.................................

Answer:

A = 16 units²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 6 [tex]\frac{2}{5}[/tex] and h = 2 [tex]\frac{1}{2}[/tex] , then

A = 6 [tex]\frac{2}{5}[/tex] × 2 [tex]\frac{1}{2}[/tex] ← convert mixed numbers to improper fractions

  = [tex]\frac{32}{5}[/tex] × [tex]\frac{5}{2}[/tex] (  cancel 5 on numerator and denominator )

  = 32 × [tex]\frac{1}{2}[/tex]

 = 16 units²

The value of (gof)(x) is (5x²-10)(x).

Here f(x) is given to us,

f(x) = x²-2

The value of g(x),

g(x) = 5x-8

Here we have to find a composite function, a composite function is a function in which two different functions are combined to form a third different function, in simple words we can understand it as a function inside a function

To find (gof)(x) means,    

We have to find, g(f(x))(x),

we have to put the value of f(x) in g(x) at the place of x.

Let us say that our final function is h(x),

h(x) = (gof)(x)

h(x) = g(f(x))(x)

h(x) = (5f(x)-8)(x)

h(x) = (5(x²-2))(x)

h(x) = (5x²-10)(x)

So, the value of (gof)(x) is (5x²-10)(x).

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Answer:

Not enough information.

Step-by-step explanation:

I don't believe this equation can be solved without more information, what process would you normally use to solve this equation? Do you know how many numbers X is worth? if not I would have to guess the answer would be 4x but i'm not sure that's correct.

Answer:

35.

Step-by-step explanation:

The term "absolute value" asks for the number without any negativity, e.g. distance. Even if you go backwards from your original spot, you still move.

According to the linear equations, At 4 hours both companies charge the same rate.So Company A is cheaper if the time is less than 4 hours. After 4 hours, company B is cheaper.

According to the statement

We have to find that the comparison of the linear equation.

So, For this purpose, we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the given information:

Company A charges $45 per hour and a $300 equipment fee. Company B charges

$70 per hour and a $200 equipment fee.

Then

Let A(t) = 45t + 300

Let B(t) = 70t + 200

We can determine time t when both companies charge the same rate by equating the two equations.

45t + 300 = 70t + 200

Subtract 25t from both sides and subtract 150 from both sides

25t = 100

Divide both sides by 25

t = 4

So, According to the linear equations, At 4 hours both companies charge the same rate.So Company A is cheaper if the time is less than 4 hours.After 4 hours, company B is cheaper.

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Answer:

[tex]f(8) = - 42[/tex]

Step-by-step explanation:

Hi there!

You have to substitute x = 8 into:

[tex]f(x) = 6(1 - x)[/tex]

It then becomes:

[tex]f(8) = 6(1 - 8)[/tex]

Calculate the above

[tex]f(8) = - 42[/tex]

Option B - Teachlet tutorials.

The approach uses Teachlet Tutorials, a combination of traditional seminar–type teaching with interactive exploration of the content by the audience, and development of self-contained tutorials on the topic. In addition to a presentation, an interactive software tool is developed by the students to assist the audience in learning and exploring the topic's details. This process is guided through set tasks. The resulting course material is developed for two different contexts:

(a) for classroom presentation and

(b) as an interactive, self-contained, self-learning tutorial.

Teachlet tutorial is a form of presentation module that comprises lessons and instructions.  It provides learners to get academic as well skill-enhancing lessons that could be easily comprehended.

It is a type of tech learning lesson plan where online study modules and materials are available in the presentation format to make people learn and evaluate themselves thereon. Therefore, it is an online course to get immediate results out of self- learning tutorials and online practice tests.

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The distance between the given pair of points (7,4), (3,5) is √17.

Hence, option C)√17 is the correct answer.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point 1( 7,4 )

Point 2( 3,5 )

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 3 - 7 )² + ( 5 - 4 )² )

D = √( ( -4 )² + ( 1 )² )

D = √( 16 + 1 )

D = √( 17 )

D = √17

The distance between the given pair of points (7,4), (3,5) is √17.

Hence, option C)√17 is the correct answer.

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If a classroom has 8 light bulbs and the probability that each individual light bulb works is 0.8 and each light bulb works independently of the other light bulbs then the probability that all 8 of the light bulbs work is equal to 0.1678.

