flying with the wind, a small plane flew 338 mi in 2 h. flying against the wind, the plane could fly only 312 mi in the same amount of time. find the rate of the plane in calm air and the rate of the wind.

Using the equations we know that the square should be finished by adding 9 to both sides.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

So, write the equation so that the terms with x are on the left and the constants are on the right:

x² – 6x = 5

Ensure that the x2 term's coefficient is 1:

x² – 6x = 5

Including a phrase on both sides will complete the left side's square. The x term's coefficient is multiplied by two and squared to achieve this.

To make the equation equal on both sides, add the same amount to the right side.

x² – 6x + 9 = 5 + 9

(x-3)² = 14

Therefore, using the equations we know that the square should be finished by adding 9 to both sides.

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Correct question:

What number should be added to both sides of the equation to complete the square?

x2 – 6x = 5

Answer:

≈ 9144 ft^2

Step-by-step explanation:

Given:

H = 30 ft

d = 52 ft

π = 3,14

Find: A (surface) - ?

First, let's find the radius:

r = 0,5 × d

r = 0,5 × 52 = 26 ft

Now, we can find the surface area of the cylinder ( the cylinder's surface area contains 2 circle bases and a lateral surface):

[tex]a(surface) = 2\pi {r}^{2} + 2\pi \times r \times h[/tex]

[tex]a(surface) = 2 \times 3.14 \times {26}^{2} + 2 \times 3.14 \times 26 \times 30 ≈9144 \: {ft}^{2} [/tex]

The total area of the pool and the walkway will be 210 square feet, the walkway should be 1.8 feet wide.

In mathematics, area is a measure of the size or extent of a two-dimensional shape or surface. It is typically measured in square units, such as square meters, square feet, or square inches. The area of a shape is calculated by multiplying its length by its width or by using a formula specific to that shape.

The concept of area is fundamental to many areas of mathematics, science, and engineering. It is used to calculate the size of land and buildings in real estate, the amount of material needed for construction, the amount of paint needed to cover a surface, and many other practical applications. In addition, the study of area is important in geometry, calculus, and other areas of mathematics.

Let's start by finding the area of the pool, which is 9 feet by 8 feet:

Area of pool = 9 feet * 8 feet = 72 square feet

Next, we need to add the width of the walkway to each dimension of the pool to find the dimensions of the entire area:

Width of area = 9 feet + 2(width of walkway)

Length of area = 8 feet + 2(width of walkway)

The total area of the pool and walkway is given as 210 square feet, so we can set up the equation:

Area of pool + Area of walkway = 210 square feet

Substituting the formulas for the area of the pool and area of the walkway, we get:

72 + (9 + 2x)(8 + 2x) = 210

Expanding the right side and simplifying, we get:

4x² + 34x - 33 = 0

We can solve for x using the quadratic formula:

x = (-34 ± √(34² - 44(-33))) / (2*4)

x = (-34 ± √(1660)) / 8

x = (-34 ± 40.74) / 8

x = 1.8 or x = -5.075

Since the width of the walkway cannot be negative, the width of the walkway should be 1.8 feet.

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Answer:45 & 90

Step-by-step explanation:

Answer:

∠x = 159° and ∠y = 149°

Step-by-step explanation:

∠a = 31°

∠b = 52°

∠x = ?

∠y = ?

∠a and ∠y are supplementary angles so:

∠a + ∠y = 180

31 + ∠y = 180

∠y = 180 - 31

∠y = 149°

∠b also has a supplementary angle which is not labeled in the question so let's label that ∠c.

