An airplane flies on a compass heading of 120° at a speed of 500 kilometers per hour. How far East and how far
South of the starting point is the plane after 60 minutes?
What is the plane's distance from its starting point at that time?

The 8th term of the given sequence is [tex]a_8= \frac{78125}{243}[/tex].

A unique kind of sequence is a geometric sequence. Every term in the series (aside from the first term) is multiplied by a fixed amount to determine the following term.

The given sequence 9, 15, 25, . . . is a geometric progression series. The common ratio of the given GP is:

[tex]r= \frac{15}{9} =\frac{5}{3}[/tex]

Now, the nth term of the geometric sequence can be found out using the following formula, where a is the first term of the given series:

[tex]a_n= ar^{n-1}\\\\a_8= 9(\frac{5}{3} )^{8-1}\\[/tex]

[tex]a_8= \frac{78125}{243}[/tex]

Hence the 8th term of the given geometric sequence is [tex]a_8= \frac{78125}{243}[/tex].

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The value of x is 11.5.

Triangle ABC is a right-angle triangle.

We can apply the Pythagorean Theorem to get,

x² + 8² = 14²

We now solve for x to get,

⇒x² = 14² - 8²

The right-hand side is a difference of two squares, this factor gives us,

⇒x²  = (14 +8 )(14-8)         (using formula of a² -b²)

⇒x²  = 22 × 6

⇒ x² = 132

We take the positive square root of both sides to get,

x = [tex]\sqrt{132}[/tex]

⇒ x = 11.48

∴ x = 11.5 (  round to the nearest tenth)

So, the value of x is 11.5.

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Answer:

my personal guess is 45⁵

Step-by-step explanation:

9 times 5 is 45 and 2 plus 3 is 5

The information about 2 x 3 ratio file is given below.

What is 2 x 3 ratio?

In the rectangle, a grid of squares measuring 2 inches high by 3 inches wide can fit, and 4 inches high by 5 inches wide can.

The most popular aspect ratio for digital Single Lens Reflex (dSLR) cameras is 2x3, which was inspired by the vintage 35mm film format, in which the negative was 24x36mm in size.

24x36 can be reduced to 2x3 or 2:3. In this aspect ratio, print sizes include 4x6, 8x12, 10x15, 12x18, 16x24, 20x30, and so forth.

An image with a 2:3 aspect ratio, for instance, would be 2 inches high by 3 inches wide (two-to-three).

When you order prints from digital files, the size of the digital image is typically adjusted to fit the size of the print that you choose.

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The additive inverse of 4 /- 9 is 9 /- 4. This means that if you add 4 /- 9 and 9 /- 4 together, the result is 0.

The additive inverse of a number is the number that, when added to the original number, will result in a sum of 0. In other words, it is the opposite of the original number. For example, the additive inverse of 4 /- 9 is 9 /- 4. Adding 4 /- 9 and 9 /- 4 together will result in a sum of 0. This is because 4 /- 9 means -4 + 9 and 9 /- 4 means -9 + 4. When these two numbers are added together, the result is -4 + 4 which is 0. Additive inverses are often used in algebra and calculus to simplify equations and find solutions to problems. For example, if you have an equation with two unknowns and you know the value of one of the unknowns, you can use the additive inverse to find the value of the other unknown. This is because adding the two unknowns together will result in 0, and subtracting the known value from 0 will give you the value of the unknown.

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It will take time Alex 4.25 weeks to work 51 hours, as 51 hours can be broken down into 4.25 weeks of 12-hour work weeks.

1. You are asked to find out how many weeks it would take Alex to work 51 hours.

2. A good plan for solving the problem is to divide the number of hours Alex needs to work (51) by the number of hours he works each day (3) and each week (12). This will give you the total number of weeks it will take Alex to work 51 hours.

3. Yes, the answer makes sense. Dividing 51 by 12 gives the total number of weeks it will take Alex to work 51 hours (4.25 weeks). This is because 51 hours can be broken down into 4.25 weeks of 12-hour work weeks.

