Q 9-1 Pythagorean Theorem and Trig

A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.

Number of pens  x=10.

Number of pencils  y=30.

The Five Principles are: freedom, efficiency, mutuality, responsibility, and quality. Victoria that she always incorporates The Five Principles into her conversations with other businesses, government officials, and other partners and leaders. The writing core is tougher and leaves a lighter trace on the paper as the number increases.

Let number of pens =x

And number of pencils =y

⇒ x+y=40

⇒(5+y)+(x−5)=4x

⇒3x=y

Substituting in above equations ;

⇒x+3x=40

⇒x=10

⇒y=30

∴number of pens =x=10

⇒number of pencils =y=30

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Answer:

cash

Step-by-step explanation:

debit - account payable

credit - cash



The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.

Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.

Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?

1. Describe one way to estimate the solution to this problem.

By dividing the amount of milliliters of water in the baker by 16.5 ml

2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?

No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.

Therefore, the correct answer should be 36 test tubes.

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X is 55 after rearranging the equation given

Using percentage and equations, Greg has 734 songs, Raj has 426 songs and Mark has 720 songs

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol, "%". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentages have no dimension, which it's why they are dimensionless number. for example 60% of a number, then it means 60 per cent of its whole.

In this problem, we can write an equations and solve to determine the number of songs Greg has on his computer.

Let;

Since Mark has 720 songs in his computer;

x = 14 + 720

x = 734

Greg has 734 songs

We can calculate the number of songs Raj has by;

y = 60%(720) - 6

y = [(0.6) * 720] - 6

y = 426

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7th interval is not perfect

7th interval is not perfect

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤1. The group of numbers such that 0 < x< 1 and the group of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Real intervals are the simplest sets whose "length" (or "measure" or "size") is straightforward to define, making them significant in the theory of integration. The Borel measure and ultimately the Lebesgue measure can subsequently be produced by applying the concept of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing method that automatically generates assured enclosures for all formulas, even in the presence of errors, approximations in mathematics, and arithmetic roundoff.

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The measure of the angle ∠C in the triangle ABC can be gotten using tan m∠C = 2

An equation shows how two or more numbers and variables are related to each other.

On the other hand, trigonometric ratios are used to show the relationship between the sides and angles of a right angled triangle.

The basic equations of the trigonometry ratios are

Using the above as a guide, and the given triangle:

We have:

tan m∠C = opposite/adjacent

Substitute the known values in the above equation, so, we have the following representation

tan m∠C = 6/3

Evaluate

tan m∠C = 2

Hence, the true equation is (d) tan m∠C = 2

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The correct statement regarding the probabilities from the table is given as follows:

C The golf ball is 2 times as likely to be orange as it is to be pink.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of balls for this problem is given as follows:

4 + 11 + 8 + 18 = 41.

Hence the probability of selecting each ball is obtained as follows:

Hence statement C is correct, as:

2 x 4/41 = 8/41.

(which is the probability of orange, obtained multiplying the probability of pink by two).

The number of pink balls is of 4.

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The correct solutions for "x" after factorizing the cubic equation are:

x1 = -4

x2 = 0.5

x3 = 3

Cubic Equation:

A cubic polynomial in mathematics is a polynomial whose highest degree is three. A cubic equation is one that contains a cubic polynomial.

Either one real root or three real roots are present in every cubic equation. The cubic equation is written as ax^3+bx^2+cx+d=0.

Therefore, standard form of the cubic equation is: ax^3 + bx^2 + cx + d = 0

Given: 2x³ +x² -25x +12

On comparing with the standard form of the cubic equation, we get;

a=2

b=1

c=-25

d=12

After factorizing the cubic equation, we have three roots.

x1 = -4

x2 = 0.5

x3 = 3

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ln() is a function in Excel that calculates the natural logarithm of a number. The natural logarithm is the logarithm to the base e, where e is an irrational number approximately equal to 2.718281828.

1. Enter the number for which you want to calculate the natural logarithm in a cell.

2. Click on the cell and enter "=ln()" function (without the quotation marks) in the formula bar.

3. Within the parentheses, enter the cell reference or the number for which you want to calculate the natural logarithm.

4. Press the Enter key and the natural logarithm of the number will be calculated and displayed in the cell.

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Answer:

Undecidable Problems

Step-by-step explanation:

Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.

a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.

Here,

There is no programme that can resolve the halting difficulty for sufficiently general computer programs,

making it the most frequently encountered problem that has been discovered to be insoluble.

The type of computer software we're discussing must be made clear.

Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.

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The peak is located at R=1 according to a power curve analysis. To put it another way, the load and source resistance must match.

The ski area's name needs to be changed first. Squaw is not a kind way to refer to a woman. It is an expression that refers to female genitalia. (a decent slang equivalent in English begins with "c" and rhymes with "runt") During my time as a teacher in an Indian school, I learned this in a very embarrassing manner.

If we suppose that each person weighs roughly 70 kilograms (154 lbs) on Earth, then the power required to simply raise the people is P = W/t, and since W = mgh in this situation, P = W/t = mgh/t = (47,000 people)(70 kg/person).

(2 MW) = (1791222.222 W)(9.8 N/kg)(200 m)/(3600 s).

The complete question is:

Squaw Valley ski area in California claims that its lifts can move 47,000 people per hour.  If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.

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The estimated solution of the system 3x + y = 10 and y = 6x + 1 is (1, 7)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the linear equation:

3x + y = 10

y = -3x + 10   (1)

y = 6x + 1     (2)

Subtracting equation 2 from 1 to solve using elimination method gives:

0 = -9x + 9

9x = 9

x = 1

put  x = 1 in eqn 2:

y = 6(1) + 1

y = 7  

The solution is (1, 7)

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Answer: $52.57 for each basic yearbook and $153.5 for each deluxe yearbook

Step-by-step explanation:

First, do Mr. Boyer's class to find out how much each deluxe yearbook is:

2,763 ÷ 18 = $153.5

Then do, Mrs. Wu's class: First, multiply 153.5 by the 6 deluxe yearbooks ordered;

153.5 x 6 = 921

After, subtract 921 from 2,025:

2,025 - 921 = 1104

The remaining $1104 is the total cost of the 21 basic yearbooks ordered. Divide the total cost by the number of yearbooks ordered to find the unit price:

1104 ÷ 21 = 52.5714285714

Round to the nearest hundredth: $52.57

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The value of [tex]\lim _{x \rightarrow 2}[/tex] f(x) by Sandwich theorem is 2.

As per the given data the function limits are:

2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0

Here we have to determine the value of [tex]\lim _{x \rightarrow 2}[/tex] f(x)

Hence by Sandwich theorem:

The sandwich theorem, also known as the squeeze theorem, asserts that if two functions, g (x) and h (x), are squeezed between one another and their respective limits at a given position are both equal to L, then the limit of f (x) at that point is also equal to L.

We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" [tex]\frac{sin(x)}{x}[/tex] between two nicer functions and ​using them to find the limit at x = 0.

[tex]& \lim_{x \rightarrow 2}(2 x-2) \leq\lim_{x \rightarrow 2} f(x) \leq \lim_{x \rightarrow 2}\left(x^2-2 x+2\right) \\[/tex]

[tex]& \Rightarrow 2 \leq \lim _{x \rightarrow 2} f(x) \leq 2 \\[/tex]

Hence [tex]\lim _{x \rightarrow 2}[/tex] f(x) = 2

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The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)

An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.

They are also made up of some arithmetic operations, such as;

From the information given, we have the algebraic expression;

14x⁴y³ - 42x³y⁴

Now, factor the common numbers, we have;

14(x⁴y³ - 3x³y⁴)

Factor the common variables, we get;

14x³y³(x - y)

Hence, the expression is 14x³y³(x - y)

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Log to exponential form is very useful to easily perform complicated numeric calculations. The logarithmic form

loga N=x

can be easily transformed into the exponential form as:

ax=N

Normally, large astronomical and scientific calculations are written in exponential form, and here we can use the log to exponential form of transformation.

Logarithms are occasionally transformed using antilog tables to normal form, rather than transforming into exponential form.

Log to exponential form required specific formulas of logarithms and exponents. Logarithms help in easily transforming the multiplication and division across numbers into addition and subtraction.

And exponentials help in working across numbers with different bases and different powers.

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Answer: 62 inches

Step-by-step explanation:

26÷13 =2

so 2 is the scale factor

so 36÷2= 18

18+18+13+13=62

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Answer: 112 degrees

Explanation:

By the alternate interior angles theorem, m<CAD=40 and m<ACD=28. The quadrilateral is divided into two triangles. The sum of the angles of a triangle is equal to 180 degrees. Now that you know the measurements of two out of the three angles, you can add them up and subtract them from 180.

180-(40+29)=112

The two vectors are equal in magnitude and opposite in direction. This means that they cancel each other out, resulting in a net displacement of 0.