∠b + ∠c = 180

52 + ∠c = 180

∠c = 180 - 52

∠c = 128°

∠a and ∠c  are both inside a triangle formed by all the lines crossing with each other. Since the sum of angles inside a triangle is 180°, find the third angle in this triangle (∠d) using all the values we were given and solved for:

∠a + ∠c + ∠d = 180

31 + 128 + ∠d = 180

∠d = 180 - 31 - 128

∠d = 21°

∠d and ∠x are supplementary angles so:

∠d + ∠x = 180

21 + ∠x = 180

∠x = 180 - 21

∠x = 159°

∠x = 159° and ∠y = 149°

Answer:

Step-by-step explanation:

x + 5 < 7

x + 5 - 5 < 7 - 5

x < 2

The number line will have a open circle at 2 and be shaded to the left

completely.  The solution is all numbers less than positive 2.

The linear equation that passes through the given points is:

y + 9 = -10*(x - 1)

A general linear equation that passes through two points (x₁, y₁) and (x₂, y₂) has a slope given by:

a = (y₂ - y₁)/(x₂ - x₁)

Then using any of these points we can write the line as:

y -  y₁ = a*(x - x₁)

Here the points are (1, -9) and (-10, 101), then the slope is:

a = (101 + 9)/(10 - 1) = 110/-11 = -10

And using the point (1, -9) we can write the line as:

y + 9 = -10*(x - 1)

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Answer: D Mario owes the bank a little less than $50

In the above mentioned similar triangles the length of DE is 5.25 cm.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

Since triangles ABC and ADE are similar, their corresponding sides are proportional. We can use this fact to set up a proportion:

AB / AD = BC / DE

Substituting the given values, we get:

8 / AD = 6 / DE

Multiplying both sides by DE, we get:

8DE / AD = 6

Dividing both sides by 8/AD, we get:

DE = (6/8)AD

We need to find AD to solve for DE. To do this, we can use the fact that BD is an altitude of triangle ABC and triangle ADE is similar to triangle ABC. Therefore, triangle ABD is also similar to triangle ABC, and we can set up another proportion:

BD / AB = AD / AC

Substituting the given values, we get:

4 / 8 = AD / (8 + 6)

Simplifying, we get:

1/2 = AD / 14

Multiplying both sides by 14, we get:

AD = 7

Substituting this value back into the first equation, we get:

DE = (6/8)AD = (6/8)7 = 21/4 = 5.25

Therefore, the length of DE is 5.25 cm.

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Answer to Whats the answer for that question?:

A correct response to a question asked to test one's knowledge.

Step-by-step explanation:

The way you answer a question depends on how you view it. This could entail thought process, method, and calculations. So overall it depends on perspective.

The probability that a chosen point, in the figure lies in the shaded region is 3.18.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

The probability of the point chosen in the shaded region is calculated by the formulae

Probability = [tex]\frac{Area of shaded region}{Total area}[/tex]

To find the total area we need to find the area of a triangle and the area of a semicircle.

Area of triangle = 1/2 * Base * Height

                          = 1/2 * 15 * 6

                          = 45

Area of semicircle =  [tex]\frac{\pi r^{2} }{2}[/tex]

                              = [tex]\frac{\pi (3)^{2} }{2}[/tex]

                              =14.13

Therefore the probability that chosen point = [tex]\frac{45}{14.13}[/tex] = 3.18

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The slope intercept form of the given line whose coordinate of point is (- 5,9) and slope is - 5 would be y = -5x - 16.

Equation of a straight line: y = mx + b ------(i)

Given that

y = 9, x = -5

and slope, m = - 5

By putting above values in equation (i)

9 = -5 (-5) + b

9 = 25 + b

-16 = b

b = -16

y = -5x - 16

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

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The standard form of the equation of the hyperbola is 49y² - 2401x² = 2401.

Standard form of an equation is a specific format in which an equation is written. In the context of mathematics, there are several types of standard forms depending on the type of equation.

The standard form of the equation of a hyperbola with center at the origin, vertices on the y-axis, and horizontal asymptotes is given by:

(y / b)² - (x / a)² = 1

where a is the distance from the center to each vertex along the x-axis and b is the distance from the center to each point where the hyperbola intersects the y-axis.

From the given information, we can see that the center of the hyperbola is at the origin and the distance from the center to each vertex on the y-axis is 7. Therefore, b = 7.

