Use a definition, postulate, or theorem to find the value of x in this figure described.
Y is the midpoint of XZ. If XZ = 6x-2 and YZ = 2x + 2, find x.
Select each definition, postulate, or theorem you will use.
A Segment Addition Postulate
B definition of segment bisector
C Linear Pair Theorem
D definition of a midpoint
The solution is x =__?

The linear programming model that can be used to determine the number of units of each model in order to maximize the profit is x2 <= 280 (Lady-Sport Frames), 2 x1 + 2.5 x2 <= 1000 (Assembly & Test).

When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

A linear programming problem can be solved by determining the best value.

a)Let x1 be number of EZ-Riders produced.

Let x2 be number of Lady-Sports produced.

The Objective is to maximize the profit contribution:

Max 2,400 x1 + 1,800 x 2

The Constraints are: Engine Manufacturing Time <= 2100 hours

Lady-Sport Frames <= 280 frames

Assembly & Test <= 1000 hours

6 x1 + 3 x2 <= 2100 (Engine Manufacturing)

x2 <= 280 (Lady-Sport Frames)

2 x1 + 2.5 x2 <= 1000 (Assembly & Test)

We also need bounds x1 and x2 => 0.

So the full model is:

Max 2,400 x1 + 1,800 x2

Subject to 6 x1 + 3 x2 <= 2100 (Engine Manufacturing)

x2 <= 280 (Lady-Sport Frames)

2 x1 + 2.5 x2 <= 1000 (Assembly & Test)

x1 => 0, x2 => 0

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Please find attached the graph of the parabola, y = x² - 4·x + 4, created with MS Excel, showing the points;

A parabola is the locus of a point that moves such that its distance from a point (known as the focus) and a line (known as the directrix), are the same.

1. The quadratic function is; y = x² - 4·x + 4

The x-coordinates of the vertex of the quadratic function, f(x) = a·x² + b·x + c, can be found using the formula;

x = -b/(2·a)

The x-coordinates of the graph of the equation, y = x² - 4·x + 4, is the point;

x = -(-4)/(2 × 1) = 2

The y-value of the vertex is therefore;

y = 2² - 4 × 2 + 4 = 0

The coordinates of the vertex is therefore; (2, 0)

2. The y-intercept is the point the graph intersects the y-axis, which is the point the x-value is zero, therefore;

The coordinate of the y-value of the y-intercept is therefore;

y = 0² - 4 × 0 + 4 = 4

The y-intercept is therefore; (0, 4)

3. A point on a function can be plugging a value of the input as follows;

The point at x = 1 is; y = 1² - 4×1 + 4 = 1

Therefore, another point on the graph is; (1, 1)

4. The axis of symmetry is the vertical line passing through the vertex, with an equation which is the x-value of the vertex

The x-value of the vertex is; x = 2, therefore, the axis of symmetry is the line; x = 2

The reflection of a point (x, y) about the vertical y-axis is the point (-x, y)

Therefore, the image of the reflection of the y-intercept, (0, 4) about the line x = 2 will be the point (4, 4)

The reflection of the point (1, 1), about the line x = 2 is the point (3, 1)

The above points can be used to graph the parabola, y = x² - 4·x + 4.

Please find attached the graph of the parabola created with MS Excel.

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Answer: the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Step-by-step explanation:

(-2, 5) and (-4,-5) are two points in the coordinate plane.

The first point (-2, 5) has an x-coordinate of -2 and a y-coordinate of 5. This point is 2 units to the left of the y-axis and 5 units above the x-axis.

The second point (-4, -5) has an x-coordinate of -4 and a y-coordinate of -5. This point is 4 units to the left of the y-axis and 5 units below the x-axis.

To find the distance between these two points, we can use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the coordinates of the two points, we get:

distance = sqrt[(-4 - (-2))^2 + (-5 - 5)^2] = sqrt[(-2)^2 + (-10)^2] = sqrt[104]

So the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Answer:

24 inch cubes are needed to fill the bottom layer of the prism.

Answer: it will be square or rhombus

Step-by-step explanation:

The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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I think the radius would be 2

The total price of the sofa is £3000.

