Is A ={ x x² 4 and 3x 9 an empty set justify your answer?.

The distance between two points (2, 3) and (5, 7) is 5 units.

Therefore the answer is 5.

To find the distance between the points (2, 3) and (5, 7), we can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) = (2, 3) and (x₂, y₂) = (5, 7)

Substituting the coordinates of the two points into the formula:

d = √((5 - 2)² + (7 - 3)²)

d = √((3)² + (4)²)

d = √(9 + 16)

d = √(25)

d = 5

So the distance between the points (2, 3) as well as (5, 7) will be  5 units by solving the above expression.

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Answer:

x = 5

Step-by-step explanation:

Angles on a straight line add up to 180, so add up the angles and equate to 180:

9x + 85 + 10x = 180

Now we can solve for x by simplifying further:

19x + 85 = 180

Subtract 85 on both sides:

19x + 85 - 85 = 180 - 85

19x = 95

Divide 19 on both sides which cancels out the 19 on the left:

x = 95/19 = 5

Answer:

[tex]y=-\frac{6}{5} x[/tex]

Step-by-step explanation:

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{7-(-5)}{-5-5}[/tex]

[tex]\frac{7+5}{-10}[/tex]

[tex]-\frac{12}{10}[/tex]

[tex]y=-\frac{6}{5} +b[/tex]

[tex]-5=-\frac{6}{5} (5)+b[/tex]

- 5 = - 5 + b

b = 0

[tex]y=-\frac{6}{5} x[/tex]

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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The distance between the pair of points with the coordinates ( 3, 4 ) and (0, 0) is given by 5 units.

As given in the question,

Given pair of points with the coordinates are as follow :

( x₁ , y₁ ) = ( 3,4 )

( x₂ , y₂ ) = ( 0, 0 )

General formula to determine the distance between two pair of points with the coordinates is :

= √( y₂ - y₁ )² + (x₂ - x₁ )²

Now, substitute the values of the coordinates to find the distance between two pair of points :

= √ ( 0 - 4 )² + ( 0 - 3 )²

= √4² + 3²

= √16 + 9

= √25

= 5 units.

Therefore, the distance between the given pair of points with the coordinates is equal to 5 units.

The above question is incomplete , the complete question is:

What is the distance between the pair of points (3, 4) and (0, 0) ?

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This problem may be simplified by substituting the number seven into the original equation. The result will then be obtained by solving the given expression.

Put the supplied value of h, which is seven, in the given phrase to begin solving this problem. Then, using the BODMAS rule, the bracket will be solved first, followed by the addition, from which this can be solved yielding a result of 50.

This may be resolved as follows:

For h=7, in 5 x ( h + 3 )

= 5 x ( 7 + 3 )

= 5 x ( 10 )

= 50

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Answer: We can use the formulas for conditional probability to calculate the percentage of people in the village who speak both French and English.

P(French and English) = P(French) x P(English|French)

We know that P(French) = 64% and P(English|French) is the probability of someone speaking English given that they already speak French, which is 58%. So we can plug these values into the formula:

P(French and English) = 64% x 58% = 37.12%

Therefore, 37.12% of the inhabitants of the village on the Nigerian border speak both French and English.

Note that this is an estimation since this formula assumes independence and the real probabilities might be different.

Step-by-step explanation:

The total number of miles Reuben biked last year and this year is the sum of the miles he biked last year and this year.

You can represent the total number of miles he biked as:

Total miles = 496 + m

Where 496 is the number of miles biked last year and m represents the number of miles biked this year.

So the expression for the total number of miles he biked is 496 + m

x/sin 45 = 4√22/sin 90

CB = 4√22/sin 90 × sin 45

CB = 4√11

or

CB = √(4√22)²-(4√11)²

= 4√11

Answer:

CB = AC = 4√11

Step-by-step explanation:

We know that the sum of the angles of a triangle is 180°. If angle A = 45° and C = 90°, then angle B = 180° - 90° - 45° = 45°. This shows us that the triangle is isosceles and the leg AC is equal to the leg CB.

Consequently: CB = AC = 4√11

If we didn't know the length of AC, then it can be calculated from the hypotenuse:

AC² + CB² = AB²
2 * CB² = (4√22)²
CB² = (4√22)² / 2
CB² = 16 * 22 / 2
CB = √(16 * 11)
CB = 4√11

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Answer:

190,217

Step-by-step explanation:

Let x = number of doctors.