Probability is a branch of mathematics and can be defined as the one which deals with the explanation of the possibility of an event to occur or take place. Probability has a range between 0 to 1. In probability, 0 indicates the impossibility of an event to occur and 1 indicates the certainty of that event to occur or take place.

As the light bulbs are not dependent on each other and work independently, the probability that all eight of the light bulbs will work can be calculated by multiplying the probability of each of the eight light bulbs.

As the probability of each of the eight light bulbs to work = 0.8

probability all the eight light bulbs work = 0.8^8

probability all the eight light bulbs work = 0.1678

Hence, 0.1678 is the probability that all the light bulbs work.

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The value of the maximum profit of the function is 680

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation of the profit function is given as

P(x) = 230 + 30x - 0.5x^2

Differentiate the function

So, we have

P'(x) = 0 + 30 - x

Evaluate the like terms in the function

So, we have

P'(x) = 30 - x

Set the function to 0

So, we have

30 - x = 0

Evaluate

x = 30

Substitute x = 30 in the equation P(x) = 230 + 30x - 0.5x^2

So, we have

P(30) = 230 + 30 x 30 - 0.5 x 30^2

Evaluate

P(30) = 680

Rewrite as

Pmax = 680

Hence, the value of the maximum profit of the function is 680

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Answer:

[tex] \sf \: 6 \frac{ 7}{8}[/tex]

Step-by-step explanation:

Rewriting our equation with parts separated

=8+5/2−3−5/8

Solving the whole number parts

8−3=5

Solving the fraction parts

5/2−5/8=?

Find the LCD of 5/2 and 5/8 and rewrite to solve with the equivalent fractions.

LCD = 8

20/8−5/8=15/8

Simplifying the fraction part, 15/8,

15/8=1 7/8

Combining the whole and fraction parts

5+1+7/8= 6 7/8

Answer:

BC= AB+AC = 35+93

BC= 128

or

BC= AC - AB = 93-35

BC= 58

Answer: 11

Step-by-step explanation:

Just go through the order of operations. (PEMDAS)

Evaluate the exponent first,

X=3

3^1=3

then multiply 2 and 3, which gives you 6

then finally add 5

this gives you the answer of 11

Answer:

Step-by-step explanation:

new position is (-5, 4)

The length of BD is 5√2

AB = 5cm

It is given that AB = BF = FD = 5cm

∠A = 60° and ∠BFA = 60°( as the side are equal then the angle opposite to it will be equal )

Hence we get ΔAFB as an equilateral angle

∠BFA + ∠BFD = 180°

60° + ∠BFD = 180°

∠BFD = 120°

It is given that BF = FD, so in ΔBFD we have

∠B + ∠D +∠F = 180

∠B = ∠D

2∠B + 120° = 180

2∠B = 60°

∠B = 30°

cos Ф = base / hypotenuse

Now from ΔBFC, we get

cos 30° = BC / BF

√3/2 = BC / 5

BC = 5√3/2

Now from ΔFDB, we get

cos 30° = CD/ FD

√3/2 = CD/ 5

CD = 5√3/2

BD = BC + CD

     = 5√3/2 + 5√3/2

     = 5√3

Therefore the length of BD is 5√3.

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The coordinates of B is (-6,1) , where midpoint of AB is M(1, 4) and coordinates of A (8, 7) .

The Midpoint of the two points A(a,b) and B(c,d) is calculated using the formula M=((a+c)/2 , (b+d)/2) .

In the question

it is given that the mid point of AB is M(1,4)

the coordinate of A are (8,7)

let the coordinate of B be (x,y) .

By Midpoint Formula

we get ,

[tex]1=\frac{8+x}{2} , 4=\frac{7+y}{2}[/tex]

Simplifying further we get ,

2 = 8+x       ,      8 = 7 + y

x = 2 - 8      ,      y = 8 - 7

x = -6          ,      y = 1

Therefore , the coordinates of B is (-6,1) , where midpoint of AB is M(1, 4) and coordinates of A (8, 7) .

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The highest altitude of an altocumulus cloud is 3⁹ ft in power.

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward way.

The amount of times a number has been multiplied by itself is shown by its exponent.

Given the lowest altitude of an alto cumulus cloud is about 3⁸ feet. The highest altitude of an altocumulus cloud is about 3 times the lowest altitude.

