If the perimeter of the window is 28 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.

Check the picture below.

if the segment AD is an angle bisector, that means it makes two twin angles, and let's also keep in mind that the side AG is shared by both triangles, so is not shorter or longer for either, is the same for both, which means Andrea rules!!!

The two equations for this system are C = 0.60f + 15 and C = 0.80f + 13.

The number of fish for which the cost is the same is 10 fishes.

The cost of this fish is equal to $21.

In order to write a system of linear equations to model and describe this situation, we would assign variables to the number of fish and the cost of fish respectively, and then translate the word problem into algebraic equation as follows:

Note: 1 dollar is equal to 100 cents.

Since the starter aquarium kit costs $15 plus 60 cents per fish at wet pets, we have:

C = 0.60f + 15     ........equation 1.

Since the starter aquarium kit costs $13 plus 80 cents per fish at gills and frills, we have:

C = 0.80f + 13          ........equation 2.

Next, we would solve the system of equations as follows:

0.80f + 13 = 0.60f + 15

0.80f -0.60f = 15 - 13

0.20f = 2

Number of fish, f = 2/0.20

Number of fish, f = 10 fishes.

From equation 1, we have:

Cost of fish, C = 0.60f + 15

Cost of fish, C = 0.60(10) + 15

Cost of fish, C = 6 + 15

Cost of fish, C = 21 dollars.

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The area of an L-shaped room is calculated by cutting off the Leg of the L and finding the area of the rectangles separately.

Area of the floor space occupied by an objected which is measured in unit squares.

A rectangle is an object which is bounded by four sides, four vertices

The area (A) of a rectangle is;

A=Length x Width

The Area of the L-shaped room is calculated by

A = Area of the Vertical rectangle + Area of the Leg

A = LW + lw

where

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Answer:

No because their ratios are not the same

Step-by-step explanation:

The scalar from 5 to 10 is 2 but from 3 to 4, its 4/3.

Answer:

235.15 sq.cm

Step-by-step explanation:

Perimeter of a triangle is sum of all three sides.

    Ratio of sides = 5 : 6 : 7

Sides are 5x , 6x , 7x

  Perimeter = 72 cm

5x + 6x + 7x = 72

Combine like terms.

             18x  = 72

Divide both sides by 18,

                x = 72÷ 18

               x = 4

5x = 5*4 = 20 cm

6x = 6*4 = 24 cm

7x = 7*4 = 28 cm

Sides: 20cm , 24 cm , 28 cm

So, it is a scalene triangle.

   To find the area of scalene triangle use Heron's formula.

a = 20 cm  ; b = 24 cm and c = 28 cm

   [tex]\sf s = \dfrac{a + b+ c}{2} \ where \ s \ is \ the \ semi \ perimeter.[/tex]

      [tex]\sf =\dfrac{72}{2}\\\\\\ = 36 \ cm[/tex]

    s - a = 36 - 20 = 16 cm

   s -b   = 36 - 24 = 12 cm

   s - c  = 36 - 28 = 8 cm

          [tex]\sf \boxed{Area = \sqrt{s(s-a)(s-b)(s-c)}}[/tex]

                      [tex]\sf =\sqrt{36*16*12*8}\\\\ = 6*4*4\sqrt{6}\\\\= 96 *2.45\\\\=235.15 \ cm^2[/tex]

There is a modest rise in arrival rates as compared to the prior arrival because the value is bigger than 0.05. It is a minuscule rise.

Given that,

The Message is arrive at an electronic mall server at the average

rate is 4 messages for every 5 minutes. Then the average

number of message is said to be a and mean is 4 to 5 interval.

Therefore ,we can use poission's approximation  to binomial  distribution in this case,

λ=4/5 min

( a ) Then , The Number of messages arrived in 1 hour

4x 12 = 48 . , So 48 messages per hour.

