Is the equation y=-2x+7 parallel

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statement yeah i hope it's correct

Among angles i , k , g , a  ,i and k are the exterior angles.

Given i°, k° ,g° ,a° are some angles and we have to find which angle is exterior angle.

The angle between a side of a polygon and an extended side is known as exterior angle of polygon. The sum of exterior angles of a polygon is equal to 180 degrees. We have to identify exterior angles among i° ,k° ,g° ,a°.

The angle i is an exterior angle because it is formed on a line opposite to angle d.

Angle k is also an exterior angle because it is also formed on opposite side of an angle.

Angle g is not an exterior angle.

Angle a is not an exterior angle.

Hence i and k are exterior angles among i, g, k, a.

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Step-by-step explanation:

1 kilometers = 1000 metre

1.6 km = 1.6 * 1000 metres = 1600 metres.

The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Each t-shirt costs $15, and each pair of gym shorts costs $16.

Let's call the cost of each t-shirt "x". Then the cost of each pair of gym shorts is x + $1.

We know that the total cost of the t-shirts is 5 * x, and the total cost of the gym shorts is 2 * (x + $1).

We also know that the total cost of all items is $107, so we can write an equation to represent this information:

5x + 2(x + $1) = $107

5x + 2x + 2 = $107

7x + 2 = $107

7x = $105

x = $15

So, each t-shirt costs $15, and each pair of gym shorts costs $15 + $1 = $16.

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Answer:

9 and 29.

Let us denote the older brother’s age 4 years ago by x and the younger brother’s age 4 years ago by y

Their combined ages 4 years ago is 38–8 =30

So we have the equation x+y=30

We also know that x=y^2

X=25 and y=5 will satisfy that condition

So 4 years ago the older was 25 years old and the younger 5.

4 years later the older brother is 29 years old and the younger brother is 9

Answer:

a. 3x = 2x + 10, b. x = 10, c. 30 degrees

Step-by-step explanation:

Angle 4 and angle 6 = 180 degrees, so

3x = 2x + 10

x = 10

Angle 7 is congruent to angle 6, so it is also 2x + 10, x = 10, so it is 30 degrees.

Answer:

see explanation

Step-by-step explanation:

∠ 4 and ∠ 6 are same- side interior angles and sum to 180° , that is

(a)

3x + 2x + 20 = 180 , simplifying

(b)

5x + 20 = 180 ( subtract 20 from both sides )

5x = 160 ( divide both sides by 5 )

x = 32

(c)

∠ 6 and ∠ 7 are vertically opposite angles and are congruent , then

∠ 7 = 2x + 20 = 2(32) + 20 = 64 + 20 = 84°

Answer:

10.37

Step-by-step explanation:

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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The car accelerates at a rate of 2.25 m/s² as it comes to a stop.

The rate at which an object's velocity changes is referred to as its "acceleration" in mathematics.

In other words, it is the rate of change in velocity with respect to time.

The units of acceleration in the International System of Units (SI) are often expressed in metres per second squared (m/s2).

The acceleration of a car refers to the rate at which its velocity changes.

The velocities are 9 m/s at the beginning and 0 m/s at the end.

The velocity change takes 4 seconds to complete.

Applying the equation provided below, we can determine the acceleration:

(Final velocity-Initial velocity)/Time=Acceleration

Substituting the values we have:

acceleration = (0-9 m/s) / 4 s

acceleration = -9 m/s / 4 s

acceleration = -2.25 m/s²

As expected for a slowing object, the negative sign shows that the acceleration is moving in the opposite direction of the initial velocity.

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Answer:

The paper clip that has the SMALLEST width is the blue paper clip

Step-by-step explanation:

To find the paper with the SMALLEST width, we convert each clip's width to decimal

For blue paper clip

A blue paper clip is 1/6 inch wide.

1/6 inch = 0.1666666667 inch

For sliver paper clip

A silver paper clip is 3/8 inch wide.