To find the highest altitude of an altocumulus cloud, we must solve as follows:

Let the lowest altitude be x. Then,

3⁸ = x

The highest altitude will be 3x which is 3(3⁸).

⇒3(3⁸) = 3x

⇒3(6561) = 3x

Simplifying further,

⇒3x6561= 19683

⇒3 (3 x 3 x 3 x 3 x 3 x 3 x 3 x 3) = 19683

⇒3⁹= 19683

Therefore, the highest altitude of an altocumulus cloud is 3⁹ ft in power.

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Let J be the intersection of the diagonals

[tex]pj = \frac{po}{2} = \frac{6}{2} = 3[/tex]

[tex]rj = \frac{rq}{2} = \frac{8}{2} = 4[/tex]

Applying the Pythagorean theorem:

[tex](pr) {}^{2} = (pj) {}^{2} +( {rj})^{2} \\ pr = \sqrt{(3) {}^{2} + (4) {}^{2} } = \sqrt{9 + 16} \\ pr = \sqrt{25} = 5[/tex]

Answer: The difference of temperature (T) = 91° celsius.

Step-by-step explanation:

Phalodi, in Rajasthan, recorded one of India's highest temperatures is = 51 celsius.

Drass, in Kashmir, recorded one of India's lowest temperatures is = -40° celsius.

Find out the difference of two temperatures.

Let us assume,

                Rajasthan temperature = T1

                 Kashmir temperature = T2

Then,

we can write,

India's highest temperatures Rajasthan = (T1) = 51° celsius.

India's lowest temperatures Kashmir = (T2) = -40° celsius.

Then, the difference of temperature is equal to the difference between India's highest temperatures Rajasthan to India's lowest temperatures Kashmir.

So,

we can write,

difference of temperature (T) = Rajasthan temperature - Kashmir temperature

                                       T = T1 - T2  

                                       T = 51 - (-40)

                                       T = 51+40

                                      T =  91° celsius.

Therefore, the difference of temperature (T) = 91° celsius.

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It should be noted that since Latanya said 5 3/8 ÷ 1 1/8 could represent the average number of pitchers the restaurant serves per day if it takes 1 1/8 days to serve all of the lemonade, Latanya is correct.

It should be noted that Latanya said 5 3/8 ÷ 1 1/8 could represent the average number of pitchers the restaurant serves per day if it takes 1 1/8 days to serve all of the lemonade. This is right.

On the other hand, Jada said 5 3/8 ÷ 1 1/8 could represent the number of total servings if there are 1 1/8 servings per pitcher. This is wrong. In this case, it should be multiplication.

Therefore, it can be seen that Latanya is correct.

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A restaurant has 5 3/8 pitchers of lemonade. Jada said 5 3/8 ÷ 1 1/8 could represent the number of total servings if there are 1 1/8 servings per pitcher. Latanya said 5 3/8 ÷ 1 1/8 could represent the average number of pitchers the restaurant serves per day if it takes 1 1/8 days to serve all of the lemonade. Who is correct?

The area of the triangle is expressed as 6x² + 23x + 7/ 2

The formula for area of a triangle is expressed as;

Area = 1/ 2 × b × h

Where;

Substitute into the formula

Area = 1/ 2 × (3x+ 1) (2x + 7)

expand the bracket

Area = 1/ 2 ×(6x² + 21x + 2x + 7 )

collect like terms

Area = 1/ 2 (6x² + 23x + 7)

Area = 6x² + 23x + 7/ 2

Thus, the area of the triangle is expressed as 6x² + 23x + 7/ 2

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Answer:

(-11, 11]

Step-by-step explanation:

The domain of a graph is the set of x-values.

An open circle means the endpoint is not included, whereas a closed circle means the endpoint is included.

The value of a that we get after solving the expression, we get that a = - 56.

We are given the expression that:

a - 4 - 5 c = 0

We are also given that:

c = - 12

Now we will substitute the value of c in the equation.

So, we get that:

a - 4 - 5 ( -12 ) = 0

Now, we multiply the brackets, we get that:

a - 4 + 60 = 0

Now combining the like terms, we get that:

a + 56 = 0

Subtract 56 from both sides, we get that:

a + 56 - 56 = 0 - 56

a = - 56

Therefore, the value of a that we get after solving the expression, we get that a = - 56.