Now , our New arrival rate of messages , λ =48

By using possion's distribution ,

θ = time/rate

= 60/48= 1.25

NOW

probability density function of X is given as

f (x ) = θ e^-θx

for X>0

Given , the probability of new message arrival during given frame

equal is 0.05

p (X > x ) = 0.05

Now , of θ ∫e^-θx dx  = 0. 05 .

then, e^-θx =0.05

Apply logarithm on both sides , then

In( e^-θx) = In 0.05

By solving,

1- 25

X = 2. 39658

(b) Now , probability of arrival of 50 messages in 60 minutes

p (X>2.39658 ) = 0.05

Now arrival gap is θ = 60/50 = 1.2

P(x> 2.39658 ) =e^-θx

=e^- 1- 2 * 2.39658 = 0.0564

NOW ,

p(x>2- 39658) = 0.0564.

It is greater than 0.05 , so it is called there is slight increase in arrival rates as compared to the previous arrival. It is very small increase .

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Poncho ha recorrido más trayecto de la carrera de bicicletas, con una fracción de 3/4 del recorrido.

Problema de comparación de fracciones:

Carmen lleva: 3/5 del trayecto

Memo: 4/7

Poncho: 3/4

Jocelyn: 1/2

Una forma de comparar las fracciones es usando un mismo denominador, esto es posible con el Mínimo Común Múltiplo (MCM):

MCM(2,4,5,7) = 2² · 5 · 7 = 140

Fracciones con mismo denominador:

3/5 = (3 · 7 · 4)/(5 · 7 · 4) = 84/140

4/7 = (4 · 5 · 4)/(7 · 5 · 4) = 80/140

3/4 = (3 · 5 · 7)/(4 · 5 · 7) = 105/140

1/2 = (1 · 2 · 5 · 7)/(2 · 2 · 5 · 7) = 70/140

Comparando:

70/140 < 80/140 < 84/140 < 105/140

  1/2     <     4/7  <     3/5    <     3/4

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The two numbers that we requires are; y=−3+3√5 or y=−3−3√5

We know that in this question, we are required to obtain the two numbers that multiply to -36 and add up to -6. Now we have to write the problem into a system of simultaneous equations.

Thus;

Let the numbers by x and y

x + y = -6 ---- (1)

xy = -36 ------ (2)

x = -36/y ------ (3)

If we substitute (3) into (1)

-36/y + y = -6

-36 + y^2/y = -6

Multiply through by y

-36 + y^2 = -6y

Forming a proper quadratic;

y^2 + 6y - 36 = 0

Solving the quadratic for y

y=−3+3√5 or y=−3−3√5

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The interest rate in tenth of percentage that would be required in order for Joseph to end up with $1.710 is 4.4%.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal

To calculate the interest rate that would be required, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for R

Hence, the interest rate is 4.4%.

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Answer:5.76

Step-by-step explanation:

-2 2/5=-2.4

(-2.4)^2=5.76

Let's call the price before the VAT "x".

Then x plus that 20% VAT totals 14400.

The VAT is calculated as 20% of the original price, so 20% of x or 0.20x.

This gives us x + 0.20x = 14400.

Simplifying, we get 1.2x = 14400.

Dividing by 1.2 on both sides, we get x = 14400/1.2 = 12000.

Answer:

£18000

Step-by-step explanation:

[tex]x[/tex] x 80/100=14400

80x=1440000

x=1440000/80

x=£18000

The measure of the line segment AB is  36cm .

In the question ,

it is given that ,

The triangle ABC is a isosceles triangle ,

that means side AB = side BC ,

and the length of base AC = 24 cm .

given the perimeter of the triangle is 96 cm .

So ,

AB + BC + AC = 96

AB + AB + AC = 96       .....because AB = BC

2AB + AC = 96

Substituting the value of AC = 24 cm

2AB + 24 = 96

Subtracting 24 from both the sides , we get

2AB = 96 - 24

2AB = 72

Dividing both sides by 2 ,

we get ,

AB = 72/2 = 36 .

Therefore , The measure of the line segment AB is  36cm .

The given question is incomplete , the complete question is

Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is Line segment A C and measures 24 centimeters.

What is the measure of Line segment AB ?

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In the equation y= 17x + 8 ,

the value of x = (1,25) ,(2,42) ,(3,59) ,(4,76).