To calculate this, multiply the given amount by "0.2", which equals "20%".

[tex]2500*0.2=500[/tex]

[tex]2500+500=3000[/tex]

The total price of the sofa is £3000.

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

So if we want to add 20% of any amount to said amount, we may multiply it by (1+0.2), which equals "1.20", and it'll give us the result immediately:

[tex]2500*(1+0.2)\\ \\2500*1.2=3000[/tex]

Now, working on the opposite way, let's say we want to reduce that same number (2500) by 25%, maybe because there's a discount on the product. In that case, we must multiply by (1-0.25), which equals 0.75:

[tex]2500*(1-0.25)\\ \\2500*(0.75)=1875.[/tex]

Given :-

To Find:-

Solution:-

Here we are given that Ryan purchases a sofa for £2500 . In order to find the cost of sofa after VAT , find 20% of the price of the sofa,

20% of £2500

20/100 * £2500

£500

Now add this to the original price of the sofa,

£2500 + £500

£3000

Hence the cost of the sofa after VAT is £3000 .

Answer:

So we have two possible values for the width: W = 16 or W = 7.5.

If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.

If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.

Step-by-step explanation:

Let the length of the rectangular plot be L, and let the width be W. Then we have:

The perimeter of the plot is 2L + 2W, and this must equal the length of fencing that Morgan has, which is 46 m. So we have the equation:

2L + 2W = 46

The area of the plot is LW, and we know that this equals 130 square meters. So we have the equation:

LW = 130

We can solve for one variable in terms of the other from the second equation, so let's solve for L:

L = 130/W

Now we can substitute this expression for L into the first equation:

2(130/W) + 2W = 46

Simplifying this equation, we get:

260/W + 2W = 46

260 + 2W^2 = 46W

2W^2 - 46W + 260 = 0

Dividing by 2, we get:

W^2 - 23W + 130 = 0

This is a quadratic equation that we can solve using the quadratic formula:

W = [23 ± √(23^2 - 4(1)(130))] / (2(1))

W = [23 ± 9] / 2

So we have two possible values for the width: W = 16 or W = 7.5.

If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.

If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.

Answer:

Length = 13

Width = 10

Step-by-step explanation:

Let L = length and W = width of the plot

The area is given by LW and is given as 130 square meters

LW = 130   (1)

The perimeter = 2(L + W) and given as 46 meters(length of fencing)
2(L + W) = 46
L+W = 23        (2)

In equation 1, isolate L by dividing both sides by W
LW/W = 130/W
L = 130/W

Substitute this value for L in equation (2)
L + W = 23
130/W + W = 23

Multiply throughout by W:
130/W x W + W x W = 23x W
130 + W² = 23W

Subtract 130W from both sides:
130 + W² - 23W= 0

Rewrite as

W² - 23W + 130 = 0

This is a quadratic equation which can be solved by factoring

Factoring W² - 23W + 130 = 0
(W - 13)(W-10) = 0

This means W = 13 or W = 10
If W = 13, L = 130/W = 120/13 = 10
If W = 10, L = 130/W= 130/10 = 13

So the possible values for L, W are
L = 13, W = 10

or

L = 10, W =13

Choosing the larger value for L gives us:
L = 13, W = 10

For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: B. not a function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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After 2.5 years the price of land and the price of house will be equal.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.

And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.

Since, The price of land increases at the rate of 20% per annum.

Hence, We get;

A = 80,00,000 (1 + 20/100)ⁿ

And, The price of house depreciates at the rate 20% per annum.

Hence, We get;

A = 2,70,00,000 (1 - 20/100)ⁿ

Let after n years the price of land and the price of house will be equal.

Thus, We get;

80,00,000 (1 + 20/100)ⁿ =  2,70,00,000 (1 - 20/100)ⁿ

8 (120/100)ⁿ = 27 (80/100)ⁿ

8 (6/5)ⁿ = 27 (4/5)ⁿ

Take log both side,

log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)

0.9 + n × 0.8 = 1.4 + n × 0.6

0.9 + 0.8n = 1.4 + 0.6n

0.2n = 0.5

n = 2.5 years

Therefore, After 2.5 years the price of land and the price of house will be equal.

