Given the image below, find the maximum value for x.

Length of wall = 10km

side of square= 10km

area of square= 10²= 100km²

radius of circle = 10/2 = 5km

area of circle = 3.14 × 5²

area of circle = 3.14 × 25

area of circla = 78.5 km²

area of square >>> area of circle

1. Linear pair theorem

2. Substitution property of equality

3. Subtraction property of equality

4. Definition of congruence

The given results can be proved by the linear pair property of angles on a straight lines.

The linear pair property can be defined as the sum of all the angles on the one side of a straight line is equal to 180°.

In the given diagram the following data is given,

The angles ∠DEH and ∠DEF are on the straight line HEF.

And, the angles ∠DEF and ∠FEG are on the straight line DEG.

As per the linear property of angles, it can be written as,

m∠DEH + m∠DEF = 180°.

And,  m∠DEF + m∠FEG = 180°.

Which implies that m∠DEH + m∠DEF = m∠DEF + m∠FEG

Subtract the common terms from both sides to get,

m∠DEH + m∠DEF - m∠DEF = m∠DEF + m∠FEG - m∠DEF

⇒ m∠DEH = m∠FEG

⇒ ∠DEH ≅ ∠FEG

This is also known as the property of vertically opposite angles.

Hence, the given result m∠DEH = m∠FEG is proved by the linear pair property.

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Answer:

Monthly cost with 11 slices: $28.75

Monthly cost with x slices: C = 15 + x * 1.25

Step-by-step explanation:

If Austin bought 11 slices of pizza this month, he would have to pay the pizza shop a total of $15 + 11 * $1.25 = 28.75. This includes the cost of the membership fee of $15 and the cost of the 11 slices of pizza at the discounted price of $1.25 per slice.

The monthly cost for x slices of pizza can be represented by the equation C = 15 + x * 1.25, where C is the total cost and x is the number of slices of pizza purchased. This equation shows that the total monthly cost is equal to the membership fee of $15 plus the cost of the x slices of pizza at the discounted price of $1.25 per slice.

Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume and length definitions are connected.

Here,

Cone has a radius of 4ft

A height of 2ft.

Thus,

The formula for volume of cone is used

V=π[tex]r^{2} \frac{h}{3}[/tex]

V=3.14*[tex]4^{2}[/tex]*2/3

V=50.24*2/3

V=100.48/3

V=33.51 [tex]ft^{3}[/tex]

Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

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There is no such a number whose absolute value is -2. This is because the absolute value of any number is its distance from 0 irrespective of the direction.

An absolute value of a number is the distance of the number from 0 on a number line irrespective of the direction.

Consider the number "x".

Then its absolute value is written as

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

For example x = -9; then its absolute value is

|(-9)| = -(-9) = 9; (Since x = -9 < 0; we applied |x| = -x)

So, we can conclude that irrespective of the direction (positive or negative), the absolute value of any number remains positive.

We know that the absolute value of any number is calculated by

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

And the absolute value of any number irrespective of its direction on the number line remains positive.

So, no such number has a negative absolute value.

Hence, the answer is none for the given question.

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Answer:

  2378 m

Step-by-step explanation:

You want the ground distance from the takeoff point to an airplane that has flown 2500 m in the air at a takeoff angle of 18°.

The cosine relation tells you ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse · Cos

Here, the hypotenuse of the right triangle model is 2500 m, the angle is 18°, and we want to find the side of the triangle adjacent to the angle:

  AD = AP·cos(18°) = 2500·0.9510565 ≈ 2377.64 ≈ 2378 . . . . meters

The ground distance is about 2378 m.

The illustration based on the Gestalt principles of grouping are:

(A) Closure principle.

(B) Proximity principle.

(C) Continuity principle.

(E) Similarity principle.

The principles of grouping, also known as the Gestalt rules of grouping, are a collection of psychological concepts first put out by Gestalt psychologists to explain why people naturally perceive items as structured patterns and objects, or Prägnanz.

Gestalt psychologists asserted that these principles hold true because the mind is predisposed to recognize patterns in the stimulus based on predetermined rules.

Gestalt grouping guidelines include:

Continuity principle.

Similarity principle.

Proximity principle.

Closure principle.

Common region principle.

Figure-ground principle.

Focal point principle.

Therefore, the illustration based on the Gestalt principles of grouping are:

(A) Closure principle.

(B) Proximity principle.

(C) Continuity principle.

(E) Similarity principle.