It will take time Alex 4.25 weeks to work 51 hours, as 51 hours can be broken down into 4.25 weeks of 12-hour work weeks.

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The degree of the polynomial 7x³ 5x 4x³ 2x² is 5.

This can be calculated using the formula Degree of polynomial = Highest Degree of the Variable. In this case, the highest degree of the variable is 3, so the degree of the polynomial is 3.

To calculate the degree of the polynomial, we first need to determine the degree of each term. The degree of each term is determined by the highest power of the variable. For example, 7x³ has a degree of 3, 5x has a degree of 1, 4x³ has a degree of 3, and 2x² has a degree of 2.

So, when we add up all the degrees of the terms, we get 3 + 1 + 3 + 2 = 9. The highest degree among these terms is 3, so the degree of the polynomial is 3. Therefore, the degree of the polynomial 7x³ 5x 4x³ 2x² is 5.

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By using the fact that the sum of the interior angles must be equal to 180°, we will find that the value of x is 18.

I assume you need problem 4 solved.

There we can see the triangle JKL, such that the angles are:

K = (5x - 5)°

L = (3x)°

J = 41°

Remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write the linear equation:

(5x - 5)° + (3x)° + 41° = 180°

We can solve that linear equation for x (i will remove the degree symbol so it is easier to follow it)

(5x - 5) + 3x + 41 = 180

(5x + 3x) + (41 - 5) = 180

8x + 36 = 180

8x = 180 - 36

8x = 144

x = 144/8 = 18

That is the value of x.

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The percentage of healthy Americans becoming infected, hospitalizations, and death will be 16.67%, 0.267%, and 2.34%, respectively.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

There are 48 million cases of foodborne illness (FBI) per year. That is the equivalent of 1 in 6 Americans. Each year these illnesses result in about 128,000 hospitalizations and 3,000 deaths.

The percentage of healthy Americans becoming infected is given as,

P = (1/6) x 100

P = 16.67%

The percentage of hospitalizations will be given as,

P = (128,000 / 48,000,000) x 100

P = 0.267%

The percentage of death will be given as,

P = (3,000 / 128,000) x 100

P = 2.34%

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The length of the perpendicular is approximately 11.31 units, rounded to two decimal places.

Given that in a right angle triangle, the hypotenuse is equal to 16 and the angle is 45, we can use the sine function of the triangle to find the length of the perpendicular side (also known as the opposite side). The sine function of an angle in a right triangle is defined as the ratio of the opposite side over the hypotenuse.

sin(theta) = opposite / hypotenuse

So, you can use the following equation to find the opposite side:

opposite = sin(theta) * hypotenuse

Plugging in the given values:

opposite = sin(45) * 16

opposite = 0.7071067811865476 * 16

opposite = 11.313708498984761

The length of the perpendicular is approximately 11.31 units, rounded to two decimal places.

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Latitude and longitude are two different measurements used to locate points on the Earth.

1. Latitude is the angular distance of a point north or south of the equator, measured in degrees. Longitude measures the angular distance east or west of the prime meridian, also measured in degrees.

2. Latitude is measured in a north-south direction, while longitude is measured in an east-west direction.

3. Latitude is the position of the point relative to the equator, while longitude is the position of the point relative to the prime meridian.

4. Latitude is also known as "parallels," while longitude is known as "meridians."

5. Latitude ranges from 0° to 90° North and 0° to 90° South, while longitude ranges from 0° to 180° East and 0° to 180° West.

Latitude and longitude are two different measurements used to locate points on the Earth. Latitude measures the angular distance north or south of the equator, while longitude measures the angular distance east or west of the prime meridian. Latitude is referred to as "parallels" and ranges from 0° to 90° North and 0° to 90° South, while longitude is known as "meridians" and ranges from 0° to 180° East and 0° to 180° West.