Given that,

           y= 17x + 8

When x = 1

y = 17 × 1 + 8 = 25

when x=2,

y = 17 × 2 + 8 = 42

When X=3,

y = 17 × 3+ 8 = 59

when X=4

y = 17 × 4+ 8 ]= 76

Therefore, the required solution is :

x = (1,25) ,(2,42) ,(3,59) ,(4,76).

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The strategies that would eliminate a variable to help solve the system of equations are

B. Multiply the first equation by -2 and add it to the second equation

C. Multiply the first equation by 1/3 and add it to the second equation

D. Multiply the second equation by 3 and add it to the first equation

From the question we are to determine the strategies that would eliminate a variable to help solve the system of equations.

The given system of equations is

12x + 5y = 7

-4x + 10y = -7

To eliminate y,

Multiply the first equation by -2 and add it to the second equation

-2 × [12x + 5y = 7]

-24x - 10y = -14

Now add to the second equation

 -24x - 10y = -14

+ (-4x + 10y = -7

-----------------------------

-28x = -21

To eliminate x

Multiply the first equation by 1/3 and add it to the second equation

1/3 × [12x + 5y = 7

4x + 5/3y = 7/3

Now, add it to the second equation

   4x + 5/3y = 7/3

+ (-4x + 10y = -7

------------------------------

5/3y + 10y = 7/3 + (-7)

Also, to eliminate x

Multiply the second equation by 3 and add it to the first equation

3 × [-4x + 10y = -7

-12x + 30y = -21

Now, add to the first equation

  -12x + 30y = -21

+ (12x + 5y = 7

----------------------------

35y = -14

Hence, the required strategies are the ones explained above.

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Answer: 10

Step-by-step explanation:

Set the equal angles as x, as shown below.

Then, [tex]sin(x)=\frac{x+4}{8}[/tex] and [tex]sin(x)=\frac{2x+1}{12}[/tex]. Set them equal to each other and solve for x:

[tex]\frac{x+4}{8} =\frac{2x+1}{12} \\ \\12(x+4)=8(2x+1)\\12x+48=16x+8\\48-8=16x-12x\\4x=40\\x=10[/tex]

This is assuming those two triangles are right triangles. I'm actually not sure if they're right triangles.

Answer:

X = -3, y = -8

Please see the link to view the Graph:

Answer:

6*v=102

Step-by-step explanation:

The total cost of your trip to the movie theater is $43.50.

The total cost will be the sum of money spent on ticket and soda and popcorn.

Ticket cost for or cost price of Ticket for:

         5 years old brother = $4.25

          Grandparents = $6.00 × 2 = $ 12.00

           For self= $7.25

Total cost of tickets = $4.25 + $ 12.00 + $ 7.25

                                 = $ 23.50

Total Money spent = Cost of ticket + cost of soda and popcorn

                                = $ 23.50 + $20

                                = $ 43.50

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Answer:

It's D.

Step-by-step explanation:

I know I can't see that option, but it's D. If you use A for the first one, you get 4(-4) which is -16 and you add 3 to that, it's -12, so that's not 2 so it can't be A. If you use B for the first one, you get 2(-4) which is -8, and if you add 3, you get -5, not 2, so it can't be that either. If you use C, you get 0.5(-4) which is -2, and if you add 3 to that, you just get 1, so it can't be C either. I assume there is fourth option, so it's D.

y = -3x +2

The general equation for a linear line is y = mx + b

Where:

To find the slope of a line we can use the formula [tex]\frac{rise}{run}[/tex]

Rise over run can be found suing two different points on the line.

in this case: (-1,5) and (1,-1)

The rise is the difference in y values: [tex]y_2 -y_1[/tex]

rise = (-1) - 5

rise  = -6

run = [tex]x_2 - x_1[/tex]

run = 1 - (-1)

run = 2

rise/run = [tex]\frac{-6}{2}[/tex]

rise/ run = -3

We now have y = -3x + b

To find b we just look at the graph and locate a what point x = 0

The probability that a car buyer bought an alarm system or bucket seats is 0.50.