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The amount of coverage that you will have on the contents of your home would be = $68,750

The total amount of money that was insured for the house = $125,000

The percentage of insurance that was left for the contents of the house = 55% of insurance.

That is;

= 55/100 × $125,000

= 6875000/100

= $68,750.

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The current population of Algeria is 38 million

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

P = 38(1 + r)^t

In the initial year, we have

t = 0

Substitute the known values in the above equation, so, we have the following representation

P = 38(1 + r)^0

Evaluate

P = 38

Hence, the population is 38 million

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The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,

⇒ 1/3

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.

Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,

⇒ 1/3

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Answer: To find the unit price for each fork, we need to divide the total cost of the box by the number of forks in the box.

The cost of the box is $4.98, and the box contains 96 forks. So the unit price for each fork is:

$4.98 ÷ 96 = $0.051875

Rounding to the nearest cent, the unit price for each fork is $0.05.

Step-by-step explanation:

Using the unitary method, we found that the cost of one fork of brand B is $0.051.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or more items by multiplication.

Given,

The number of forks in a box of brand B = 96

  Price of 96 forks = $4.98

The unit price of brand B = Cost of one fork

Using the unitary method,

96 forks = $4.98

1 fork = $4.98 / 96 = $0.051

Therefore using the unitary method, we found that the cost of one fork of brand B is $0.051.

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A total of 23800 cubes can fit inside the box of the given dimensions.

The volume of a cube is given by -

Volume = a x a x a = a³

Given is that a box has a length of 10 inches, a width of 8[tex]\frac{3}{4}[/tex] inches, and a height of 4[tex]\frac{1}{4}[/tex] inches.

The volume of the box would be -

V = 10 x 8[tex]\frac{3}{4}[/tex] x 4[tex]\frac{1}{4}[/tex]

V = 10 x 35/4 x 17/4

V = 371.875 inches³

The volume of cube -

v = 1/4 x 1/4 x 1/4

v = 0.015625 inches³

Number of cubes that will fill the box would be -

n = V/v

n = 371.875/0.015625

n = 23800

Therefore, a total of 23800 cubes can fit inside the box of the given dimensions.

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Answer: I am in high school so this may not be the best answer, but I would say that eventually eye sight would simply become useless to the fish because they live in a cave and don’t really need to see, there for I would say that the second answer is correct.

Answer:

Step-by-step explanation:

n+7=8

n=1

The point slope form of a linear equation is an equation that describes the relationship between two variables, x and y, in terms of their linear relationship.

It takes the form:.y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope of the line.

In this form, you can find the equation of a line if you know a point on the line and the slope of the line. You can also use this form to find the equation of a line if you are given two points on the line, by first finding the slope using the two points, and then plugging in one of the points and the slope into the equation.

The point slope form can be useful in a variety of contexts, such as in graphing and in solving problems involving rates of change.

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Answer:picture is not clear on my side, please re-upload thx!

Step-by-step explanation:

Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given a linear function which represents the profit of Bethany, y after x hours of dog walking.

(a) From the graph, we have to estimate the zero.

The graph seems to intersect the X axis in between 20 and 22, approximately 21.

(b) To solve this algebraically, we have the profit function,

y = 23x - 480

When y = 0,

23x - 480 = 0

23x = 480

x = 20.87 ≈ 21

Hence the graphical method gives the same estimate as the algebraic method.

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Answer:

[tex]\text{Numerical length of $\overline{FG}$ = 7}[/tex]

Step-by-step explanation:

We are given the following data:

[tex]EG = 5x + 7\\EF = 5x\\FG=2x-7\\[/tex]

Point F is the line segment [tex]\overline{EG}[/tex]

So F is between E and G

We get the relationship
EG = EF + FG

→ 5x + 7 = 5x + (2x - 7)

→ 5x + 7 = 5x + 2x - 7
→ 5x + 7 = 7x - 7

Moving x terms to the left and the constant 7 from left to the right gives
→ 5x - 7x = -7 +(-7)

