1:

Part a) For finding the residues of the given function, we can factorize the denominator of the function as shown below:f(z) = 1 / [(z + 4)(z - 1)³]The singular points of the function are -4 and 1.

Therefore, the residues of the function at these singular points are given by: Residue at z = -4: Residue at z = 1:

Part b) For evaluating the given contour integral, we need to know the function f(z) and the curve C. However, the information regarding the function f(z) and the curve C is missing.

Part c) For finding the general solutions of the given differential equations, we can use the following methods: Part c(i) For solving the differential equation, yy" + y + 2x = 0, we can use the method of undetermined coefficients. The characteristic equation of the given differential equation is given by:r² + 1 = 0r = ±i

Thus, the general solution of the differential equation is given by:y = c₁ cos x + c₂ sin x - 2x + c₃

where c₁, c₂, and c₃ are constants.

Part c(ii) For solving the differential equation, -y dy - 2x + 3y dt = 0, we can use the method of separation of variables.-y dy + 3y dt = 2xSeparating the variables, we get:-y dy / y + 3 dt = 2x

Integrating both sides, we get:-ln y + 3t = x² + c₁ where c₁ is a constant.

Rearranging the terms, we get:y = e^(3t) / (c₂ e^(x²))where c₂ = ±e^(-c₁) is a constant.

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To verify that fxy = fyx for the given function f(x,y)=e^(x+y+3), we need to find the partial derivatives of f with respect to x and y, and then check if they are equal.

Let's begin by finding the partial derivative of f with respect to x (f_x): f_x = (∂f/∂x) = (∂/∂x) e^(x+y+3) = e^(x+y+3) * (∂/∂x) (x+y+3) [using chain rule] = e^(x+y+3)

Now, let's find the partial derivative of f with respect to y (f_y): f_y = (∂f/∂y) = (∂/∂y) e^(x+y+3) = e^(x+y+3) * (∂/∂y) (x+y+3) [using chain rule] = e^(x+y+3)

Now, let's find the mixed partial derivative of f with respect to x and y (f_xy): f_xy = (∂^2 f/∂y∂x) = (∂/∂y) e^(x+y+3) = e^(x+y+3) * (∂/∂y) (x+y+3) [using chain rule] = e^(x+y+3)

Similarly, the mixed partial derivative of f with respect to y and x (f_yx) can be found as: f_yx = (∂^2 f/∂x∂y) = (∂/∂x) e^(x+y+3) = e^(x+y+3) * (∂/∂x) (x+y+3) [using chain rule] = e^(x+y+3)

Now, we can see that fxy = fyx, as both are equal to e^(x+y+3). Hence, we have verified that the given function f(x,y)=e^(x+y+3) satisfies the condition fxy = fyx.

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Answer:

12 inches

Step-by-step explanation:

I just took the unit test review on edge

Since the minor arc AB measures 9π inches, the length of the radius of circle C is equal to: B. 12 inches.

Given the following data:

Mathematically, the length of an arc formed by a circle is calculated by using this formula:

Arc length = rθ

Where:

Substituting the given parameters into the formula, we have:

9π = r × 3π/4

36π = 3πr

36 = 3r

r = 36/3

Radius, r = 12 inches.

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Answer:

y = 3x+3

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The distance from Jim's house to the mall is given as follows:

11.25 miles.

Suppose that we have two points with coordinates given as follows:

\((x_1, y_1)\) and \((x_2, y_2)\)

Then the equation for the distance between these two points is given as follows:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates are given as follows:

Hence the distance is given as follows:

\(D = \sqrt{(17 - 8)^2+(13 - 1)^2}\)

D = 15 units.

Each unit represents 0.75 miles, hence the distance in miles is given as follows:

15 x 0.75 = 11.25 miles.

The problem is given by the image presented at the end of the answer.

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John Barker's repair shop in Ontario is required to calculate the HST payable or refund for the first reporting period. The HST rate is 13% and the amount before HST sales is $150,000. The total HST collected from sales is $19,500 and the total ITCs are $19,790. The net HST payable/refund is $19,500 - $19,790 and the correct option is d) A refund of $5,980.