3/8 inch = 0.375 inch

For red paper clip

A red paper clip is 1/3 inch wide

1/3 inches = 0.333 inch

For green paper clip

a green paper clip is 1/4 inch wide.

1/4 inch = 0.25 inch

The paper clip that has the SMALLEST width is the blue paper clip with a width of 1/6 inch (0.1666666667 inch)

Answer:

3/2

Step-by-step explanation:

Count the steps up and to the side from a point you see where the line crosses through. This is a trick I learned:

"up 3 over 2"

3/2

HTH :)

Probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs is 0.0596.

\(\sigmaT = \sigma / \sqrtn = 1.25 / \sqrt15 = 0.3227\)

\(= P[(9 - 10) / 0.3227 < (T - \muT ) / \sigmaT < (9.5 - 10) / 0.3227)]\)

= P(-3.10 < Z < -1.55)

= P(Z < -1.55) - P(Z < -3.10)  

= 0.0606 - 0.001

=  0.0596

Probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs = 0.0596

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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The solution is Option B.

The area of the triangle is A = 10 units which is one-half the area of a rectangle of length 4 units and width 5 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the coordinates of the triangle ABC be

The coordinate of A = A ( 4 , 6 )

The coordinate of B = B ( 6 , 1 )

The coordinate of C = C ( 2 , 1 )

Now , the base of the triangle B = 4 units

The height of the triangle H = 5 units

And , The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

The area of the triangle = ( 1/2 ) x 4 x 5

The area of the triangle = 10 units

Now , one-half the area of a rectangle of length 4 units and width 5 units

Substituting the values in the equation , we get

Area of rectangle = ( 1/2 ) Length x Width

Area of rectangle = ( 1/2 ) 4 x 5

Area of rectangle = 10 units

Hence , the area of triangle is 10 units

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Answer:

66

Step-by-step explanation:

\(\binom{12}{2}=\frac{12!}{10!21}=\frac{12 \cdot 11}{2}=66\)

The area of the sector is approximately 10.61 square miles of a circle and My central angle is 135 (degrees) and my radius is 3mi.

What is a circle?

A circle is a geometrical shape consisting of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius of the circle.

To find the area of a sector of a circle, you can use the formula:

Area of sector = (central angle / 360) x πr²

where r is the radius of the circle.

In this case, the central angle is 135 degrees and the radius is 3 miles, so we have:

Area of sector = (135/360) x π(3 mi)²

= (3/8) x π(9 mi²)

= 10.61 mi² (rounded to two decimal places)

Therefore, the area of the sector is approximately 10.61 square miles.

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(a) The sample size for the above sample is 15.

(b) The sample mean for these data is 3.8.

(c) The sample median is 3.6.

(d) To compute the 20% trimmed mean for the above data set is 3.7.

(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.

The following measurements were recorded for the drying time, in hours

3.4      2.5      4.8      2.9      3.6 is:

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

(a) We have to determine the sample size for the above sample.

The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.

Sample Size (n) = 15

(b) We have to calculate the sample mean for these data.

Sample Mean = Total Sum of data/Total Number

Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15

Sample Mean = 56.8/15

Sample Mean = 3.8

(c) We have to calculate the sample median.

To define the sample median we first represent the data in ascending order.

2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6

Sample Size(n) = 15

So Median = (n+1)/2th term

Median = (15 + 1)/2th term

Median = 16/2th term

Median = 8th term

So the 8th term in the given data is 3.6. So,

Median = 3.6

(d) We have to compute the 20% trimmed mean for the above data set.

To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.

New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8

New Mean = 33.3/9

New Mean = 3.7

(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.

The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.

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The complete question is:

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.

3.4      2.5      4.8      2.9      3.6

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

Assume that the measurements are a simple random

sample.

(a) What is the sample size for the above sample?

(b) Calculate the sample mean for these data.

(c) Calculate the sample median.