To find a, we can use the fact that the slope of the asymptotes is ±b/a. We are given the equation of asymptotes as y = ±(7/4)x. Comparing this to the standard form of the equation of the asymptotes (y = ±(b/a)x), we can see that b/a = 7/4. Solving for a, we get:

a = b / (4/7) = 7(7/4) = 49/4

Substituting these values into the standard form of the equation of a hyperbola, we get:

(y / 7)² - (x / (49/4))² = 1

Multiplying both sides by (49/4)², we can rewrite the equation in standard form:

49y² - 2401x² = 2401

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Answer:

Frequency is high hope this help you

1) For A Plus Plumbing

A. The cost per hour of work is $60 per hour.

B. The one-time fee is $320.

2) For Quality Plumbing:

The cost for x hours of work is given by the equation cost = 50x - 50

1) For A Plus Plumbing:

A. To calculate the cost per hour of work, we need to find the slope of the line connecting two points on the table. Let's use the first two rows:

slope = (cost2 - cost1) / (time2 - time1) = (140 - 80) / (2 - 1) = 60

So the cost per hour of work for A Plus Plumbing is $60 per hour.

B. The one-time fee is given in the table as the cost when time is zero. From the table, we can see that the one-time fee for A Plus Plumbing is $320.

2) For Quality Plumbing,

We can see from the graph that the cost starts at $50 for two hours of work and increases by $50 for each additional hour. This means that the cost for x hours of work can be calculated using the equation:

cost = 50 + 50(x-2) = 50x - 50

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The given question is incomplete, the complete question is:

Two plumbing companies charge money for each hour of work, plus a one-time fee. A Plus Plumbing charges according to this table: time (hours) cost (dollars) row 10 80 row 21 140 row 3 4 320 Quality Plumbing charges according to this graph 2501 200 cost (dollars) 150 100 50 2 3 4 5 6 time (hours) 1. For A Plus Plumbing A. How much does it cost for each hour of work? B. What is the one-time fee? 2. For Quality Plumbing A. How much do they charge for each hour of work?

r offers to pay $1,000 over the dealer' cost for a luxury coupe. The base price is $62.685 and options total $5,209. There is no destination charge. If the dealer' costs are 87 percent of the base price and 89 percent of the options, what is Huster's offer?The dealer's cost for the base price would be 87% of $62,685, which is $54,508.95. The dealer's cost for the options would be 89% of $5,209, which is $4,638.01. Therefore, the total dealer's cost would be $54,508.95 + $4,638.01 = $59,146.96. Brad Huxter's offer is $1,000 over the dealer's cost, so his offer would be $59,146.96 + $1,000 = $60,146.96.

The correct equation to isolate principal, P, is:

Simple interest refers to the interest that is earned on an initial amount of money, known as the principal, over a fixed period of time. It is called "simple" because it is calculated based only on the initial principal amount and does not take into account any interest earned on the interest itself, which is known as compound interest.

To isolate principal, P, we need to rearrange the given formula as follows:

[tex]A - P(1 + rt) =[/tex] Interest earned on principal (I)

The interest earned on the principal (I) is given by:

[tex]I = Prt[/tex]

Now, we can rewrite the above formula as:

[tex]A = P + I[/tex]

Substituting the value of I, we get:

[tex]A = P + Prt[/tex]

Now, we can isolate P by subtracting Prt from both sides:

[tex]A - Prt = P[/tex]

Therefore, the correct equation to isolate principal, P, is:

[tex]P = (A - Prt)[/tex]

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The correct equation to isolate P is c. P = A/(1 + rt)

Simple interest is the term used to describe the interest that is accrued over a predetermined amount of time on an initial sum of money, known as the principal. It is known as "simple" interest because it is computed just using the initial principal sum and ignores any interest that has been earned on top of the interest itself, a concept known as compound interest.

