The table below shows a relationship between x and y values. Which of the following equations describes this relationship?

Answer:

(a) = 13

(b) = 8

(c) = 5

Step-by-step explanation:

Addition theorems on sets are

Theorem 1 :

n(AuB) = n(A) + n(B) - n(AnB)

Theorem 2 :

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Total number of students in the school is not given

so let there are 60 students in the school

using theorem 2

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

   60             =    40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)

60 +73 -120 = n(AnBnC)

         13         = n(AnBnC)

therefore, there are total 13 students who take all three subjects

Number of students who had taken only Mathematics  =
n(A) - n(AnB) - n(AnC) + n(AnBnC)

40 - 20 - 25 + 13

53 - 45 = 8 students

Number of students who had taken only Physics  =

n(B) - n(BnA) - n(BnC) + n(AnBnC)

42 - 20 - 28 + 13

53 - 48 = 5 students

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Answer: y+6 = 1/3(x-4

The equation of line perpendicular to the given line and passes through the point P ( 4 , -6 ) is y + 6 = ( 1/3 ) ( x - 4 )

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

Now , the value of A is

y + 1 = -3 ( x - 5 )

So , the slope of the line is m = -3

Now , the lines are perpendicular , so the slope of the line m₂ is

m₂ = 1/3

Let the first point be P ( 4 , -6 )

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

On simplifying , we get

y - ( -6 ) = ( 1/3 ) ( x - 4 )

y + 6 = ( 1/3 ) ( x - 4 )

Hence , the equation of line is y + 6 = ( 1/3 ) ( x - 4 )

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The range of the function given the domain x > -2 is; Range; y < -8.

The range of a function is the set of all possible outcomes of the function. In this scenario, since the domain of the function is given as X > -2. It follows from the function that at all times, the range of the function is given by; y < -8 from; y < 5(-2) +2; y< -8.

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Answer:

function

Step-by-step explanation:

Answer:

[tex]IK = IJ\sqrt{2}[/tex]

Step-by-step explanation:

First, it's an isosceles right triangle, which means there is a 90 degree angle and the two other angles are equal.

To find what the two other angles are, you can set up a quick equation:

let x be angle

90 + 2x = 180, since the sum of the interior angles in a triangle is always 180.

then,

[tex]2x = 90\\x = 45[/tex]

Therefore, the triangle is a 45-45-90 triangle.

You have the measure of IJ, which is one of the legs of the triangle. The way you can find the length of the hypotenuse of a 45-45-90 triangle is by multiplying the length of one of the legs by [tex]\sqrt{2}[/tex].

This means the equation is [tex]IK = IJ\sqrt{2}[/tex]

Answer:

[tex]\sf IK=IJ\sqrt{2}[/tex]

Step-by-step explanation:

The interior angles of a triangle sum to 180°.  Therefore, if ΔIJK is an isosceles right triangle where m∠J = 90°:

To calculate the base angles:

⇒ m∠K + m∠I + m∠J = 180°

⇒ m∠K + m∠I + 90° = 180°

⇒ m∠K + m∠I = 90°

⇒ m∠K = m∠I = 45°

Therefore, IJ and JK are the legs of the right triangle and IK is the hypotenuse.

To find the length of the hypotenuse, use Pythagoras' Theorem.

Pythagoras’ Theorem:  [tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for IK:

[tex]\sf \implies IJ^2+JK^2=IK^2[/tex]

[tex]\sf \implies 4^2+4^2=IK^2[/tex]

[tex]\sf \implies IK^2=32[/tex]

[tex]\implies \sf IK=\sqrt{32}[/tex]

[tex]\implies \sf IK=\sqrt{16 \cdot 2}[/tex]

[tex]\implies \sf IK=\sqrt{16}\sqrt{2}[/tex]

[tex]\implies \sf IK=4\sqrt{2}[/tex]

As IJ = 4 then:

[tex]\implies \sf IK=IJ\sqrt{2}[/tex]

Answer:

Kathy

Step-by-step explanation:

Answer:

I think it's C. transitive property of equality

Answer:

The domain is t ≥ 0

The range is D ≥ 0

Step-by-step explanation:

[tex]rate = \frac{distance}{time}[/tex]

D(t) = 100t + d₀

t is the time measured in hours.

d₀ is the initial position of the train.

We can assume the distance they go is not negative so...

The domain is t ≥ 0

The range is D ≥ 0

The correct option is the mean for set 2 is equal to the mean for set 1. (option A).

Mean is a measure of central tendency that is used to determine the average of a set of numbers.  

Mean = sum of the numbers / total number

Mean of set 1 = (29 + 31 + 27 + 33 + 30) / 5

= 150 / 5 = 30

Mean of set 1 = (33 + 31 + 26 + 31 + 29) / 5

= 150 / 5 = 30

Median is the measure of center of a dataset. It determines the value that is at the center of a dataset that is arranged in either ascending or descending order.

