19. A rectangular lawn is to be laid with turf. James measures the sides of the rectangle as 30 m by
40 m, with both values being given to the nearest metre. He sends his friend Toby to buy the
turf.
a. Find the area of the maximum area of turf that Toby needs to buy, giving your answers
to 2 decimal places.
b.
Find the area of the minimum area of turf that Toby needs to buy, giving your answers
to 2 decimal places.

It is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles.

What is Pythagorean theorem?

The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This is the basis for the Pythagorean identities, which relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle.

In a right triangle, one angle is a right angle (90 degrees) and the side opposite the right angle is called the hypotenuse. It is the longest side of the triangle and is always opposite the right angle. The other two sides are called the legs of the triangle, and are referred to as the opposite side and the adjacent side.

The reason that one side is equal to all angles while the other two sides are not, is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles. In a right triangle, the hypotenuse is opposite the right angle and has a unique relationship with the legs, which are the opposite and adjacent sides. This is the foundation of the theorem and identities.

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It is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles.

What is Pythagorean theorem?

The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This is the basis for the Pythagorean identities, which relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle.

In a right triangle, one angle is a right angle (90 degrees) and the side opposite the right angle is called the hypotenuse. It is the longest side of the triangle and is always opposite the right angle. The other two sides are called the legs of the triangle, and are referred to as the opposite side and the adjacent side.

The reason that one side is equal to all angles while the other two sides are not, is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles. In a right triangle, the hypotenuse is opposite the right angle and has a unique relationship with the legs, which are the opposite and adjacent sides. This is the foundation of the theorem and identities.

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The domain and range of f(x) = -24 are given as follows:

The domain and range of f(x) = 0.5(x + 4)² - 11 are given as follows:

The range of y = -2x² + 12x - 13 is given as follows:

y <= 5.

The domain of a function is the set that contains all the input values that can be assumed by the function.

As neither of the functions in this problem have any restriction, the domain is all real values for the two of them.

The range of a function is the set that contains all the output values that can be assumed by the function.

The ranges are given as follows:

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Answer:

Yes

Step-by-step explanation:

y = 110 + 32x

Let x = each value in the table and calculate the corresponding value of y.

You get the following.

x = 0; y = 110

x = 2; y = 174

x = 4; y = 238

x = 6; y = 302

x = 8l y = 366

Since every value from evaluating the function gives the same value as the table, then the answer is yes, the table and the equation represent the same function.

The Boeing F-14 was superseded by the F/A-18E/F Super Hornet.

The F-14 is what?

The two-seat F-14 Tomcat was used by the US Navy as a shipboard air defense, intercept, strike, and reconnaissance aircraft. The new aircraft was created by Northrop Grumman to replace the F-4 Phantom fighter, and the US Navy started employing it in 1972.

Jan 12, 2023 · In 1987, the F-14B, which featured a superior engine, entered production. The F-14D Super Tomcat was developed as a result of further developments in the radar, avionics, and missile capacity, and it made its first flight in 1988.

The F/A-18E/F Super Hornet took the place of the 338 F-14s in all three versions that were in use by the US Navy.

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The probability that a student passed the test given that they completed the homework is 0.8 (or 80%).

To calculate this probability, we can use the formula:

P(A|B) = P(A and B) / P(B)

Where A is the event of passing the test and B is the event of completing the homework.P(A and B) is the probability that a student both passed the test and completed the homework, which is the number of students who did both divided by the total number of students in the class.

16 students passed the test and completed the homework of 28 students in total, so:

P(A and B) = 16/28 = 0.57

P(B) is the probability that a student completed the homework, which is the number of students who completed the homework divided by the total number of students in the class.

19 students completed the homework out of 28 students in total, so:

P(B) = 19/28 = 0.68

Now we can use these values to find the probability that a student passed the test given that they completed the homework:

P(A|B) = P(A and B) / P(B) = 0.57 / 0.68 = 0.8 or 80%

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Correctly written question:

In a math class with 28 students, a test was given on the same day that an assignment was due. 20 students passed the test and 19 students completed the assignment. Out of the students who passed the test, 16 also completed the assignment. What is the probability that a student passed the test given that they completed the homework?

r = annual interest rate

F = final value (amount owed including interest)

P = principal (initial amount borrowed)

n = number of years the loan is taken out for

Plugging in the given values:

r = (1300 - 1200) / 1200 * 2

r = 0.15 or 15%

This formula also gives the same result, that the annual simple interest rate on Zhen's loan is 15%.