The formula for the final amount earned using simple interest is A = P(1 + rt), where A is the total amount at the end of t years, P is the principal amount, r is the interest rate, and t is the time in years.

To isolate P, we can rearrange the formula as:

A = P(1 + rt)

Divide both sides by (1 + rt):

A/(1 + rt) = P

Therefore, the correct equation to isolate P is:

c. P = A/(1 + rt)

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According to the question the length of the real airplane is 63 feet and the wingspan of the airplane in the scale drawing is 10 inches.

If 1 inch in the scale drawing represents 9 feet in the real airplane, then 7 inches in the scale drawing represents:

7 inches x 9 feet/inch = 63 feet

So, the length of the real airplane is 63 feet.

(b) If 1 inch in the scale drawing represents 9 feet in the real airplane, then X inches in the scale drawing represents 90 feet in the real airplane. We can construct a ratio to find the value of X:

1 inch / 9 feet = X inches / 90 feet

Cross-multiplying, we get:

9 feet * X inches = 1 inch * 90 feet

Simplifying, we get:

X inches = 10 inches

As a result, the scale drawing's scale model's airplane has a 10 inch wingspan.

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The value of X in the bottom question is 3.

The MidSegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

To solve for X in the top and bottom questions using the MidSegment theorem, we need to first identify the midpoints of the two sides and the third side.

For the top question, we can see that the midpoints of AB and BC are D and E respectively. So, DE is parallel to AC and half its length. We know that AC = 12, so DE = 6. We also know that DE = X + 1, so we can set up an equation:

X + 1 = 6

Solving for X, we get:

X = 5

Therefore, the value of X in the top question is 5.

For the bottom question, we can see that the midpoints of AB and AC are D and F respectively. So, DF is parallel to BC and half its length. We know that BC = 14, so DF = 7. We also know that DF = X + 4, so we can set up an equation:

X + 4 = 7

Solving for X, we get:

X = 3

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A 0.025kg golf ball is hit off a tee with a force of 450N. If the golf club was in contact with the ball for 0.012 s, the velocity of the golf ball will increase by 216 m/s.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

To solve this problem, we can use the equation:

F = m*a

where F is the force applied, m is the mass of the object, and a is the acceleration.

We can rearrange this equation to solve for acceleration:

a = F/m

Using this equation, we can find the acceleration of the golf ball:

a = 450N / 0.025kg = 18000 m/s²

Next, we can use the equation:

v = v0 + a*t

where v is the final velocity, v0 is the initial velocity (which we'll assume is 0 m/s), a is the acceleration, and t is the time.

We know the acceleration and the time, so we can solve for the final velocity:

v = 0 + (18000 m/s²) * 0.012 s

v = 216 m/s

Therefore, the velocity of the golf ball will increase by 216 m/s.

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Answer: 4, -7

Step-by-step explanation:

Plug the numbers into the variables and solve;

(6)(12) / 6+12

Multiply the values in the numerator and add the values in the denominator.

72/18

Then divide and the answer will be 4.

For the second one:

4+3 / 3-4

Add the values in the numerator and subtract the values in the denominator.

7/-1

Dividing this will make 7 a negative, so the answer is -7.

Hope that helped ^^;;

If the amount of time is exponentially distributed with mean 20 minutes, then the standard deviation of the time a student would spend at a terminal is also 20 minutes.

The amount of time which the student spends at a terminal in ISEN computer-room is said to be exponentially distributed, and

The mean-time spent at computer room is = 20 minutes,

We know that, for an exponentially-distributed random variable, the standard deviation is equal to the mean.

So, the standard deviation of the time a student spends at a terminal is also 20 minutes, since the mean is given as 20 minutes.

Therefore, the standard deviation is 20 minutes.

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The steps involved in finding the standard deviation are finding mean, then calculating the square of difference, adding all and dividing by observations and at last the square root.

What is standard deviation?

The standard deviation assesses how widely distributed the data are relative to the mean.