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The correct numerical values that should be used in completing Melissa's table are:

Mathematically, the area of a square can be calculated by using this formula;

A = x²

Where:

A is the area of a square.

x is the side length of a square.

Substituting the given parameters into the formula, we have;

338 = x²

x = √338

x = √2 × √169

x = 13√2 or 18.384776 feet.

For row 2, we have:

A = 6.5²

A = 42.25 square feet.

For row 3, we have:

147.25 = x²

x = √147.25

x = 12.13466 feet.

For row 4, we have:

A = 7²

A = 49 square feet.

We can determine that Melissa's vegetable garden is square-shaped from the data in the table displayed in the image below.

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Answer:

No solution.

Step-by-step explanation:

2y-8=6x

y=3x+2

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

2(3x+2)-8=6x

6x+4-8=6x

6x-4=6x

6x-6x=4

0=4

The expression that shows time, t, it will now take Rashid to make the trip relative to the speed, v with which he slows down is t = (240 - (v/120) * 240) / (120 - v)

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The relation between time, t, and the speed at which Rashid slows down, v, is given by the formula:

t = (240 - (v/120) * 240) / (120 - v)

t = time

v= speed.

This formula can be derived by using the distance formula (distance = speed x time) and the fact that the distance traveled is constant (240 km).

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The perimeter of the triangle will be 40 feet. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

The lengths of the edges of the triangle are (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet.

The perimeter of the triangle is given as,

P = 3x - 4 + x² - 1 + 2x² - 15

P = 3x² + 3x - 20

If the value of x is 4. Then the perimeter is given as,

P = 3(4)² + 3(4) - 20

P = 48 + 12 - 20

P = 40 feet

The perimeter of the triangle will be 40 feet. Then the correct option is C.

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The correct expressions are given below.

The lengths of the edges of the triangle are (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet.

Answer: 2

Step-by-step explanation:

6x - 7 - 2x + 4 = 13
4x - 3 = 13
4x = 13 + 3
4x = 16
x = 16/4
x = 4

=======================================================
10 - 2x is 10 - 2(4)
10 - 2(4)
= 10 - 8
= 2

Answer:

2

Step-by-step explanation:

Let's for solve for x:

Solve for x:

6 x - 2 x - 7 + 4 = 13

Grouping like terms, 6 x - 2 x - 7 + 4 = (6 x - 2 x) + (-7 + 4):

((6 x - 2 x) + (-7 + 4)) = 13

6 x - 2 x = 4 x:

4 x + (-7 + 4) = 13

4 - 7 = -3:

4 x + -3 = 13

Add 3 to both sides:

4 x + (3 - 3) = 3 + 13

3 - 3 = 0:

4 x = 13 + 3

13 + 3 = 16:

4 x = 16

Divide both sides of 4 x = 16 by 4:

(4 x)/4 = 16/4

4/4 = 1:

x = 16/4

The gcd of 16 and 4 is 4, so 16/4 = (4×4)/(4×1) = 4/4×4 = 4:

Answer:  x = 4

Plug in the numbers;

10 -2(4) = 2

Therefore, as a result of congruency along the line DE, one triangle is simply the other triangle reflected and DE = 1/2CB is proven.

When two shapes or items are similar in shape, or when one is a perfect mirror of another and is similar in size and shape, they are said to be congruent in geometry. Two forms are congruent if their dimensions match. It is also true that mirror representations of two forms are the same if different systems are congruent. Objects with exact matching dimensions and shapes are referred to be matches. The forms hold true regardless of rotation, flipping, or reversal. Use the to create two circles.

Here,

When ΔABC and ΔDEF are used,

∠ABC = ∠ DEF (given)

AB = DE, and (same length)

∠BAC = ∠FED (same angle)

The  ΔABC and ΔDEF triangle is similar

Thus , as there are similar we can say that:

=> DE = 1/2CB

As a result, along the line DE, one triangle is simply the other triangle reflected and DE = 1/2CB is proven.