Answer:

11 students studied history

21 students studied French

8 students studied both

Step-by-step explanation:

first you have to subtract the number of students who studied both classes.

40-8=32

this leaves you with 32 students to study either history or French.

we know 10 more students studied French than history so subtract that from the 32 students because we already know where they go.

32-10=22

we're left with 22 students that can be equally split between the 2 classes.

22/2=11

so there are 11 more students in each history and French.

but don't forget to add the 10 more students that we already knew were in the French class.

11+10=21

The equation of line is y = -72x + 360

The time for the tank to drain 18 liters of water is t = 4.75 minutes

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Let the first point be P = P ( 0 , 360 )

Let the second point be Q = Q ( 5 , 0 )

Now , the slope of the line between the points is

Slope m = ( 360 - 0 ) / ( 0 - 5 )

On simplifying the equation , we get

Slope m = ( - 360/5

Slope m = -72 liters per minute

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = ( -72 ) ( x - 5 )

On simplifying the equation , we get

y = -72x + 360

Now , the tub loses 72 liters every minute

So , 1 minute is = - 72 liters

So , for every 18 liters , substitute the value of y = 18 ,  we get

18 = -72x + 360

Adding 72x on both sides of the equation , we get

72x + 18 = 360

Subtracting 18 on both sides of the equation , we get

72x = 342

Divide by 72 on both sides of the equation , we get

x = 4.75 minutes

Hence , it will take 4.75 minutes for 18 liters of water to be drained

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The end behavior of a function describes the trend of graph for x approaches to infinity(Right)  and x approaches to negative infinity (Left) .

The end behavior of the graph of polynomial function is behavior of the graph of the function "f(x)" as x approaches positive infinity or negative infinity.

Consider the function , y = x² ;

we know that the graph of this function is a U shaped graph facing in upward direction ;

we see that as "x" approaches negative infinity , "y" tends to positive infinity ;

and as "x" approaches positive infinity , "y" tends to positive infinity .

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If the fourth horse weighs more than 1420 pounds, it cannot be hauled on the trailer.

Inequality

The concept of inequality is used to show how two or more numbers and variables cannot fairly be compared. In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another. Therefore, equity is a result of imbalance.

Let x signify the fourth horse's weight.

From the inquiry:

x + 890 + 1250 + 940 ≤ 4500

x + 3080 ≤ 4500

x ≤ 1420

The fourth horse cannot be transported on the trailer if its weight is greater than 1420 pounds.

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The cost of each cup of coffee at a kiosk is $ 4.

Let the cost of each cup of coffee is $ x.

A person buys 5 cup of coffee at a kiosk in the mall.

This question is related to unitary method problems.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Then, the cost of 5 cup of coffee is 5x.

Given that bill is under $20.

So the cost of 5 cup of coffee will be $20.

5x=20

x=20/5

x=4

Therefore,  the cost of each cup of coffee is $4.

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The ratio of the orbital speed of Phobos to that of Deimos is approximately 0.3078.

The ratio of the orbital speed of Phobos to that of Deimos can be calculated using the following formula:

Speed ratio = (Radius of orbit of Phobos)^(3/2) / (Radius of orbit of Deimos)^(3/2)

Plugging in the given values, we get:

Speed ratio = (9,378 km)^(3/2) / (23,459 km)^(3/2) = (9378^(3/2) / 23459^(3/2))

Which is approximately equal to 0.3078

So the ratio of the orbital speed of Phobos to that of Deimos is approximately 0.3078.

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The number more than 5 is 6.

Number:

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits.

Greater than Number:

Greater than or equal to in mathematics is an inequality used to compare two or more numbers, quantities, or values. Used when one quantity or number is greater than or greater than the second or remaining quantity or number. This indicates that one value is greater than or greater than or greater than the other. The above symbol is ">". This is also called greater than. We can also compare the length, weight and capacity of the compared number. For example, Bella has a red pencil that is 5 cm long and a blue pencil that is 3 cm long.

According to the Question:

The number is 1 more than 5

adding 1 to 5

5+1=6

The answer is 1 more than 5 = 6.

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the system of linear equations by graphing - y=-x+7,  y=x+1; values for y is (6,6).