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Answer:

first option

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 , then the 2 roots are real and irrational

• If b² - 4ac > 0, and a perfect square, then 2 roots are real and rational

• If b² - 4ac = 0 , then 2 roots are real and equal

• If b² - 4ac < 0 , then 2 roots are not real

3x² + 4x - 2 = 0 ← is in standard form

with a = 3, b = 4 and c = - 2 , then

b² - 4ac = 4² - (4 × 3 × - 2) = 16 - (- 24) = 16 + 24 = 40

since b² - 4ac > 0 , then 2 real and irrational roots

Answer:

2. d = 40; 2 rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] is:

[tex]\boxed{\mathrm{d =} \ b^2 - 4ac}[/tex].

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation [tex]3x^2 + 4x - 2 = 0[/tex]. Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)

             = 16 - (-24)

             = 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.

Answer: y = 4x + 1

Step-by-step explanation: Simple...

You have your equation... y=mx+b

You are given a coordinate. That is your x and y, and "m" is given already, and it's your slope.

First, you plug them in. You are solving for the unknown y-intercept or the "b".

5=4(1)+b

Then, you solve!

5=4+b

1=b

Parallel lines have the same slope, so the equation would be...

y=4x+1

If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

[tex]\boxed{8-2=6}\\\boxed{6/2=3}[/tex]

We are going to take that 25% and multiply it with 3 to get are final answer.

[tex]\boxed{25*3=75}\\\boxed{So,2=75}[/tex]

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Answer:

Corresponding angels:

a,f

h,b

e,d

c,g

y = 80  Vertical angles are congruent

x = 50 Sum of the interior angles of a triangle is 180

180 - 80 -50 = 50

Step-by-step explanation:

y = 25x + 263 this equation represents how much money she will have, including her saving.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The saved amount of $263 by Jenna,

and also she earns $25 per day

if x represents the number of days she works,

and let's take y as the total amount she will have.

Then the equation becomes:
y = 25x + 263

Hence, y = 25x + 263 this equation represents how much money she will have, including her saving.

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The slope of line p is 3, and the slope of line q is -3

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

Line p

From the line p, we have the following ordered pairs

(2, 2) and (0, -4)

Line q

From the line p, we have the following ordered pairs

(0, 2) and (2, -4)

Rewrite the above points properly

So, we have the following ordered pairs

Line p, (x, y) = (2, 2) and (0, -4)

Line q, (x, y) = (0, 2) and (2, -4)

The slopes of the lines are then calculated using the following slope equation

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation

So, we have the following equation

Slope of line p = (-4 - 2)/(0 - 2)

Evaluate

Slope of line p = 3

Slope of line q = (-4 - 2)/(2 - 0)

Evaluate

Slope of line q = -3

Hence, the slopes are 3 and -3, respectively

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From the statistical point of view , the type I error was made , the correct option is (c) .

In the question ,

it is given that ,

the machine was working well, but on the basis of our statistical hypothesis test, it was concluded that the machine was under-filling or over-filling and hence it was shut down .

but after examination by the engineers , there was nothing wrong with the filling machine .

that means that the null hypothesis was rejected when it was actually true .

which refers to the type I error .

Therefore , the correct option is (c) A Type I error was made.  

The given question is incomplete , the complete question is

The result of a hypothesis test is used to prevent a machine from under-filling or overfilling quart size bottles of olive oil. on the basis of sample, the hypothesis is rejected and the machine is shut down for inspection. a thorough examination reveals to engineers there is nothing wrong with the filling machine. from a statistical point of view:

(a) correct decision was made.

(b) Both, a Type I and a Type II errors were made.

(c) A Type I error was made.

(d) A Type II error was made.

(e) None of these answers.

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The equation of line perpendicular to the given line is,

[tex]y = \frac{5}{2}x - 13[/tex].

What is slope point form of the line?

The general form of a linear equation is y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Consider the given equation of line,

[tex]y = -\frac{2}{5}x - 1[/tex]

Compare it with y = mx + c

where m is the slope.

⇒ Slope of the line is -2/5.

We have to find the equation of line perpendicular to the given line.

Since the slope of the perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is [tex]-\frac{1}{(\frac{2}{5}) } = 5/2[/tex].

The point passes through (2, -8).

Now consider, the point slope form of the line

[tex]y-y_1 = m(x-x_1)\\[/tex]

Plug [tex](x_1, y_1) = (2, -8) , m = \frac{5}{2}[/tex] in the above equation.

⇒

[tex]y - (-8) = \frac{5}{2}(x-2)\\ y+8 = \frac{5}{2}x - 5\\ y = \frac{5}{2}x-5-8\\ y = \frac{5}{2}x - 13[/tex]

Hence, the equation of line perpendicular to the given line is,

[tex]y = \frac{5}{2}x - 13[/tex].

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Answer: 45 dogs will eat 135 pounds of dog food.