Set 1 arranged in ascending order : 27, 29, 30, 31, 33

Median of set 1 = 30

Set 2 arranged in ascending order : 26, 29, 31, 31, 33

Median of set 2 = 31

Differnce in the median = 31 - 30 = 1

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Answer: No

Step-by-step explanation:

Weight limit = 40 Lb

Weight given = 21 kg

Conversion factor

2.2 Lb = 1 kg

2.2 x 21 = 46.2

46.2 Lb = 21 kg

46.2 > 40, the stand cannot support the TV

TV > stand

Answer:

f

Step-by-step explanation

Answer:

Denes Dynamos =

2012 attendance = 34500

2013 attendance = 30705

change = 30705 - 34500= -3795

change percentage = -3795 * 100 / 34500 = -11%

Edgefield Eagles =

2012 = 24100

2013 = 21208

change = -2892

change Percentage = -2892 * 100 / 24100 = -12%

Answer: Choice [D] - "power of a power" ✅

Step-by-step explanation:

Hii, do you need to know which law you should use to simplify [tex]\sf\bigg(x^4\bigg)^9[/tex]?

No problem!

The law we will use here is "power of a power".

What "power of powers" means is we raise a power to a power, which is exactly what we do here: We raise x^4 to the power of 9. To simplify our expression, we multiply the powers. ([tex]\boldsymbol{4\cdot9}[/tex])

So the right answer is: Choice [D] - "Power of a power"

The simplified answer is [tex]\LARGE\boldsymbol{x^{4\cdot9}=x^{36}}[/tex]

Voila! There's our answer, cheers!

--

Hope that this helped! Best wishes.

[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.}[/tex]

--

Answer:

In triangle TEI and ERI

TI = RE ( given)

angle TDI = angle ROE ( given).

TE = RI ( given).

by side angle side criteria

both the triangles are congruent

by cpct ( corresponding parts of congruent triangles)

TD is congruent to RO

Answer:

B is correct.

Answer:

i think the answer would be 53?

Step-by-step explanation:

i could be wrong

Step-by-step explanation:

the answer is d= -46/-7

or in simplest form

d= 6.57

hope this is correct...

Answer:

The answer will be equation

To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.

From the information given about the probability, the goal here is to design a simulation for this situation.

In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.

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Answer:

(2,-3)

Step-by-step explanation:

Thats where the parabola is the lowest at

Mitch and Terry were 0.5 km away from the scenic cliff

Sea level is the base for calculating the depth and the elevation of Earth

It is given that

Total Height of the scenic Cliff = 6.6km

After 1 hour the brothers are at = 6.6 - 1.3 km = 5.3 km from the sea level.

They climb back 0.8 km in the next hour so they will be

5.3 +.8 = 6.1 km from the sea level

6.6 - 6.1 = 0.5 km

Therefore the brothers are 0.5 km away from the scenic cliff

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It should be reported as a restricted cash in the long-term section of the company balance sheet.

Note payable  can be defined a the money a company or an organization owes or the money they are expected to payback..

Note payable is classified as long term liabilities. Hence, the cash amount of $100,000 should be reported or recorded in the balance sheet as a restricted cash.

Therefore  the $100,000 is reported as a restricted cash.

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Based on the calculations, the length of side AB is equal to 13.93 units.

Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:

AM = AD - BC

AM = 7 - 2

AM = 5 units.

Now, we can determine the length of side AB by applying Pythagorean's Theorem:

AB² = BM² + AM²

AB² = 13² + 5²

AB² = 169 + 25

AB = √194

AB = 13.93 units.

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Answer:

[-3, 5)

Step-by-step explanation:

At x = -3, the circle is filled in, so -3 is part of the domain. At x = 5, the circle is not filled in, so 5 is not part of the domain. So the domain is [-3, 5).

Answer:

21500

Step-by-step explanation:

21500 people would have to see the movie to recuperate their losses.

The number of people would have to see the movie is given by the equation A = 2600 people

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of people to see the movie in first four weeks be A

Now , the equation will be

The cost of movie license per week = ₹ 1500

The cost of movie license per month = 4 x ₹ 1500

The cost of movie license per month = ₹ 6000

And ,

The cost of keeping the stuff and hall for a month = ₹ 20,000

So ,

The cost of movie license and the hall for a month = 20,000 + 6000

The cost of movie license and the hall for a month = ₹26,000

The cost of charge of each seat = ₹ 10

So , the number of people to see the movie in the first four weeks in order for them to recoup the costs A = cost of movie license and the hall for a month / cost of charge of each seat

Substituting the values in the equation , we get

Number of people to see the movie in first four weeks A = 26000/10

Number of people to see the movie in first four weeks A = 2600 people

Hence , the number of people is 2600 people

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Answer:

[tex]\mathsf {y =\frac{15}{7}x }[/tex] < [tex]\mathsf {y=\frac{13}{6}x }[/tex] < [tex]\mathsf {y=\frac{11}{5}x }[/tex] < [tex]\mathsf {y=\frac{21}{9}x }[/tex] < [tex]\mathsf {y= \frac{19}{8}x}[/tex]

Step-by-step explanation:

Finding the unit rate of the graph :

Now, the equations with greater unit rates (in increasing order) are :

Answer:

Step-by-step explanation:

If AC is a supplementary line, then

x + 90° + x = 180°

solution:

2x + 90° = 180°   |subtract 90° from both sides

2x = 90°    |divide both sides by 2

x = 45°

Answer:

[tex] \sf \: b) \: {45}^{o} [/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + x + 90° = 180°

Then the value of x will be,

→ x + x + 90° = 180°

→ 2x = 180° - 90°

→ 2x = 90°

→ x = 90° ÷ 2

→ [ x = 45° ]

Hence, the value of x is 45°.

Answer:

I really don't know

Step-by-step explanation:

what is even that