27.6% of x is 52,500

0.276x = 52,500

x = 52,500/0.276

x = 190,217

Answer:

The equation x2+6x+9 = 0 has roots of 3+i and 3-i. By the fundamental theorem of algebra, this equation has three roots, two of which may be equal. The standard quadratic equation using the given set of solutions {3+i,3-i} is y=x2+6x+9.

Using exponential function, The value after 10 will be P(10) = 2125.0.05¹⁰.

A mathematical function with the following form is an exponential function: f ( x ) = an x. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

This is an exponential behavior expressed as:

P(t) = Abⁿ

P(t) = Ae^(n ln b)

Where P(t) is the  worth after 10 years,

A is the original investment,

and b is the percentage (87% in this case).

From the problem, we identify:

A = 2125

b = 0.05

The final model is:

P(t) = 2125.0.05¹⁰

After 10 years (t = 10),

the investment will be (to the nearest whole number):

P(10) = 2125 ×0.05¹⁰

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The slope of a line is determined by the formula:

(y2 - y1) / (x2 - x1)

So for the points (9, 5) and (21, -5), the slope would be:

(-5 - 5) / (21 - 9) = -10 / 12 = -5/6

So the slope of the line that passes through the points (9, 5) and (21, -5) is -5/6 in simplest form.

There are 364 solutions to the given inequality: x1 + x2 + x3 <= 11.

To get the solution of the inequality x1 + x2 + x3 <= 11, we first need to include an additional variable in the inequation to write in as an equation.

Therefore, let the additional variable be x4.

Thus, equation is x1 + x2 + x3 + x4 = 11

The number of solutions of an equation can be calculated by the formula,

[tex]( \left \ {{n+ r - 1} \atop {n}} \right.)[/tex], where n is the constant value of the equation and r is the number of variables in the equation.

In this case, n = 11 and r = 4

Therefore,

[tex]( \left \ {{n+ r - 1} \atop {n}} \right.)[/tex] = [tex]( \left \ {{11+ 4 - 1} \atop {11}} \right.)[/tex] = [tex]( \left \ {{14} \atop {3}} \right.)[/tex]

= 14 * 13 * 12 * 11!/(3 * 2 * 1 * 11!)

=2184/6 = 364

Therefore, there are 364 possible solutions of the inequality.

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A fraction is said to be in standard form when both the numerator and denominator are co-prime numbers.

A well-known form of a range in Maths is largely cited for the illustration of large numbers or small numbers. We use exponents to symbolize such numbers in general shape. Any number that we can write as a decimal range, between 1. zero and 10.0, multiplied by means of a power of 10, is stated to be in general shape.

“ Standard form” is likewise known as “clinical Notation” depending on the mathematical lingo of the u. s. you are in. within the UK and the international locations that comply with the same conventions as the UK, the time period “medical Notation” is most typically used while in nations that comply with the usa conventions majorly talk to this shape of writing as the “fashionable form”.

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Answer: The Declaration of Independence, adopted by the Continental Congress on July 4, 1776, is a reflection of the colonists' motivations in several ways. Firstly, the Declaration states that the colonists believed that all men are created equal and have the right to life, liberty, and the pursuit of happiness. This reflects the colonists' belief in the Enlightenment principles of natural rights and individual liberty, which were influential in shaping their motivations for seeking independence from British rule.

Secondly, the Declaration cites a long list of grievances against King George III, accusing him of violating the colonists' rights and abusing his power. This reflects the colonists' growing frustration and anger towards British rule, which had been building for many years prior to the drafting of the Declaration.

Thirdly, the Declaration states that the colonists had attempted to resolve their differences with the British government through peaceful means, but that these efforts had been unsuccessful. This reflects the colonists' desire for a peaceful resolution to their issues, but their willingness to fight for their rights if necessary.

In summary, the Declaration of Independence reflects the colonists' belief in natural rights and individual liberty, their growing frustration and anger towards British rule, and their desire for a peaceful resolution to their issues but their willingness to fight for their rights if necessary.

Step-by-step explanation:

The value of Expression √x + 1/√x=(4√5+2√2)/3.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable.

There are three terms in this example: x2, x, and -12.