Step-by-step explanation:

The amount of food required for 45 dogs in a week will be equal to 135 pounds.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Total number of dogs = 9

Amount of food eaten by dogs in a week = 27 pounds

Now, the number of dogs is 45.

Let the amount of food eaten by 45 dogs in a week is x.

So,

x = (27 × 45)/9

x = 1215/9

x = 135 Pounds.

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Answer:1/6 barrels=1 batch

Step-by-step explanation:

4/.666666666666666=6 batch's came from one barrel

6 batch's came from one barrel

1/6= 1 batch

Calculating the cost of 4.25 kilogram(kg) is £2.38, by multiplying it by 4.25 kg by 1 kg.

Costs are the expenses incurred in the manufacture, marketing, or preparation of a good or asset for regular use. In other terms, it's the cost incurred to produce a good, buy inventories, sell goods, or prepare equipment for use in a commercial activity.

Given,

2.5 kg cost  £1.40 i.e,

2.5 kg = £1.40

For 1 kg= [tex]\frac{1.40}{2.5}[/tex]

= £0.56

To find the cost of 4.25 kg:

Then,

1 kg = £0.56

4.25 kg = 0.56 x 4.25

= £2.38

£2.38 is the cost of 4.25kg after calculating it.

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The number of bracelets and the number of necklaces will be 10 and 5, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

A gem dealer had a proper measure of gold to make wristbands and pieces of jewelry. The amount of gold in every armband is 5 grams and the amount of gold in every accessory is 16 grams. A goldsmith utilized 130 grams.

Let 'x' be the number of Bracelets and 'y' be the number of Necklaces. Then the equation is given as,

5x + 16y = 130

The term 16y in the equation should be a multiple of 5 to get the whole value.

If the value of y is 5. Then the number of bracelets is given as,

5x + 16(5) = 130

5x + 80 = 130

5x = 50

x = 10

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

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The evaluation of the composite figures, distances and coordinates in the question indicates;

24. The volume of the figure is about c) 1440 cm³

25) The distance of the airport from the plane is about c) 41,043.6 feet

26) The coordinates of the vertex U are c) (-5, -7)

A composite figure is a figure that is composed of two regular figures.

24. The figure is a composite figure comprising of a cylinder and a cone.

Volume of the cylinder = π × 5² × 15 = 375·π

Volume of the cone = (1/3) × π × 5² × (25 - 15) = (83 1/3)·π

The volume of the figure is therefore; 375·π + (18 1/3)·π ≈ 1440

25) The height of the plane = 12,000 ft

The angle of elevation to the airplane = 17°

Let r represent the direct distance of the airport from the plane, we get;

sin(17°) = 12000/r

x = 12000/(sin(17°) ≈ 41,043.6

The direct distance from the plane to the airport which is the hypotenuse side of the right triangle in the figure is about; d) 41,036.6 feet

26) The coordinates of the vertices of the triangle are; R(-6, -3), S(3, 3), and T(4, -1)

The type of quadrilateral represented by quadrilateral RSTU = A parallelogram

The slope of the side ST = (-1 - 3)/(4 - 3) = -4

Equation of the side RU is therefore;

y - (-3) = (-4) × (x - (-6)) = -4·x - 24

y = -4·x - 24 - 3 = -4·x - 27

y = -4·x - 27

The slope of the side RS = (3 - (-3))/(3 - (-6)) = 2/3

Equation of the side TU = y - (-1) = (2/3)·(x - 4) = (2/3)·x - (8/3)

y = (2/3)·x - (8/3) - 1 = (2/3)·x - (11/3)

y = 0.2·x - 1.8

The x-coordinate of the point U can be therefore obtained from the equation;

-4·x - 27 = (2/3)·x - (11/3)

x = -5

y = -4×(-5) - 27 = -7

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Answer:

A) 14

Step-by-step explanation:

Nuts:

[tex]\frac{6}{\frac{1}{3} }[/tex] = [tex]\frac{6}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]  Get a common denominator of 3 and divide

[tex]\frac{18}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{\frac{18}{1} }{\frac{3}{3} }[/tex] = [tex]\frac{18}{1}[/tex] = 18

We can make 18 bags with the amount of nuts given.

Raisins:

[tex]\frac{8}{\frac{1}{4} }[/tex] = 8 ÷[tex]\frac{1}{4}[/tex]  Gert a common denominator of 4 and divide

[tex]\frac{32}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{\frac{32}{1} }{\frac{4}{4} }[/tex] = [tex]\frac{32}{1}[/tex] = 32

We can make 32 bags with the amount of raisins given.

32 - 18 = 14

14 more bags need nuts agged.