Probability of ,

Alarm system p(A) = 40/100 = 0.40

Bucket seat p(B) = 30/100 = 0.30

Alarm system and bucket seat p(A and B) = 20/100 = 0.20

Probability of alarm system or bucket seat is :

= p(A)+p(B)-p(A and B)

= 0.40+0.30-0.20

= 0.50

In mathematics, probability is the likelihood of an event occurring. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is to occur. A simple example is the tossing of a coin, where the probability of either head or tail is 1/2.

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Answer:

Match

1) 5 hours = H. 300 minutes

2) 72 hours = D. 3 days

3) 360 seconds = G. 6 minutes

4) 540 minutes = J. 9 hours

5) 4 days = A. 96 hours

6) 60 minutes = C. 1 hour

7) 720 seconds = 12 minutes

8) 6 days = E. 144 hours

9) 3 1/2 hours = F. 210 minutes

10) 3 minutes = I. 180 seconds

Equivalent times:

11) 7 hours = 420 minutes

12) 480 = 6 minutes

13) 120 hours = 5 days

14) 180 minutes = 3 hours

15) 11 minutes = 660 seconds

a) The graph of f(x) is as shown below.

b)

The domain of f(x) is: [-4, 4]

The range of function f(x) is [-2, 6]  

In this question we have been given a piecewise function [tex]f(x)=\left \{ {{\frac{-(x+2)}{2} ~~~-4\leq x\leq 2} \atop {4x-10}~~~~2 < x\leq 4} \right.[/tex]

We need to graph the given function.

The table of (x, f(x)) values is as shown below.

  x             f(x)

 -2             0

 -4              1

  0             -1

  2             -2

 2.5           0

  3.5          4

  4             6

The graph of f(x) is as shown below.

The domain of f(x) is: [-4, 4]

The range of function f(x) is [-2, 6]          

Therefore, for given piecewise function,

a) The graph of f(x) is as shown below.

b)

The domain of f(x) is: [-4, 4]

The range of function f(x) is [-2, 6]  

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The minimum number of swaps required to flip the list is 2.

Array : Generally, in the field of applied sciences, knowledge structures called arrays and typically regarded as just arrays, each containing at least one array-index award or key. Arrays are stored so that formulas can use each component's index tuple to determine the placement of that component within the array.

Given an array with values 5, 10, 15, 20,25

swap reverses the array:

25, 10, 15, 20, 5

25, 20, 15, 10, 5

So, for reversing the number of swaps required list is 2 ..

This may be the smallest variation possible.

Hence, the minimum exchange required to achieve list reversal is two.

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the relationship is a function because she "made up time".

A relation that states that there should only be one output for each input are called a function. alternatively, a function is a particular kind of relation—a set of ordered pairs—that adheres to a specific rule—each X-value should be associated with only one y-value.

if a relation is one-to-one or many-to-one it is a function.

Function            Not a Function

one-to-one        many-to-many

many-to-one     one-to-many

In the above-mentioned scenario, She basically made up for the time she had spent standing at the location by increasing her pace. Since she picked up the pace, you can assume that she completed the task in the same amount of time as if she had not stopped.

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The function that represents the relationship is y = 40x

The total area that he painted = 200 square feet

Time is between 8 am and 1 pm

Then the time taken = 5  hours

The relationship is given by the area a person can paint varies directly with the amount of time he works

Here we have to apply the unitary method

The area that he painted in one hour = 200 / 5

= 40 square feet

Consider the y is the total area that he painted and x is the number of hours

Then the function will be

y = 40x

Hence, the function that represents the relationship is y = 40x

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Convert the inequality to interval notation: a > 10:

(10, ∞)

As we know 1 kilometer = 39370.079 inches

and, 8.39 kilometer = 330,315 inches.

Kilometers: - It is a unit of length in the international system of units (SI) equal to one thousand meters. It is now the measurement unit used for expressing distances between geographical places on land in most of the world.

Inches: - It is a unit of length in the British imperial and united states customary system of measurement. It is equal 1/36 yard or 1/12 of a foot.

To convert a kilometer measurement to an inch measurement, multiply the length by the conversion ratio.

Since 01 kilometer = 39,370.07874 inches,

We can use this simple formula to convert:

          inches = kilometers × 39,370.079

Now, according to the question:

inches = 8.39 × 39370.079

inches = 33.315

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