→ -2x = -14

→ x = -14/-2 = 7

Therefore length of FG = 2x - 7

= 2(7) - 7

= 14 - 7

= 7

Step-by-step explanation:

study by the University of London found that participants who multitasked during cognitive tasks, experienced an IQ score decline similar to those who have stayed up all night. Some of the multitasking men had their IQ drop 15 points, leaving them with the average IQ of an 8-year-old chil

Answer:

Answer:

See attached image and explanation below

Step-by-step explanation:

For the first table:
The cumulative frequency for each class interval is obtained by adding that class frequency to the sum of all frequencies less than that class interval

So the table will look as in the first image attached

The second table talks about cumulative relative frequency and it uses the same technique as above but we are dealing with relative rather than absolute frequencies

The second image shows the correct values

Your relative frequency table (the third image you posted) is correct

The length of CF is solved to be 12

In the figure the value of CF is solved using the vertical angle theorem and sum of angles in a triangle

In triangle GBC

angle C = 180 - 90 - 45

angle C = 45

Using vertical angle theorem

angle DCB = angle DCF

Using trigonometry relation we have

cos 45 = CF / 12√2

CF = cos 45 * 12√2

CF = 12

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Value of integral ∫cos(x) + sin(x) 9 dx sin(2x) is  

-9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x)

In mathematics, integrals are the continuous analogues of sums and are used to calculate areas, volumes, and their generalizations. Integration (the process of computing an integral) is one of the two basic operations in calculus, the other being differentiation.

Given,

∫(cos(x) + sin(x).9)dx . sin2x

simplifying

sin(2x) ∫(9sinx + cosx)dx

sin(2x) (9∫sin(x)dx+∫cos(x)dx)

sin(2x) (-9cos(x) + sin(x) + c)

Using distributive law

= sin(2x)(-9cos(x)) + sin(2x)sin(x) + sin(2x).c

= -9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x)

Hence,  -9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x) is the value of integral

∫(cos(x) + sin(x) . 9)dx sin(2x)

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The measurement of x, in the given circle, is 5 cm.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle with a tangent of 6 cm and a secant of length 4+x, we need to find the measurement of x,

Using properties of circle,

6² = 4·(4+x)

36/4 = 4+x

9 = 4+x

x = 5

Hence, the measurement of x, in the given circle, is 5 cm.

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The accrued amounts are $32,796.58 and $706,396.44.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P (1+r/n[tex])^{rt}[/tex]

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

(a) If you invest $9,500 per period for 13 years at 10 percent.

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 9,500.00(1 + 0.1/1[tex])^{13}[/tex]

A = 9,500.00(1 + 0.1[tex])^{13}[/tex]

A = $32,796.58

(b). If you invest $9,500 per period for 50 years at 9 percent,

First, convert R as a percent to r as a decimal

r = R/100

r = 9/100

r = 0.09 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 9,500.00(1 + 0.09/1[tex])^{50}[/tex]

A = $706,396.44

Therefore, the amounts are$32,796.58 and $706,396.44.

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Answer:

Step-by-step explanation:

(a) To find the number of students who did not like either sport, we can use the formula:

Total students = Students who like basketball + Students who like hockey - Students who like both sports + Students who like neither sport

We know that the total number of students surveyed is 30, and we also know the number of students who like basketball, hockey, and both sports. We can use this information to solve for the number of students who like neither sport:

30 = 13 + 18 - 4 + Students who like neither sport

Simplifying this equation, we get:

3 = Students who like neither sport

Therefore, there were 3 students who did not like either sport.

(b) To find the number of students who liked exactly one of the sports, we can subtract the number of students who liked both sports from the total number of students who liked at least one of the sports. We know that 13 students liked basketball, 18 students liked hockey, and 4 students liked both sports. To find the number of students who liked at least one sport, we can add the number of students who liked basketball and the number of students who liked hockey, but we need to make sure we don't count the 4 students who liked both sports twice:

Number of students who liked at least one sport = Students who like basketball + Students who like hockey - Students who like both sports

Number of students who liked at least one sport = 13 + 18 - 4 = 27

Therefore, the number of students who liked exactly one sport is:

Number of students who liked exactly one sport = Number of students who liked at least one sport - Number of students who liked both sports

Number of students who liked exactly one sport = 27 - 4 = 23

So there were 23 students who liked exactly one of the sports.