Answer:

10 yrs old and 35 yrs old

Step-by-step explanation:

I figured it out by trial and error but here's the thinking process.

10 + 35= 45

Son becomes dad's age so 35-10=25, so plus 25 year to each age.

10+25=35

35+25= 60

35+60=95

I hope that makes enough sense!

The probability that it takes Emma more than 5 minutes to wait for the train is 0.8571.

Given :

the amount of time emma must wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes.

Let the random variable X denotes the amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes.

the distribution function of X is:

F ( x ) = x - 4 / 11 - 4

4 < x < 11

P ( X > 5 ) = 1 - P ( X < 5 )

= 1 - F ( 5 )

= 1 - 1 / 7

= 7 - 1 / 7

= 6/7

= 0.8571

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Answer:

0.692

Step-by-step explanation:

Given: The computer that controls a bank's automatic teller machine crashes a mean of 0.5 times per day.

Mean per day = 0.5

Mean per 7 day = 7*0.5 = 3.5

X = Number of times the computer will crash

We have to find:

P( the computer will crash more than 1 time in any seven-day week) =?

P(x >1) = ?

P(X > 1) =1- P(X < or = 1)

P(X < or = 1) = 0.320847

P(X < or = 1) = 0.3208

P(x > 1) = 0.6792

So, the answer is 0.6792

Hugo will buy car B.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Car A travels 702 miles on 12 gallons of gasoline.

And, Car B travels 873 miles on 15 gallons of gasoline.

Now,

Since, Car A travels 702 miles on 12 gallons of gasoline.

And, Car B travels 873 miles on 15 gallons of gasoline.

Hence, The distance of car A for travels in per gasoline = 702 / 12

                                                                                      = 58.5 miles

And, The distance of car B for travels in per gasoline = 873 / 15

                                                                                  = 56.2 miles

Since, Hugo wants to buy a car with lower fuel consumption.

Clearly, The car B consume lower fuel.

Hence, Hugo will buy car B.

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Answer:

Jeff is Incorrect

Step-by-step explanation:

If x ≤ 1/2, the value will either be 2 or less than 2.

x = 1/2 =>  2(1/2)+1 = 2

x = 0 =>  2(0)+1 = 1

x = -1 =>  2(-1)+1 = 0

The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°

According to the question,

A spring is attached at one end to support B and at the other end to collar A.

Part A: Given that : Reference angle (θ) = 28°

We have to find out the distance of point A to point B.

Adjacent = 3 ft (given)

To find AB, apply the trigonometry function which is:

cos θ = adj / hypotenuse

Substituting all the values ,

=> cos 28°= 3/AB

=> AB = 3/cos 28°

=>  AB = 3.4 ft (nearest tenth of a foot)

Part B:

It is given that Distance  from point A to point B is 5.2 feet

We have to calculate the Value of θ

adj = 3 ft

hypotenuse = AB = 5.2 ft

To find θ , We will again apply the trigonometry function

cos θ = adj/hypotenuse

Substituting all the given values

=> cos θ = 3/5.2

=> θ = cos⁻¹ ( 3 / 5.2)

=> θ = 54.8°

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Option (A) ΔDAB ~ΔDAC this similarity statement would be true for the figure.

We know that two triangles are similar if they have the same ratio of corresponding sides and equal of corresponding angles.

The fundamental theorem of similarity states that a line segment splits of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Similar triangles are the triangles that look similar to each other but their sizes might not be exactly the same. Two triangles will be similar if the angles are equal and sides are in the same ratio or proportion. Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

In Δ DAB and Δ DAC

DA = DA

∠D = ∠D

and AB proportional to AC.

Therefore Δ DAB ~ Δ DAC would be true for the figure.

Given question doesn't provide figure. I have attached figure of triangle to complete the question.

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Answer:

D

Step-by-step explanation:

A Hyperbola looks like a Parabola and its reflection, each Parabola curving opposite directions.

Answer:

D.  Hyperbola

Step-by-step explanation:

A conic is the intersection of a plane and a right circular cone.

Formed when a cone is intersected by a plane so that the plane is parallel to the circular base.

Formed when a cone is intersected by a plane so that the plane is at an angle with respect to the circular base.

Formed when a cone is intersected by a plane so that the plane is parallel to an edge.

Formed when a double-cone is intersected by a plane so that the plane is perpendicular to the circular bases.

The result of the expression is 60.

The given expression can be solved by applying the principle of BODMAS.

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression.

This indicates that numerous operator expressions must only be spelled out in this order, from left to right. We begin by resolving the brackets, then move on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).

Given, 50+20/10*5 = 50+2*5=50+10=60

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