We know that the standard deviation formula is represented as

√Σ[tex]{\frac{|x - mean|^{2} }{N} }[/tex]

The various steps undertaken are:

Step 1 : We are required to calculate the mean of the data by dividing the sum with the number of observations.

Step 2 : We subtract each observation from the mean and find the square.

Step 3 : All the values obtained in the previous step are added.

Step 4 : The value so obtained is divided by the number of observations.

Step 5 : This is the last step wherein the square root of the value obtained in the previous step is to be calculated.

Hence, these are the steps for finding the standard deviation.

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When two numbers appear side by side, the number and number should be written together for clarity. The statement is true.

The term numeric expression consists of two words, number for a number and expression for a sentence. Therefore, it is a word containing numbers. Teaching mathematics is the combination of numbers and mixed numbers using mathematical operations such as addition, subtraction, division, or division. There are many number expressions such as word form and number form. Numerical expressions are mathematical expressions that contain only numbers and one or more operators.

Examples of symbol operations are addition, subtraction, multiplication, and division. It can be represented by a radical symbol (square root symbol) or a real value.

Equations consist of numbers and contain multiple digits. There is no limit to the number of operators a shared account can have. Some numbers use only one operator of the two numbers, while others may have more than one operator. The only requirement for a numeric expression is that it only contains a number and an operator. Some numbers have only one operator code others have two or more.

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The arc for the following circle is arc YZ that is option D.

In geometry, an arc is a part of a circle's circumference. It is defined as the portion of the circle that is contained between any two points on the circle. The length of an arc is proportional to the measure of its central angle, which is the angle formed by the two radii drawn to the endpoints of the arc. The measure of an arc is typically expressed in degrees, and it can be calculated using the formula:

arc length = (central angle measure / 360 degrees) x (circumference of the circle)

In addition to being a fundamental concept in geometry, arcs are commonly used in fields such as engineering, architecture, and physics to describe the shape and motion of objects that move along curved paths.

Here,

In the given options, we have four letters X, W, Y, and Z, which represent the points on the circle. The arcs are defined by the pairs of these points as follows:

Arc YZ is the arc of the circle that starts at point Y and ends at point Z.

Therefore, the answer is that the arcs of the circle mentioned in the options are O arc YZ.

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Answer:

$39.60

Step-by-step explanation:

10% of 36 is 3.6

36 + 3.6 = 39.6

The value of imports is $304,533,333.33 and the value of exports is $311,633,333.33. So, option B is correct.

Let's denote the value of exports as E and the value of imports as I. We can then use the following system of equations to solve for E and I:

E - I = 7,100,000 (balance of trade equation)

0.12E + 0.21I = 9,148,200 (tariff revenue equation)

Multiplying the first equation by 0.12 and adding it to the second equation, we get:

0.12E - 0.12I + 0.21I = 9,148,200 + 0.12(7,100,000)

0.12E + 0.09I = 9,988,000

Multiplying both sides by 100, we can eliminate decimals:

12E + 9I = 998,800,000

We can now use this equation with the balance of trade equation to solve for E and I:

E - I = 7,100,000

12E + 9I = 998,800,000

Multiplying the first equation by 9 and subtracting it from the second equation, we get:

12E + 9I - 9E + 9I = 998,800,000 - 63,900,000

3E = 934,900,000

E = 311,633,333.33

Substituting this value into the balance of trade equation, we get:

311,633,333.33 - I = 7,100,000

I = 304,533,333.33

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Answer:

here are the factors

Cost of living data includes the expenses incurred for food, shelter, transportation, energy, clothing, education, healthcare, childcare, and entertainment. A cost of living index tracks how much basic expenses rise over time and among different regions.

here

How To Calculate Cost Of Living

Subtract the index of your current city from the index of the city you want to move to: 115.1 - 90.9 = 24.2.

Divide the resulting difference by the index of your current city: 24.2 ÷ 90.9 = 0.266.

Multiply the resulting quotient by 100 to get the percentage: 0.266 x 100 = 26.6%