A linear equation is an equation in which the highest power of the variable is 1. The general form of a linear equation is "ax + b = 0", where "a" and "b" are constants and "x" is the variable. For example, "2x + 3 = 0" is a linear equation. The solution to a linear equation is the value(s) of the variable that make the equation true. Linear equations can be solved using various methods such as algebraic manipulation, substitution and elimination. Linear equations can be represented graphically as a straight line, and the solution of the equation is the point where the line crosses the x-axis (or y-axis if the equation is in terms of y). Linear equations have a wide range of applications in many fields, including physics, engineering, economics, and many others.

To solve the system of linear equations by graphing, we can first graph each equation on the coordinate plane.

y = -x + 7 represents a line with a slope of -1 and y-intercept of (0,7) y = x + 1 represents a line with a slope of 1 and y-intercept of (0,1)

If we graph these two lines, we can see that they intersect at a single point, which represents the solution to the system of equations.

The x-coordinate of the point of intersection can be found by setting y equal to each other and solving for x. x = y

And the y-coordinate of the point of intersection can be found by setting x equal to each other and solving for y. y = x

Therefore the solution of the system is (x,y) = (x,x) = (6,6)

So the solution of the system is (6,6)

We can check this point by substitute x=6 and y=6 in each equation of the system and see if it makes both equations true.

y = -6 +7 = 1 y = 6 + 1 = 7

So the point (6,6) is a solution for the system of equations.

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The words that complete the fragment correctly are money, and profit.

To identify the correct terms to complete the fragment we have to identify the term that correspond to this definition, in this case is business. So, we have to look for some definitions to get a general idea of the definition.

Also, we can find those terms by inference. For example, is easy to know that the first term is money because we interact every day with this type of economic relation. So, according to the above, the correct terms would be:

A business provides goods or services in exchange for money. The goal of a business, if it wants to survive over time, is to profit.

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Answer:

Yes SAS they are congurent

a. Ratio of 60 :80 = 0.75

% decrease = 25%

b . Ratio of 32: 36 = 0.89

% decrease = 11.11%

c. Ratio of 100.8 : 63 = 1.6

% increase = 60%

The degree to which a value increases expressed in percent form is known as percentage increase. Alternatively, percentage decrease is the percentage degree to which the measure of an item decreases.

% increase = increment/ original value × 100

a. two terms 80, 60

the ratio of second to first term = 60/80 = 0.75

percentage decrease = 80-60/80 ×100 = 20/80 ×100 = 25%

b. 36 , 32

the ratio of the second to first = 32/36 = 0.89

% decrease = 36-32/36 ×100 = 4/36 × 100 = 100/9 = 11.11%

c. 63 , 100.8

the ratio of second to first term = 100.8/63 = 1.6

% increase = 100.8-63/63 × 100 = 37.8/63 × 100 = 60%

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The roots of the quadratic equation 9 x 2 - 3 k x + k = 0 are equivalent. As a result, the needed values of k are 0 and 4.

Any equation featuring one condition that involves the unknown is cubed and no term in which it has been increased to a greater number is a quadratic equation.

This has the equation ax2 + bx + c = 0, where a = 9, b = -3k, and c = k.

If D=0, the solution will be implemented and will have real and equivalent roots.

Most typically, the quadratic equation is represented as ax2 + bx + c = 0. The coefficients are the recognized numbers a, b, and c, while x represents the undetermined.

Quadratic equations must be employed whether directly or indirectly in any field where speed, area, or profit must be calculated.

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Answer:

he should do nothing because he is just a passenger.

So, a 49-mile taxi ride would cost $19.60.

To find the cost of a 49-mile taxi ride, you first need to determine the unit price, which is the cost per mile of the taxi ride. To calculate the unit price, you can divide the total cost of the 18-mile ride by the distance traveled. In this case, the total cost of the 18-mile ride is $7.20, and the distance traveled is 18 miles.

$7.20 ÷ 18 miles = $0.40 per mile

This means that the unit price, or the cost per mile, is $0.40. To find the cost of a 49-mile taxi ride, you can then multiply the unit price by the distance of the desired ride.

$0.40 per mile x 49 miles = $19.60

So, a 49-mile taxi ride would cost $19.60.

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$7.20 ÷ 18 miles = $0.40 per mile

This means that the unit price, or the cost per mile, is $0.40. To find the cost of a 49-mile taxi ride, you can then multiply the unit price by the distance of the desired ride.