(d) Compute the 20% trimmed mean for the above data set.

(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

Answer: Choice C.

How many 1/4-meter long pieces of ribbon are needed to have a total of 3 1/2 meters of ribbon.

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

Explanation:

Let's consider a similar problem without the fractions.

Let's say you want to know how many 2 meter lengths of ribbon you can cut from an overall length of 24 meters. That would be 24 ÷ 2 = 12 pieces total.

So we divide the two values (large ÷ small)

The same idea applies to this problem as well. The larger amount (3 & 1/2 meters) is what we cut up, and each slice is 1/4 of a meter. To find the number of pieces, we would compute 3 1/2÷1/4

Note: it might help to convert the mixed number 3 & 1/2 to the improper fraction 7/2

Answer:

znvipahgvahgv

Step-by-step explanation:

Therefore, the diagonals PS and ET are equal, and they bisect each other. This parallelogram is a rectangle and a rhombus because its diagonals are equal and bisect each other.

The diagonals to determine whether a parallelogram with vertices P(2,4), E(4,8), S(12,4), and T(10,0) is a rectangle, rhombus, or square is described below:

Given coordinates of vertices are

P(2, 4), E(4, 8), S(12, 4), and T(10, 0).

Therefore, PS and ET are the diagonals of the parallelogram.

Here, the midpoint of the diagonal is

M = [ (x₁ + x₂)/2, (y₁ + y₂)/2 ].

The midpoint of PS is the midpoint of the line segment PS with coordinates (7,4).

The midpoint of ET is the midpoint of the line segment ET with coordinates (7,4).

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Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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The measure of B is 41.4 degree.

Hence Option B is correct.

Given that,

AB = 20

BC = 15

And the given triangle is right angled triangle

Since we know

CosΘ = (adjacent side of Θ)/Hypotenuse

Therefore,

⇒ CosB = 15/20

⇒ CosB = 0.75

Take inverse of cos both sides

B =  41.4 degree

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To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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Sylvia and Patrick gathered information on the weight of cars and the mileage they get, and then proceeded to plot the data on a graph.

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The given set of linear equations with variables x1, x2, x3, x4, and x5 and coefficients F, M, and L can be solved using Gaussian elimination by performing row operations to eliminate variables.

The set of linear equations, with the given values F, M, and L, is as follows:

Equation 1: 2x1 + Lx2 - 3x3 + 5x4 - 9x5 = 8

Equation 2: 8x1 - 2x2 + 3x3 - 4x4 - Mx5 = -7

Equation 3: -2x1 + 6x2 - Fx3 - x4 + 2x5 = 3

Using Gaussian elimination, we can solve the system of equations step by step.

The given set of linear equations is:

2x1 + Lx2 - 3x3 + 5x4 - 9x5 = 8

8x1 - 2x2 + 3x3 - 4x4 - Mx5 = -7

-2x1 + 6x2 - Fx3 - x4 + 2x5 = 3

To solve the system using Gaussian elimination, we perform row operations to eliminate variables. Starting with Equation 1, we can multiply Equation 1 by 4, resulting in:

8x1 + 4Lx2 - 12x3 + 20x4 - 36x5 = 32

Next, we multiply Equation 2 by -2:

-16x1 + 4x2 - 6x3 + 8x4 + 2Mx5 = 14

We multiply Equation 3 by 1:

-2x1 + 6x2 - Fx3 - x4 + 2x5 = 3

The system of equations is now:

8x1 + 4Lx2 - 12x3 + 20x4 - 36x5 = 32

-16x1 + 4x2 - 6x3 + 8x4 + 2Mx5 = 14

-2x1 + 6x2 - Fx3 - x4 + 2x5 = 3

By continuing the Gaussian elimination process and back substitution, we can find the solutions for x1, x2, x3, x4, and x5.

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Answer: B,C,D

Step-by-step explanation:

Since the only requirement is that the width needs to be at least 50 yds. B, C,D all work.