Given:

x=7+√40

=7+2√10

=5+2+2√10

=(√5)²+2.√5.√2+(√2)²

=(√5+√2)²

∴√x=√5+√2 (neglecting the negative sign)

1/√x=1/(√5+√2)

=(√5-√2)/(√5+√2)(√5-√2)

=(√5-√2)/(5-2)

=(√5-√2)/3

√x+1/√x

=(√5+√2)+(√5-√2)/3

=(3√5+3√2+√5-√2)/3

=(4√5+2√2)/3

=(4√5+2√2)/3

√x + 1/√x=(4√5+2√2)/3.

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The value of x in equation 2x+3y=36, when y=6 is 9.

The replacement operation can be used in a variety of situations involving formal objects that contain symbols; it involves systematically replacing occurrences of a symbol with a particular value.

Substitution is a fundamental computer algebra operation.

Given equation 2x+3y=36 ; y=6

Solve the equation for given y.

Plugging y=6 in the given equation

We get 2x + 3(6) = 36

2x +18 = 36

2x = 36 - 18

2x = 18

x = 9

Therefore, the value of x in equation 2x+3y=36, when y=6 is 9.

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Answer:

[tex]\boxed{a = 4}[/tex]

Step-by-step explanation:

Note:

[tex]\fbox{\parbox{\textwidth}{%\textrm{\textsf{\textbf{Note:}}\\\textsf{This question is stated in a confusing manner and since I cannot see\\part a I am taking whatever I see on the screen as gospel truth\\\\From the question it appears that we are given gf(a) =3 and asked to solve for a.\\\\I am proceeding on that basis}}}[/tex]

We have the following functions

[tex]f(x) = \dfrac{2}{x}\\\\g(x) = \dfrac{x + 1}{x}\\[/tex]

[tex]gf(x) = g(f(x))[/tex]

[tex]\textrm{To find g(f(x)) wherever you see an x in gx), substitute the expression for f(x)}\\[/tex]

[tex]Since f(x) = \dfrac{2}{x}\\\\\textrm and}\\\\g(x) = \dfrac{x + 1}{x}\\[/tex]

[tex]\dfrac{\dfrac{{2}}{x}+1}{\dfrac{2}{x}}\\\\\\\\\left(\dfrac{{2}}{x}+1}\right) \div \dfrac{2}{x}\\\\= \left(\dfrac{{2}}{x}+1} \right) \times \dfrac{x}{2}\\\\[/tex]

[tex]\dfrac{2}{x} + 1} = \dfrac{2 + x}{x}\\[/tex]

[tex]\left(\dfrac{{2}}{x}+1} \right) \times \dfrac{x}{2}\\\\\\= \dfrac{2 + x}{x} \times \dfrac{x}{2}\\\\\\[/tex]

[tex]\textrm{The x's cancel out giving $\dfrac{2+x}{2}$}= 1 + \dfrac{x}{2}[/tex]

[tex]\textrm{For a specific value, a, if $g(f(a)) = 1 + \dfrac{a}{2}$ = 3}}[/tex]

[tex]\textrm{Then $\dfrac{a}{2}$ = 3-1 = 2}[/tex]

[tex]\boxed{a = 4}[/tex]

The graph's shape changes depending on the base. The graph can be reflected across the y-axis by replacing x with x, and across the x-axis by replacing y with y.

How to graph an exponential function with the notation f (x) = bx f (x) = b x 1

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The system has no solution when h is not equal to ( 18x+7 )/( -6x)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

− 6(hx + 2) = 3(x − 3) + 2(x + 2) +13x

-6hx-12=3x-9+2x+4+13x

=>  -6hx-12= 18x-5

=> -6hx = 18x-5 +12

=>  -6hx = 18x+7

=> h = ( 18x+7 )/( -6x)

The system has no solution when h is not equal to ( 18x+7 )/( -6x)

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Step-by-step explanation:

The answer is gotten by 5% of 70

5/100 × 70/1

= 35/10

= 3.5

Answer: $73.50

Step-by-step explanation:

First, we need to find what is 5% worth of 70 bucks. We would divide 5 by 100 since percents are based on 100 which gets us 0.05. Next do 0.05 * 70 = 3.5. Means that she'll pay $3.50 on top of the 70 bucks, so add the two together, common sense: $73.50. Have a good day ;)

The length of EF, to the nearest tenth of a foot is found to be 14.3 ft.