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Answer:

1b= 1080 degrees

2a= pentagon is 540 degrees inside. Add all values and you get 377

540-377= 163

The single percentage change is 6.85%.

Here it is given that there is a 19% decrease and a 15% increase. And we have to find a single percentage change.

The formula of single percentage is

a + b + a .b/ 100

So let's take a = -19 as there is a decrease in the percentage and b = 15 as there is an increase.

So we get a single percentage = -19 + 15 - (19×15)/ 100

                                                    = - 4 -2.85

                                                    = -6.85

Therefore the single percentage change is 6.85%.

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Answer:

A.

Step-by-step explanation:

There is a point we can work off of within the graph; the origin. The origin has a specific point which will be substituted for our example number, x. And substituting that would make this point become the equation, [tex]\frac{-\pi }{2}[/tex] which is our assumed midpoint and that would also equal [tex]-1 + -1 + 1 + 0(?)[/tex] and that would substitute in for 0 due to the fact of our midpoint + 200 would equal 1. x - 1 is -1. And this becomes true because of -π causing an even function within the points to occur in fact of negatives which are going to be resulted in by pi being -1 - 1 - 2 - 3. This other sign that -π - π(0) is zero at multiple different [soft] points of pi alone, and 0 - 2 would represent only negative 2. Getting to the point(I know this may have sounded very confusing, apologies.) there is one option that gives you the zero at point X assuming point X is also part of the origin, and that would make this point become option A.

Hope this helps. If you have any concerns, please let me know, because I know this was a lot to explain in words.

The solution is, A.  y = sin(x - π/2) +1, is the equation for the graph.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

from the given graph, we get,

There is a point we can work off of within the graph; the origin.

The origin has a specific point which will be substituted for our example number, x.

And substituting that would make this point become the equation,  which is our assumed midpoint and that would also equal  and that would substitute in for 0 due to the fact of our midpoint + 200 would equal 1. x - 1 is -1.

And this becomes true because of -π causing an even function within the points to occur in fact of negatives which are going to be resulted in by pi being -1 - 1 - 2 - 3.

This other sign that -π - π(0) is zero at multiple different [soft] points of pi alone, and 0 - 2 would represent only negative 2.

Getting to the point(I know this may have sounded very confusing, apologies.) there is one option that gives you the zero at point X assuming point X is also part of the origin, and that would make this point become option A.

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When a scale factor of 1 to 50 centimeters is applied, the dimensions of the rectangle becomes 250cm and 150cm

A scale factor provides information of the rate at which an image would be enlarged or decreased. Looking at the scale factor provided in the question, the rectangle is being decreased because centimeters is smaller compared to meters.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension using the scale factor.

To reduce the dimensions of the rectangle, multiply the scale factor by the given dimensions.

Length = 5 x 50 = 250cm

Width = 3 x 50 = 150cm

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{3}{4}\times\dfrac{2}{5} - \dfrac{1}{5}\times\dfrac{1}{4}}[/tex]

[tex]\mathsf{= \dfrac{3\times2}{4\times5} - \dfrac{1\times1}{5\times4}}[/tex]

[tex]\mathsf{= \dfrac{6}{20} - \dfrac{1}{20}}[/tex]

[tex]\mathsf{= \dfrac{6 - 1}{20 - 0}}[/tex]

[tex]\mathsf{= \dfrac{5}{20}}[/tex]

[tex]\mathsf{= \dfrac{5\div5}{20\div5}}[/tex]

[tex]\mathsf{= \dfrac{1}{4}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The answer to this question is:

A certain type of sailboat travels at 7 nautical miles per hour.

A summer camp provides 3 meals for each camper.

The amount of units of the first quantity that correspond to one unit of the second quantity is shown as the unit rate.

Nadia pays $30 for 2 baseball tickets.

i.e. the price for two baseball tickets is $30,

By the above definition,

It is not a unit rate,

A certain type of sailboat travels at 7 nautical miles per hour.

i.e., 7 nautical miles are covered in 1 hour,

By the above definition,

It is a unit rate,

The cost of 3 hot chocolates is $2.

i.e., there are 3 chocolates for every 2 dollars.

By the above definition,

It is not a unit rate,

A summer camp provides 3 meals for each camper.

i.e., 3 meals are provided for every camper,

By the above definition,

It is a unit rate.

Therefore,

are the options that describe unit rates.

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