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Answer:

∠C = 20° & ∠B = 40°

Step-by-step explanation:

let angle c be x

A.T.Q ∠B = 2x

Using angle sum property of triangle

∠A + ∠B + ∠C = 180

120° + 2x + x = 180

3x = 60

x = 20°

∴ ∠C = 20

∠B = 40

Answer:

∠ B = 40° , ∠ C = 20°

Step-by-step explanation:

the 3 angles in the triangle sum to 180° , that is

∠ A + ∠ B + ∠ C = 180° ( substitute ∠ B = 2 ∠C )

∠ A + 2 ∠ C + ∠ C = 180°

120° + 3 ∠ C = 180° ( subtract 120° from both sides )

3 ∠ C = 60° ( divide both sides by 3 )

∠ C = 20°

∠ B = 2 × ∠ C = 2 × 20° = 40°

The inverse of p v q →  p ∧ q is ~p v -q →-p ∧ ~q. hence option c is correct

What is mean by Inverse?

Opposite in order, nature or effect is called an Inverse.

Given that;

The statement is;

p → q

Now,

The inverse of p → q is written as;

~p → ~q

Thus, The inverse of p → q is ~p → ~q.

What is inverse in simple words?

something of a contrary nature or quality : opposite, reverse. : a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem. the inverse of "if A then B" is "if not-A then not-B"

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On solving the system of linear equations 4x - 6y = 10 and 9x + 2y = 7, the value of x is x = 1 and y is y = -1.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - 4x - 6y = 10

The second linear equation is - 9x + 2y = 7

Multiply equation (2) by 3 -

3(9x + 2y) = 7 × 3

27x + 6y = 21.....(3)

Add equation (1) and (3) -

4x - 6y + (27x + 6y) = 10 + 21

4x - 6y + 27x + 6y = 10 + 21

Combine the like terms -

31x = 31

x = 1

Substitute the value of x in equation (2) -

9(1) + 2y = 7

9 + 2y = 7

2y = 7 - 9

2y = -2

y = -1

Therefore, the values of x and y is x = 1 and y = -1 respectively.

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If one bag of stones is sufficient to fill the distance of 4 yards , then to complete 5.5 yards of pond boundary, 2 bags are enough.

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Answer:

9.8

Step-by-step explanation:

Answer: 98 Times.

[tex]2450/25=98[/tex]

Answer:

perimeter = 34

Step-by-step explanation:

given EP = FP and GQ = FQ , then

4y + 2 = 2x ( subtract 2x from both sides )

4y - 2x + 2 = 0 ( subtract 2 from both sides )

4y - 2x = - 2 → (1)

and

4y + 4 = 3x - 1 ( subtract 3x from both sides )

4y - 3x + 4 = - 1 ( subtract 4 from both sides )

4y - 3x = - 5 → (2)

Solve the 2 equations simultaneously

multiplying (2) by - 1 and adding to (1) will eliminate y

- 4y + 3x = 5 → (3)

add (1) and (3) term by term to eliminate y

0 + x = 3

x = 3

substitute x = 3 into (1) and solve for y

4y - 2(3) = - 2

4y - 6 = - 2 ( add 6 to both sides )

4y = 4 ( divide both sides by 4 )

y = 1

thus x = 3 and y = 1

PQ = x + 2y = 3 + 2(1) = 3 + 2 = 5

PQ is the mid segment of Δ EFG and is half the length of GE , then

GE = 2 × 5 = 10

the perimeter (P) is the sum of the 3 sides , that is

P = FQ + QG + GE + EP + PF

  = 3x - 1 + 4y + 4 + 10 + 4y + 2 + 2x

  = 5x + 8y + 11

 = 5(3) + 8(1) + 11

= 15 + 8 + 11

= 34

The mathematical mistake that Riley made is that She used the wrong common denominator.

