Given that set A has 73 elements and set B has 29 elements, determine the maximum possible number of elements in A ∩ B

The Perimeter of a triangle ΔABC  is 27.68

Given ABC be triangle having vertices A(-2, -1), B(4, 3), C(-5, 7)

We need to find the perimeter of a triangle as

Perimeter of a triangle ΔABC = AB + BC +CA

Now we need to find distances as

D = √ (x₂ - x₁)² + ( y₂ - y₁ )²

AB = √ (4 - (-2))² + (  3 - (-1) )²

     = √ ( 4 + 2 )² + ( 3+1 )²

    = √ (6)² + (4)²

    = √ 36 + 16

    = √ 52

    = 7.21

BC = √ ((-5) - (4))² + (  7 - (3) )²

     = √ (-5 -4 )² + ( 7-3 )²

    = √ (-9)² + (4)²

    = √ 81 + 16

    = √ 97

    = 9.84

AC = √ ((-5) - (-2))² + (  7 - (-1) )²

     = √ (-5 -2 )² + ( 7+1)²

    = √ (-7)² + (8)²

    = √ 49 + 64

    = √ 113

    = 10.63

Perimeter of a triangle ΔABC = AB + BC +CA

                                                 = 7.21 + 9.84 + 10.63

                                                 = 27.68

Therefore, the Perimeter of the given triangle ΔABC  = 27.68

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Answer:

Denominator

Step-by-step explanation:

The Denominator is under the fraction bar. The numerator is above the bar

Answer:

Denominator

Step-by-step explanation:

Denominator: The number below the fraction bar in a fraction; it tells the total number of equal parts.

I hope this image helps.

The amount of gas in the tank is 13 1/3 gallons

The tank of the car holds 20 gallons of gas

The gasoline gauge shows 2/3 full

The amount of gas left in the tank can be calculated as follows

= 2/3 × 20

= 40/3

= 13 1/3

Hence there are 13 1/3 gallons of fuel left in the tank

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The mathematical expression of the statement is x - 15 <= 5

The statement is given as:

Hourly wage of $15 differs from the average by less than or equal to $5

Let the average hourly wage be x

So, we have:

Hourly wage of $15 differs from the average = x - 15

less than or equal to $5 => <=5

So, the expression is

x - 15 <= 5

Hence, the mathematical expression of the statement is x - 15 <= 5

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The calculated division of the numbers 40 divided by 20 is 2

From the question, we have the following parameters that can be used in our computation:

40 divided by 20

When represented as an equation, we have

40 divided by 20 = 40/20

Divide 40 by 20

So, we have the following result

40 divided by 20 = 2

Using the above as a guide, we have the following:

the result is 2

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Answer: 70

Step-by-step explanation:

7 days a week x 2 lawns = 14

14 lawns x 5 weeks = 70 lawns

Answer:

70 lawns

Step-by-step explanation:

If Bob mows lawns every day for 5 weeks this is how the equation would work:

2 * 7 = 14

14 * 5 = 70

I got the 7 because there's seven days per week.

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

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Answer:

3/14

Step-by-step explanation:

Answer:

3/14

Step-by-step explanation:

The one cup holds 7 ounces of juice.

According to the statement

We have to find that the How many ounces does a cup hold.

So, For this purpose, we know that the

A quantity is a property of some object or collection of objects that is measurable.

From the given information:

A large juice jug holds the equivalent of 10 drinking cups: 4 jugs hold 189 ounces more than 13 drinking cups.

Let the amount held by a cup be y ounces.

So the large jug holds 10y ounces.

4 jugs hold 189 ounces more than 13 cups

4*10y=189+13y

40y-13y=189

27y=189

y=7

A cup holds 7 ounces.

So, The one cup holds 7 ounces of juice.