$0.40 per mile x 49 miles = $19.60

So, a 49-mile taxi ride would cost $19.60.

Answer:

To divide 1.7 by 8.5, you will need to move the decimal point one place to the right in the divisor and the dividend. This would result in 17 and 85 as the new divisor and dividend respectively, and the division would be performed as 17/85.

Addition of P+Q+R= 0 when P = 3x 2+7x + 8, Q= 2x 2+x-9 and R= -5x 2-8x+1 is 0

An algebraic expression can be defined as an expression that is made up of coefficients, terms, constants, factors, and variables.

These expressions are also known to be composed of certain mathematical operations, such as;

From the information given, we have that;

P = 3x 2+7x + 8, Q= 2x 2+x-9 and R= -5x 2-8x+1,

P+Q+ R = 0

substitute the values

3x² + 7x +2x² + x - 9 + (-5x² - 8x + 1) = 0

expand the bracket

3x² + 7x + 8 + 2x² + x - 9 -5x² -8x = 1 = 0

collect like terms

3x² + 2x² - 5x² + 7x + x - 8x -9 + 8 + 1 = 0

Add or subtract like terms

0 + 0 + 0 = 0

0 = 0

Thus, P+Q+ R equals zero

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There are two types of logarithms i.e. natural log and common log.

Natural logarithm - A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

Common logarithm - The base-10 logarithm is the most widely used logarithm in mathematics. It is also known as the standard logarithm, the decadic logarithm (named after its basis), the decimal logarithm (named after its base), or the Briggsian logarithm (named after Henry Briggs, an English mathematician who invented its application).

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Tara has £40 to spend on invitations for her party. She can spend the money in either shop 1 or shop 2 ,the maximum number of invitations she can buy from each shop is 40 .

The maximum number of invitations she can buy from each shop will depend on the cost of each invitation.

If the invitations at shop 1 cost £1 each, then she can buy a maximum of 40 invitations from this shop. However, if the invitations at shop 2 cost £2 each, then she can buy a maximum of 20 invitations from this shop.

It is important to consider the quality of the invitations. If the invitations at shop 1 are of higher quality than those at shop 2, then it may be worth spending more money on fewer invitations from shop 1. On the other hand, if the quality of the invitations is not important to Tara, then she may be able to purchase more invitations from shop 2.

The maximum number of invitations Tara can buy from each shop will depend on the cost of the invitations and the quality she is looking for. With her £40 budget, the maximum number of invitations she can buy from each shop is 40 from shop 1 and 20 from shop 2.

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The value of x is 4

Given that the median of the list 2x, 3x, 5x, and 8x is 12, we can arrange the list in order to find the value of x:

2x, 3x, 5x, 8x

To find the median, we need to find the middle value of the list. Since the list has an odd number of values, the median is the middle value.

2x < 3x < 5x < 8x

The median is 3x = 12, so x = 12/3 = 4

Therefore, the value of x is 4.

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Negative numbers don't actually have square roots because a square can only be either positive or zero. No, we cannot find the square root of the negative value.

When two numbers of the same sign are added, the result is always positive.

Theorem: Negative Numbers' Square Roots Using the number as if it were a positive integer and adding an I in front of it as a coefficient is one way to simplify an expression that involves the square root of a negative number. Or, to put it another way, for any x, where x is a positive integer or if x is a negative number, x=ix x = I x.

The worth of root 4 is equivalent to precisely 2. In any case, the roots could be positive or negative or we can say there are dependably two roots for some random number. Subsequently, root 4 is equivalent to ±2 or +2 and - 2 (positive 2 and negative 2).

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Applying the theorem of angle between intersecting tangents, m<D = 30°.

The theorem states that the angle created by the intersection of two tangent lines at a point outside of a circle is equivalent to half the difference between the measures of the arcs that the tangents intercept.

Given the following:

m<B = 75°

Measure of arc AC = 2(75) [inscribed angle theorem]

Arc AC = 150°

Arc ABC = 360 - 150 = 210°

Based on the theorem of angle between intersecting tangents, we have:

m<D = 1/2(210 - 150)

m<D = 30°

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Answer: x = 6

Step-by-step explanation:

Divide 28 by 4,  gives you 7. So the parenthesis has to equal 7, i.e 6+1 equals 7.

Answer:

A = 28.8cm²

Step-by-step explanation:

multiply 9.6 by 6.0

= 57.6

divide 57.6 by 2

= 28.8