A common denominator is a factor that all of the fractions in the set of equations have in common.

Thus, the appropriate response is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the steps in the proper order below:

Step 1: The expression is as follows:

(x/(x-3)(x-2)) + (3/(x+3))

Locate the common denominator in step 2 and rewrite the formula so that the numerators are higher than the common denominators.

Thus, we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Applying the Law of Multiplicative Distribution in Step 3

Thus, we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4: Gather Related Items

This results in:  (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5: Group like coefficients together

This results in: ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6: Determine the difference or sum

This results in:(4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

To obtain, we factor and simplify the expression.

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

Your question is incomplete but most probably your full question was

Riley makes a mistake in step 2 while doing her homework. What was her mistake? StartFraction x Over x squared minus 5 x + 6 EndFraction + StartFraction x Over x + 3 EndFraction Step 1: StartFraction x Over (x minus 2)(x minus 3) EndFraction + StartFraction 3 Over x + 3 EndFraction Step 2: StartFraction x Over (x minus 2) (x + 3) EndFraction + 3 (x minus 2) Over (x minus 2) (x + 3) EndFraction Step 3: StartFraction x + 3 x minus 6 Over (x minus 2) (x + 3) EndFraction Step 4: StartFraction 4 x minus 6 Over (x minus 2) (x + 3) EndFraction She added the two fractions incorrectly. She used the wrong common denominator. She did not distribute the negative correctly. She did not multiply the first fraction by a factor. Mark this and return

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Answer:4.2

Step-by-step explanation:

When a set of eight cards were labeled with A, D, D, I, T, I, O, N. The sample space for choosing a card is

A sample space is a set or collection of potential outcomes from a random experiment.

The letter "S" stands for the sample space in a symbol. The term "events" refers to a subset of probable experiment results.

Depending on the experiment, a sample area could include a variety of results.

For the given problem, the sample space is A, D, D, I, T, I, O, N which is rearranged to be S = {A, D, D, I, I, N, O, T}

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A linear function to model the relationship between the number of days and the total cost of renting a mid-size car will be y = 40 + 45x

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, the cost is comprised of a fixed $40 administrative fee for the cleaning and maintenance of the car plus a rental cost of $45 per day.

The linear function to model the relationship between the number of days and the total cost of renting a mid-size car will be:

y = 40 + 45(x)

y = 40 + 45x

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The image will be formed at the center of curvature itself with the same size and real but it will be inverted.

If an object is placed at the center of curvature of a concave mirror, light rays meet to form an image that is real, inverted, and at the same size as that of the object. The image formed is not magnified.

When the object is located at the center of curvature, the image will also be located at the center of curvature. In this case, the image will be inverted. The image dimensions are equal to the object dimensions.

If the object lies on the center of curvature in front of a concave mirror, the image is also formed at the center of curvature.

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The two terms that describe the triangle are isosceles and right triangle. An isosceles triangle has two sides of equal length, and a right triangle has one 90-degree angle.

An isosceles triangle is a triangle with two sides of equal length and two angles of equal measure. The two equal sides are called the legs, and the third side is called the base. The two equal angles are called base angles and are located opposite the two legs. The point where the two legs meet is called the vertex. Isosceles triangles have many interesting properties, including the fact that they have two lines of symmetry and the angles opposite each leg are equal. The triangle is also isosceles if its base angles are equal.

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Graph B shows the position of Alec and Ardella after a run.

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Translation can be done upwards or downwards which changes the value of y. And if the translation is towards left or right, x coordinate changes.

Starting point of both Alec and Ardella = (2, 3)

Alec runs four units to the left and two units up.

(2, 3) becomes (2 - 4, 3 + 2) = (-2, 5)

Ardella runs four units to the left and seven units down.

(2, 3) becomes (2 - 4, 3 - 7) = (-2, -4)

These points are marked on graph B.

Hence the position of Alec and Ardella after the run are marked in graph B.

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