In rDEF, DE = 90°, DF = 81°, and DE = 14. 6 ft,

Because the given triangle is a right angled triangle, we can use the concepts of trigonometry in order to solve the given problem.

Using the trigonometric relation,

sin A = P/H

Where,

P is perpendicular and H is the hypotenuse.

We have, A = 81°,

It is given that the value of DE is 14.6 ft.

We know, sin(81°) = 0.98

So, the length of EF, to the nearest tenth of a foot is,

0.98 = EF/14.6

EF = 14.3 ft.

So, the length of the EF is 14.3 ft.

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Complete Question - In ΔDEF, ∠E = 90°, ∠F = 81° and DE = 14.6ft. Find the length of EF, to the nearest tenth of a foot.

RS is 75 units when T and q are the midpoints of legs SU and RV of a trapezoid.

The bases are in step with one another. The median runs perpendicular to each bases, and its length will be determined by averaging the bases' lengths. 360° is the sum of all of the angles in a trapezoid. A aspect's angles upload as much as an entire one hundred eighty stages.

So, imagine cutting the trapezoid from half and and rotating and join it to became a long parallelogram

Now,

VR = UV + RS = 2QT

⇒ 35 + RS = 2 × 55

⇒  RS = 110 - 35

⇒  RS = 75

Thus, RS is 75 units when T and q are the midpoints of legs SU and RV of a trapezoid.

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Amelia cut a 168 inch long ribbon into 6 equal part. Patrick cut a 14 foot long ribbon into 7 equal piece.

Amelia's ribbon pieces were 28 inches long each. Patrick's ribbon pieces were 2 feet long each.

Amelia's ribbon:

To calculate how long each piece of ribbon is, we need to divide 168 inches (the total length of the ribbon) by 6 (the number of pieces).

168 ÷ 6 = 28

Therefore, Amelia's ribbon pieces were 28 inches long each.

Patrick's ribbon:

To calculate how long each piece of ribbon is, we need to divide 14 feet (the total length of the ribbon) by 7 (the number of pieces).

14 ÷ 7 = 2

Since 1 foot is equal to 12 inches, we can convert 2 feet to 24 inches.

Therefore, Patrick's ribbon pieces were 2 feet (or 24 inches) long each.

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Bob spends 9 minutes running for every 36 minutes that he spends practicing dribbling.

What is ratio ?

A ratio is a mathematical comparison of two or more values or quantities. It is a way of expressing the relationship between different amounts or measurements.

The ratio of running to dribbling is 5 minutes of running to 20 minutes of dribbling. We can use this ratio to find out how many minutes Bob spends running if he spends 36 minutes practicing dribbling.

First, we can set up a proportion with the known ratio and the unknown value ,

5/20 = x/36

To find x we can cross-multiply to get ,

20x = 180

then divide both sides by 20 ,

x = 9

So, Bob spends 9 minutes running for every 36 minutes that he spends practicing dribbling.

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5/20 = x/36

To find x we can cross-multiply to get ,

20x = 180

then divide both sides by 20 ,

x = 9

So, Bob spends 9 minutes running for every 36 minutes that he spends practicing dribbling.

Answer:

x = 79

Step-by-step explanation:

Since PQ and RS are most likely parallel lines, we can consider the orange angles (image provided below) to be similar due to them being alternate interior angles.

Now that we know that one angle of the triangle given (orange) is 46 degrees, we can solve for the other angle of the triangle. A triangle adds up to 180 degrees, so we can find the missing angle by subtracting 180 from the given angles: 180-33-46 = 101 (marked in red).

With the red angle, we can find x by subtracting 180 from 101. Why you may ask? Because RS is parallel to PQ, so the degree will be 180. Therefore, the missing angle, x, will be 79.

Yes 360 degrees is full turn calling it a full rotation.

A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.

Each of the 360 equal segments that make up a rotation is referred to as a degree. We use a circle ° to represent a degree. 180°, for instance, denotes 180 degrees. An angle in degrees is an angle whose measure is expressed in degrees.

A 360 degree is also called as a Complete angle because it complete the whole round making the 180 degree angle twice giving us 360 degree.

A 360 when written as radian can be given by 2π ( where π= 180 degree)

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The following triangles are congruent.

Yes AAA