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The number of weeks that it takes to empty the lake is; 350/11 weeks

We are told that Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

Let w = number of weeks required to empty the lake

let the completed job = 1 (an empty lake)

Thus;

w/14 - w/25 = 1

Multiply through by 350 to get;

25w - 14w = 350

11w = 350

w = 350/11 weeks

Thus, the number of weeks that it takes to empty the lake is; 350/11 weeks

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Let us understand the properties of Logarithms. In mathematics Logarithms are the inverse of exponential function. In the simplest case, the logarithm counts the number of times same factor in present in a repeated multiplication.

A logarithm of a number 'x' to a base 'y' is defined as:

[tex]log_y^x=z (y > 0)[/tex]

which represents [tex]y^{z} =x[/tex]

According to the properties of Logarithm :

Now let us solve the given problem:

[tex]2 log (x-y)=log x+ log y\\or,log(x-y)^2=log(xy)\\or,log(x^2+2xy+y^2)=log(xy)[/tex]

[tex]or,x^{2} +2xy+y^{2}=xy\\[/tex] ( taking anti-logarithms on both sides)

[tex]or,x^{2}+y^{2}=xy+2xy[/tex]

Now let us use the above equation to solve

Left Hand Side:

[tex]2 log(x+y)\\=log(x+y)^2\\=log(x^{2} +2xy+y^{2} )\\=log(x^2+y^2+2xy)\\=log(xy+2xy+2xy)\\=log(5xy)\\=log(5)+log(x)+log(y)[/tex]

=Right Hand side

Hence the statement is proved by using the properties of logarithm.

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Answer:

n = 4

Step-by-step explanation:

8 * n = 32

Solve for n

Divide each side by 8

8*n/8 = 32/8

n = 4

Using the Pythagorean theorem, the missing sides are:

1. 5

2. 13

3. √15

4. 3

The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.

1. Missing side = √(3² + 4²) [Pythagorean theorem]

Missing side = 5

2. Missing side = √(12² + 5²) [Pythagorean theorem]

Missing side = 13

3. Missing side = √(4² - 1²) [Pythagorean theorem]

Missing side = √15

4. Missing side = √((√10)² - 1²) [Pythagorean theorem]

Missing side = √(10 - 1) = √9

Missing side = 3

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Answer: They will need to sell 1,500,000 to break even.

12,000,000 / 8 is 1,500,000

Answer:

The third graph

Step-by-step explanation:

We can immediately eliminate the 1st and last graphs because they are decreasing, not increasing. It wouldn't make sense that the more classrooms there are, the fewer students. Y = 22x would be increasing in the graph.

Let's plug some x values into the equation first, to see where our points are at.

Plug 1 into x

Y = 22(1)

Y= 22

(1,22)

Plug 2 into x

Y = 22(2)

Y = 44

(2,44)

Plug 3 into x

Y = 22(3)

Y = 66

(3,66)

Plug 4 into x

Y = 22(4)

Y = 88

(4,88)

The second graph matches the coordinates, so it works, but it isn't a complete function graph. A function graph needs a line drawn through the points. The second graph isn't your answer.

Let's look at the third graph. The coordinates also match up with the graph and it has a line drawn through the points. It's an accurate function graph representing this scenario. Therefore, the third graph is your answer.

Have a lovely day! :)

Answer: the 2nd graph is what i got right on the test

Step-by-step explanation:

Applying the distributive property, the solution of x for item c is given as follows:

x = (3a - 8 - b)/(a - b).

The distributive property is when the outside term multiplies each of the inside terms of an expression.

For example, in this problem:

Hence the solution for x of the expression is found as follows:

a(x - 3) + 8 = b(x - 1).

ax - 3a + 8 = bx - b

ax - bx = 3a - 8 - b

x(a - b) = 3a - 8 - b

x = (3a - 8 - b)/(a - b).

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For the linear function y = 0.5x. three ordered pairs are given as follows:

Using points (-2,-1) and (2,1), the graph of the function is given at the end of the problem.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the function is:

y = 0.5x.

Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.

The graph of the function is given at the end of the answer.

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To solve for x, the given equation will be transformed as x = c - b/4

What is the equation?