Given the following information for John Barker's repair shop in Ontario, we are required to calculate the HST payable or refund for the first reporting period. The HST rate for Ontario is 13%.Amount Before HST Sales $150,000 Equipment purchased $96,000 Supplies purchased $83,000 Wages paid $19,000 Rent paid $17,000Let's calculate the total HST collected from sales:

Total HST collected from Sales= HST Rate x Amount before HST Sales

Total HST collected from Sales= 13% x $150,000

Total HST collected from Sales= $19,500

Let's calculate the total ITCs for John Barker's repair shop:Input tax credits (ITCs) are the HST that a business pays on purchases made for the business. ITCs reduce the amount of HST payable. ITCs = (HST paid on eligible business purchases) - (HST paid on non-eligible business purchases)For John Barker's repair shop, all purchases are for business purposes. Hence, the ITCs are the total HST paid on purchases.

Total HST paid on purchases= HST rate x (equipment purchased + supplies purchased)

Total HST paid on purchases= 13% x ($96,000 + $83,000)

Total HST paid on purchases= $19,790

Let's calculate the net HST payable or refund:

Net HST payable/refund = Total HST collected from sales - Total ITCs

Net HST payable/refund = $19,500 - $19,790Net HST payable/refund

= -$290 Since the Net HST payable/refund is negative,

it implies that John Barker's repair shop is eligible for an HST refund. Hence, the correct option is d) A refund of $5,980.

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we know the radius has a diameter of 26 cm, so its radius must be half that, or 13 cm.

\(\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=13 \end{cases}\implies A=\pi (13)^2 \\\\\\ A=(3.14)(13)^2\implies A=530.66~cm^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=13 \end{cases}\implies C=2\pi 13 \\\\\\ C=2(3.14)(13)\implies C=81.64~cm\)

Check the picture below.

There are 26 automobiles and 13 vans available for the field excursion.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. A mathematical statement that expresses the connection between two values is simply characterized as an equation. In an equation, the two values are usually equated by an equal sign. Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). A linear equation can include several variables.

Here,

If c represents the number of cars and v represents the number of vans,

5c+8v=234

c=2v

10v+8v=234

v=234/18

v=13 vans

c=26 cars

The number of cars for field trip is 26 and number of vans is 13.

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Answer:

Step-by-step explanation:

Answer:

Hello!!

The answer to the equation \(\frac{41}{3} -8\) is...

Exact form: \(\frac{17}{3}\)

Decimal form: 5.6 repeating

Mixed number form: \(5\frac{2}{3}\)

Hope this helps!!

Answer:

103

Step-by-step explanation:

103.3's 3 is closer to 0 than 5

Answer: Neither

Step-by-step explanation: The slopes are not the same but they are also not opposite.

The product that is less than 2 is A. 7/9x2 because the fraction 7/9 is less than 1. When multiplied by 2, the product is still less than 2.


A. 7/9x2
1. Calculate 7/9 * 2
2. 14/9 (7/9 * 2 = 14/9)
3. 14/9 is less than 2 because the numerator (14) is less than twice the denominator (9*2 = 18)

B. 5/4x2
1. Calculate 5/4 * 2
2. 10/4 (5/4 * 2 = 10/4)
3. 10/4 simplifies to 5/2 which is greater than 2

C. 6/3x2
1. Calculate 6/3 * 2
2. 12/3 (6/3 * 2 = 12/3)
3. 12/3 simplifies to 4, which is greater than 2

D. 11/5x2
1. Calculate 11/5 * 2
2. 22/5 (11/5 * 2 = 22/5)
3. 22/5 is greater than 2 because the numerator (22) is more than twice the denominator (5*2 = 10)

Your answer: A. 7/9x2 is less than 2 because the fraction is less than 1 and the product of the fraction and 2 results in a value smaller than 2.

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The approximate internal rate of return (IRR) on this project is approximately 17.06%.The IRR is expressed as a percentage and serves as an indicator of the project's profitability.

To calculate the approximate internal rate of return (IRR) for the project, we need to find the discount rate at which the present value of cash inflows equals the initial investment cost. Here are the steps to solve this question:

Step 1: Calculate the present value (PV) of cash inflows:

PV = Cash inflow / (1 + Discount rate)^n

Where:

Cash inflow = $36,000 (annual cash inflow)

Discount rate = Rate of return / 100 (convert percentage to decimal)

n = Number of years

Given:

Rate of return = 8%

Initial investment cost = $91,116

Cash inflow = $36,000 (for 3 years)

Step 2: Set up the equation:

\(\$91,116 = \\$36,000 / (1 + Discount rate)^1 + $36,000 / (1 + Discount rate)^2 + $36,000 / (1 + Discount rate)^3\)

Step 3: Solve for the discount rate (IRR):

To solve this equation, use numerical methods like trial and error, or use spreadsheet software or financial calculators that have built-in functions to calculate the IRR. These tools can provide the exact IRR.

Approximately, the internal rate of return (IRR) on this project is 17.06%.

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A basis for the eigenspace corresponding to the eigenvalue λ = 4 is the set {[3; 2]}.

To find the eigenspace of the matrix A = [10 -9; 4 -2] corresponding to the eigenvalue λ = 4, we need to find the nullspace of the matrix A - λI, where I is the 2x2 identity matrix and λ is the eigenvalue:

A - λI = [10 -9; 4 -2] - 4[1 0; 0 1]

      = [6 -9; 4 -6]

To find the nullspace of this matrix, we need to solve the system of homogeneous linear equations:

6x - 9y = 0

4x - 6y = 0

We can simplify this system by dividing the first equation by 3, which gives:

2x - 3y = 0

4x - 6y = 0

We can see that the second equation is a multiple of the first equation, so we only need to solve one of the equations. We can choose the first equation and solve for x in terms of y:

2x = 3y

x = (3/2)y

So the eigenvector corresponding to the eigenvalue λ = 4 is a non-zero vector in the nullspace of A - λI, which in this case is the vector [3; 2] (or any non-zero scalar multiple of it).

Therefore, a basis for the eigenspace corresponding to the eigenvalue λ = 4 is the set {[3; 2]}.

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Answer:

1. x < 4

2. x > 1

3. x < 5

Step-by-step explanation:

By applying conversion method, 6 feet 1 inch is equals to 185.42 centimeters (rounded to two decimal places).

To convert 6 feet 1 inch to centimeters, we need to first convert the feet and inches to inches, and then convert the total inches to centimeters.

1 foot is equal to 12 inches, so 6 feet is equal to 6 x 12 = 72 inches.

Adding the 1 inch, we get a total of 72 + 1 = 73 inches.

1 inch is equal to 2.54 centimeters, so to convert 73 inches to centimeters, we multiply by 2.54:

73 inches x 2.54 cm/inch = 185.42 cm

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Answer:

\(-2\sqrt{3}\)

Step-by-step explanation:

\(\textsf{Given expression}: \quad(\sqrt{3}+1)(\sqrt{3}-3)\)

\(\textsf{Use the FOIL method to expand}\quad(a+b)(c-d)=ac-ad+bc-bd:\)

\(=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}+1(-3)\)

\(=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}-3\)

\(\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{a}=a:\)

\(=3-3\sqrt{3}+\sqrt{3}-3\)

\(\textsf{Collect like terms}:\)

\(=3-3-3\sqrt{3}+\sqrt{3}\)

\(\textsf{Combine like terms}:\)

\(=0-2\sqrt{3}\)

\(=-2\sqrt{3}\)

Hello!

Answer:

\(\huge\boxed{x = 1/2, 9/2}\)

|2x - 5| = 4

Solve for the negative and positive expressions:

2x - 5 = 4

2x = 9

x = 9/2

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

-(2x - 5) = 4

-2x + 5 = 4

-2x = -1

x = 1/2.

Therefore, the solutions are x = 1/2 and 9/2.

Answer:

4.5

Step-by-step explanation:

250 mL= 0.25 L  500 mL= 0.5 L  750mL= 0.75 L+3L