If the total displacement of two vectors is 0, it means that the final position of an object after being displaced by the two vectors is the same as its initial position. This can happen in a few ways:

The two vectors are equal in magnitude and opposite in direction. This means that they cancel each other out, resulting in a net displacement of 0.

The two vectors are parallel but pointing in opposite directions. This means that the object is displaced in one direction and then back again, resulting in a net displacement of 0.

The two vectors are perpendicular and the magnitude of each vector is the same. This means that the object is displaced in one direction and then back again in the perpendicular direction, resulting in a net displacement of 0.

Therefore, In all cases, it can be inferred that the two vectors are in some way related to each other in terms of direction and magnitude.

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The limit as x approaches 2 or lim x→2  is 4.

When calculating a limit, the goal is to find the value of the function as x approaches the given value. In this case, the given value is 2. As x approaches 2, the values of the function will approach 4, which is the upper bound of the given inequality. This means that the limit as x approaches 2 is 4.

To prove this, we can look at the inequality and find the values of the function at x = 1 and x = 3. For x = 1, the function value is -1, which is less than 4. For x = 3, the function value is 7, which is greater than 4. This means that the function values are increasing as x gets closer to 2, so the limit as x approaches 2 is 4.

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Answer:

24 students are in the class

Step-by-step explanation:

Let x represent the total number of students in the class. We have the equation:

(2/3)x = 16

x = 24 students

So, there are 24 students in the class.

Answer:

24 students

Step-by-step explanation:

16/2=8

8*3=24

Yes the product of two perfect squares is always a perfect square, But the quotient of two perfect squares is not always a perfect square.

A perfect square is a number that can be expressed as the product of an integer multiplied by itself.

Examples of perfect squares include 4 (2*2), 9 (3*3), and 25 (5*5).

The quotient is the result obtained after performing division of one number by another. It is the number of times that the divisor can be subtracted from the dividend until the remainder is smaller than the divisor.

The product of two perfect squares is always a perfect square because the root of the products is equal to the product of roots as shown below,

let us take the two perfect squares 4 and 9, so the square root of 4*9 is,

[tex]\sqrt{4*9} =\sqrt{4} *\sqrt{9} \ =2*3=6[/tex]

But , the quotient of two perfect squares is a perfect square,

When we divide two perfect squares we are not always going to get a quotient that can be represented as the square of an integer. For example, (36/16) = 9/4 which is not a perfect square.

However, if the numerator and denominator in the quotient are the same perfect square then the quotient will be 1 which is a perfect square.

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Answer: y=3/ 4x

Step-by-step explanation: in the linear equations y= Kx shows the proportionality relations . Where k is the proportionality constant which can be any number . x an y are the variables, so according to this answer will be y=3/

Answer:

y=3/4x

Step-by-step explanation:

Let's first define some words;

Proportional: If a line or a ray through the origin it proportional

Non proportional: If a line or ray that does not pass through the origin

Origin: Initial point or the starting point

Now we have define the words now let's graph these points by using Desmos.

Graphs are shown below.    

Base on the graphs below we can see that;

y=3/4x pass through the origin which means the that this linear equation is proportional.

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[tex]8x+5y=-17[/tex] when y is -5

Substitute for y with given value:

[tex]8x+5(-5)=-17[/tex]

[tex]8x-25=-17[/tex]

Add 25 to both sides:

[tex]8x-25+25=-17+25[/tex]

[tex]8x=8[/tex]

Divide both sides by 8:

[tex]\dfrac{8x}{8} =\dfrac{8}{8}[/tex]

[tex]\fbox{x = 1}[/tex]

The the wind speed of a tornado with Beaufort number 9 is 51.3 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in meters per second (m/s) in this example because the distance is measured in meters (m) and the time is measured in seconds (s).

Given:

The Beaufort Scale measures the intensity of tornadoes. For a tornado

with Beaufort number B, the formula [tex]v = 1.9B^\frac{3}{2}[/tex] may be used to

estimate the tornado's wind speed in miles per hour.

We have to estimate the wind speed of a tornado with Beaufort number 9.

Plug B = 9 in the formula [tex]v = 1.9B^\frac{3}{2}[/tex]

⇒

[tex]v = 1.9(9)^\frac{3}{2} \\v = 1.9(27)\\v = 51.3[/tex]

Hence, the the wind speed of a tornado with Beaufort number 9 is

51.3 miles per hour.

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Answer:

I have no idea tbh I need help with this too

Step-by-step explanation:

PLEASE HELP!!!!!!!!!!!!!!!