Given that,

x-b/4 = c

To solve for x, the given equation will be transformed as-

x = c - b/4

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Answer:

It is 41, 43, 47! :D

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

because -2+-1 is -3. then -3+0 is just -3. lastly -3+1 = -2 and -2 + 2 = 0

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

are you tempted to calculate the internal angles ?

that is, I guess, the trap set by your teacher here, and it would be the wrong approach.

nevertheless, quickly just as a reminder :

the sum of all internal angles in a polygon is

(n - 2)×180°

n being the number of sides.

in our case that is

(5 - 2)×180 = 3×180 = 540°

so, each internal angle is 540/5 = 108°.

but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.

we are running each vertex along a circle arc. the center of that circle being P.

after every 1/5 of the circle arc there is a vertex of the pentagon.

and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.

so, instead of a full circle rotation we need only 1/5 of that :

360 / 5 = 72°

and with every additional 1/5 of the circle arc (or 72°) we get it again.

that means at

72°

144°

216°

288°

360°

the pentagon carries onto itself.

therefore, A, D and E are correct.

The figure KLMN is being rotated by 90°, which is a rigid transformation, the true statements are therefore;

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

The given parameters are;

In KLMN, KN||LM

The transformation applied to figure KLMN = A 90° clockwise rotation about point P.

The image of KLMN following the rotation transformation is Figure RSTU.

Please find attached a drawing of the possible diagram in the question obtained from a similar question online.

The options from the question are;

(A) [tex] \overline{ST}[/tex] is parallel to [tex] \overline{RU}[/tex]

(B) [tex] \angle R[/tex] is the same measure as [tex] \angle N[/tex]

(C) [tex] \overline{RS} [/tex] is the same length as \overline{MN}

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

A rotation transformation is a rigid transformation, therefore;

The distances between any two points on the pre–image is the same as the distance between corresponding points on the image, which gives;

Figure KLMN [tex] is congruent to [/tex] Figure RSTU

Figure KLMN [tex] \cong [/tex] Figure RSTU

According to the postulate, Corresponding Angles of Congruent Figures are Congruent, we have;

[tex] \angle T \cong \angle M[/tex]

Which gives;

[tex] \angle T[/tex] = [tex] \angle M[/tex]

[tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

The correct options are therefore;

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

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The maximum and minimum value of η at q = 10 and q = 85 respectively.

The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.

η is the elasticity of demand.

Then, the elasticity of demand is given as:

η = ( dq/ dp) × ( p / q )

Now, we have p = 190/ (q + 10)

Therefore,

p ( q + 10 ) = 190

pq + 10p = 190

q = ( 190 - 10p ) / p

Now,

dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )

dq / dp =  ( -190/ p² )

Substituting these values in the elasticity demand,

η = ( dq/ dp) × ( p / q )

η = ( -190/ p² ) × ( p / q )

η = ( -190/ pq )

η = ( -190/ [190 / (q + 10 ) ]q )

η = [ - ( q + 10 ) / q ]

| η | = | - ( q + 10 ) / q |

η =  ( q + 10 ) / q = 1 + 10/q

The critical point is when | η' | = 0.

η' = ( d / dq ) ( 1 + 10/q )

η' = - 10/ q²

- 10/ q² = 0

Hence, - 10/ q² is not defined.

Therefore, the function is not defined at q = 0.

Therefore, q = 0 is not a solution.

We have 10 ≤ q ≤ 85

The value of functions at the endpoint,

At q = 10,

η = ( 1 + 10/q )

η = ( 1 + 10/10 )

η = 1 + 1 = 2

At q = 85,

η = ( 1 + 10/q )

η = ( 1 + 10/85 )

η = 1.11764

Therefore, the absolute value of the elasticity of demand is maximum at q = 10.

The absolute value of the elasticity of demand is minimum at q = 85.

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Answer:

You can flip the second fraction and multiply the fractions so 3/5 * 15/3 = 3

Step-by-step explanation: