Find the length of the missing segment.

By graphing, the solution of the system of equations is: (6, -2).

To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.

Given the following equations:

x + 2y = 2

y = -x + 4

x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).

The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).

The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.

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If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,

844.13 = 750 (1 + r)⁴

(1 + r)⁴ = 1.1255

1 + r = 1.02999

r = 0.0299

r = 2.99%

r ≈ 3%

If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

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The equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].

So, the equation to get fabric used in each bandana:

Then, the fabric in each bandana will be:

Solve as follows:

So, 1/12 yards of fabric is used in each bandana.

Therefore, the equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].

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Complete question:

The drama teacher is making bandanas for costumes. She is cutting 1/2 yard of fabric into 6 bandanas of the same size. Write and solve an equation to find how much fabric there will be for each bandana.

The amount you pay for the items is C. $41.42.

The amount that the customer pays for the two items is determined by first discounting the second item by 60%.

The result after the discount is added to the cost of the first item before the sales tax is added to get the final cost of the items.

Discount on second item = 60%

The price of the first item purchased = $30

The price of the second item purchased = $20

Discounted price on the second = $8 ($30 x (1 - 60%)

Total cost before sales tax = $38 ($30 + $8)

Sales tax = 9%

Total cost after sales tax = $41.42 ($38 x 1.09)

Thus, after discounting the second item by 60% and adding the sales tax of 9%, the customer will pay $41.42 for the items.

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Answer:

c. 41.42 my teacher told me the answer

Step-by-step explanation:

Answer:

5.68 ft

Step-by-step explanation:

12 inches = 1 feet

[tex]68 \: inches \: *\: \frac{1 feet}{12 \: inches} =\frac{68}{12} \: feet= 5.6777...\\\\68 \: inches \approx 5.68 \: feet[/tex]

The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells

Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.

The dimensions of the rectangle = 60 units by 40 units

The dimensions of each grid = 1 unit by 1 unit

The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)

The slope of the diagonal is therefore;

m = 40/(60) = 2/3

The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x

y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;

Length the diagonal, l = √(60² + 40²) ≈ 72.1

Length of the diagonal of a unit = √(1 + 1) =√2

Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units

The number of cells  cut into two ≈ 51 cells

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Answer:

Step-by-step explanation:

We know that perpendicular lines have opposite-reciprocal slopes.

Given line:

Its slope is 2 and the perpendicular line has a slope of - 1/2.

Let's find the line with the slope of - 1/2:

Answer:

c

Step-by-step explanation:

An area 825 by 550 ft gives max area for $6600.

acc to our question-

hence, 3300 + 3300 = $6600

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The probability that he is a male civilian employee is 0.13362.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that 66% of full-time law enforcement employees are sworn officers, 34% of them are civilian employees (100 - 66).

Given that 60.7% of civilian employees are women. Therefore, the percentage of men is (100 - 60.7)% or 39.3%.

Therefore, the likelihood that he works as a male civilian is 39.3% of 34%, which equals 0.393 * 0.34, = 0.13362.

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Answer: 16

Step-by-step explanation:

The correct inequality symbol that makes the statement true is:

1000 < (6²)³.

The inequality symbols, and their meaning, are presented as follows:

In the context of this problem, the numbers being compared are presented as follows:

1000 and (6²)³.

The power of power property of a number with multiple exponents means that the base is kept while the exponents are multiplied.

The number in which this property is applied in this problem is (6²)³, in which:

Hence the equivalent number is given as follows:

(6²)³ = 6^6 = 6 x 6 x 6 x 6 x 6 x 6 = 46,656

Which is a greater number than 1,000, meaning that 1,000 is less than the number, and the inequality is:

1000 < (6²)³.

The problem is given by the image at the end of the answer.

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6900 hours, make a list of multiples until lcm is found

There are 18 students who like snickers but not twix or reese's peanut butter cups.

Given, that 500 high school students was taken to determine their favorite chocolate candy.

118 like snickers, 185 like twix, 179 like reese's peanut butter cups,

60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,

and 17 like all three kinds of chocolate candy.

Let A = Set of students like snickers

B = Set of students like twix

C = Set of students like reese's peanut butter cups

Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C

A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17

A - A∩B - A∩C + A∩B∩C = 135 - 117

A - A∩B - A∩C + A∩B∩C = 18

Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.

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The equation of line with undefined slope and passes through the point

(1/2, 5) will be;

⇒ x = 1/2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point = (1/2 , 5)

And, The slope = undefined

Now,

Since, We know that;

The equation of line with undefined slope and passes through the point will be;

⇒ x = a

Where, 'a' is the x - intercept.

Here, The point = (1/2 , 5)

The slope = undefined

And, The x - intercept = 1/2

So, The equation of line with undefined slope and passes through the point (1/2, 5) will be;

⇒ x = 1/2

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Answer:

y=100t+1200, where t is years since 2013 and

Step-by-step explanation:

We only have two points from which to form an equation.  Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0).  Let's make the x axis the year and y the student population.

Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013.  "t is the number of years after 2013."  (0,1200) becomes is the data point for 2013.  The school's population will be the y-axis.

(0,1200)   [primary school had 1200 students enrolled in 2013], and

(3,1500)   [1500 students in 2016]

---

First calculate m, the slope.  Slope is the Rise/Run between the two points (the change in y over the change in x)

Going from (2013,1200) to (2016,1500) we find that:

  Rise  (in y) = (1500 - 1200) = 300 students

  Run  (on x) = (2016 - 2013) =     3 years

The Rise/Run, or slope, m, is 300/3 or 100:  m = 100

Lets put that into our equation format:

y = 100x + b

X will be the time, in years.  The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:

y = 100t +b, where t is years after 2013.

(The 100 tells us that the student population increases by 100 per year)

We now need b, the y-intercept.  One can either graph this and look for the value of y when x=0, of simply input either of the data points.  This looks easy enough to input a point and solve for b:

Remember that t is the (year - 2013)

y = 100t +b   Solve for (2013,1200)

 t = 2013 - 2013 = 0

1200 = 100*(0) + b

b = 1200

Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).

The equation becomes y = 100t + 1200

See the attached graph.

For some n or x value, neither equation can equal 107. f(x) = 2x + 7 or

t(n) = 2n + 7.

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Exactly one type of meat required = 5 choices

acc  to our question-

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Using exponents, the resultant expression after simplification is 81x⁸y⁴.

So, the expression is:

Now, simplify the power as follows:

Therefore, using exponents, the resultant expression after simplification is 81x⁸y⁴.

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It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.

We are asked the probability that an applicant scores below 552.

Now, using the formula of probability, we get

P(X < 552) = 0.8329

when the mean is given i.e. 460 and standard deviation is given i.e. 80.

Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

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It takes 35 years for the population of West Fremont to double. We have the following condition;

West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.

Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.

According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.

Doubling time = 70 / Growth rate                

= 70 / 2                        

= 35 years

So, it takes 35 years for the population of West Fremont to double.

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The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation.

a)

As per the given first system of equation,

2x - 4y = 10

x + 5y = 40 → 2x + 10y = 80

Subtract both

10y + 4y = 80 - 10

14y = 70

y = 5

And, x = 40 - 5(5) = 15

b)

As per the given first system of equation,

3x - 5y = 4 and

-2x + 6y = 18 → -x + 3y = 9 → -3x + 9y = 27

Add both

-5y + 9y = 4 + 27

4y = 31

y = 7.75

x = (4 + 5(7.75))/3 = 14.25

Hence "The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75".

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Answer:

3 feet

1ft:2ft

Step-by-step explanation:

3ft/12 inches

12 inches= 1 foot

We can simplify the denominator by turning 12 inches into 1 foot

3/1

And then we divide to make 3 feet

The width of the rectangle is 12 inches and the length is 2 feet so the ratio is

12 in.:2 ft

12 inches can be simplified to 1 foot

1 ft: 2 ft

And it is simplified as much as possible

Hopes this helps please mark brainliest

Answer:

(y + 6)(y + 13) = y² + 19y + 78

Step-by-step explanation:

[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]

Answer:

1 piece = 1 slice then the answer is 4/3 = $1.33 (still … 3 slices will be $3.99 rounded to 4). A pizza costs £5.50 and fries cost £1.00, John orders 3 pizzas and 5 fries but the …

The tank with the smallest surface area has dimensions of 6ft.

s = 12ft and h = 6ft.

A(s) = s² + 4 × (V ÷ s)

The rectangular tank has a capacity of 864 feet.

Let the square base's long sides be.

Let h represent the tank's height.

Let A represent the tank's whole area.

A = (Base Area) + (4 × Lateral Area)

Lateral Area = s × h

Lateral Area = s × (V ÷ s²)

Lateral Area = (V ÷ s)

Base Area = s²

Compared to the objective function,

A(s) = s² + 4 × (V ÷ s)

A(s) = s² + 4 × (864 ÷ s)

The area function's derivative,

A'(s) = 2s - (3456 ÷ s²)

The smallest surface area is now.

A'(s) = 0

2s - (3456 ÷ s²) = 0

2 × [tex]s^{3}[/tex] = 3456

[tex]s^{3}[/tex] = 3456

s = [tex]\sqrt[3]{3456}[/tex]

s = 12ft

The volume is,

V = s² × h

864 = 12² × h

h = 6ft

As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.

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The question is -

A rectangular tank with a square​ base, an open​ top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

No. of coins in jar of nickels is 207 and of dimes is 103.

Let the no. of coins of dimes = x

No. of coins of nickels = 2x

Total = 310

x + 2x = 310

     3x = 310

       x = 310/3

          = 103.33

          ≈ 103

No. of coins of dimes = 103

No. of coins of nickels = 310 - 103

                                     = 207

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Answer:

Step-by-step explanation:

Peter=x

Phillippa= 3x then x

Palvin= 10 then Phillippa

Step 2: Answer: Phillipa 3x+x+10

The function f(x) = 2x + 1 has its value of x to be 3 when f(x) = 7

From the possible question, the definition of the function is given as

f(x) = 2x + 1

Also, from the question, we have:

f(x) = 7

Substitute 7 for x in the equation f(x) = 2x + 1

So, we have the following representation

2x + 1 = 7

Subtract 1 from both sides of the equation

This gives

2x = 6

Divide both sides by 2

x = 3

So, we can conclude that the value of x is 3

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Possible question

Given the function below, find the value of x if f(x)=7

f(x) = 2x + 1

The product in simplest form is [tex]-250\sqrt[3]{50}[/tex] .

In the question,

It is given that,

[tex]5*\sqrt[3]{5} * (-10\sqrt[3]{50})[/tex]

By radical laws, [tex]\sqrt{a} * \sqrt{b} = \sqrt{ab}[/tex]

So,

The given question becomes:

[tex]-50*\sqrt[3]{50*5} = -50*\sqrt[3]{250} = -250\sqrt[3]{5} }[/tex]

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