Lines AE and GH are parallel in the image below. The image will be used to prove that the sum of the measures or the
interior angles of ACGH is 180°.

Which statement would be included in a proof of why m/C+m/G+mZH= 180

It would take Sarah 136.36 minutes to walk 7.5 miles around spring lake park.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Sarah walks laps around spring lake park. she can walk 4 laps in 108 minutes.

1 lap = 1.5 miles
4 lap = 6 miles

walking rate = 6 / 108 = 0.056 miles per minute

Now,
time = distance/walking rate
time = 7.5/0.056 = 136.36 minutes

Thus, It would take Sarah 136.36 minutes to walk 7.5 miles around spring lake park.

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Argument A is deductive and Argument B is inductive.

Deductive reasoning uses broad premises to arrive at specific conclusions, while inductive reasoning starts with specific premises and draws general conclusions.

If the premises are valid, deductive reasoning's conclusions cannot be false. This is so because there is nothing in the conclusion that isn't already there in the premises. Yet, an inductively drawn conclusion goes beyond the information in the premises, unlike deductive reasoning.

Argument A is deductive because from the premise it is saying that the Grand Canyon was carved out by aliens from Jupiter, which is not sure.

Argument B is inductive because from the premise it is saying that Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old, which is true.

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The complete question is:

INDUCTIVE /DEDUCTIVE ARGUMENT

Argument A: The Grand Canyon could not have been made by humans, so it follows that the Grand Canyon was carved out by aliens from Jupiter.

Argument B: Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old.

By algebra properties, the values of algebraic expression x³ - 4 · x are - 3 and 0 for x² + x = 3.

In this question we must derive the value of algebraic expression x³ - 4 · x based on the fact that x² + x = 3. First, determine the value of x by algebra properties:

x² + x = 3

x² + x - 3 = 0

x² + (2 - 1) · x + 2 · (- 1) = 0

x² + 2 · x - x - 2 = 0

x · (x + 2) - (x + 2) = 0

(x - 1) · (x + 2) = 0

x = 1 or x = - 2

The roots of x² + x = 3 are 1 and - 2.

Second, determine the values associated with the two roots found in previous step:

x = 1

y = x³ - 4 · x

y = 1³ - 4 · 1

y = 1 - 4

y = - 3

x = - 2

y = x³ - 4 · x

y = (- 2)³ - 4 · (- 2)

y = - 8 + 8

y = 0

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A triangle's median is a straight path that joins a vertices to the midpoint of the following sectors across from it.

A triangle is a three-sided polygon that consists of three vertices, three sides, and three angles. Three types of triangles—scalene, isosceles, and equilateral—can be distinguished based on the length of their sides.

It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the size of its angles. A triangle's internal angles add up to 180 degrees. Two more terms—altitude and triangle median—are introduced to you in this essay.

A triangle's median is a straight path that joins a vertices to the midpoint of the following sectors across from it.

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Answer: False

Step-by-step explanation:

-3/7 roughly equals -0.428

-2/5 equals -0.4

-0.4>-0.428

-2/5>-3/7

Equation 4x222-12x+9=5 has a solution of x=  -√4-3.  It is said to be linear when an equation has the form y=mx+b .

In algebra, a linear equation is one with the form y=mx+b. B is the slope, and m is the y-intercept. Because y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are those with two variables. There are various examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

4x²2²-12x+9=5

8x2 - 12x +4 = 0

8x2 - 6x - 6x +4 = 0

2x(4x - 3) - 2(3x +2) = 0

Equation 4x222-12x+9=5 has a solution of x=  -√4-3 . It is said to be linear when an equation has the form y=mx+b .

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Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.

A straight line of numbers is shown visually as a number line.

This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.

The collection of integers can be shown on a number line much like other sets of numbers..

Hence, Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.

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By solving an exponential equation, we can see that the investment will be doubled after 10.6 years.

The investment can be modeled by the exponential equation:

P(x) = A*(1 + 6.75%/100%)^x

Where A is the initial value of the investment (the amount invested).

We can simplify this to get:

P(x) = A*(1 + 0.0675)^x

The investment will be doubled when:

2*A = A*(1 + 0.0675)^x

We want to solve this for x.

2 = (1 + 0.0675)^x

2 = (1.0675)^x

If we apply the natural logarithm in both sides:

ln(2) = ln((1.0675)^x)

ln(2) = x*ln(1.0675)

ln(2)/ln(1.0675) = x

10.6 = x

The investment will be doubled after 10.6 years.

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Answer:

1/2 x b x h

Step-by-step explanation:

b = length of the base of the triangle.

h = height of the triangle.

Therefore, the area of the triangle = 1/2 x b x h

The original amount is (100%) if you have an increased by 30%

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage.

In the given question, the percentage increase can be calculated with the help of the percentage increase formula,

Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100

To get the original amount,

Just add the percentage increase to 100, divide 100 by it, then multiple by the final number to get the original number.

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The metal bar would displace 0.018 liters of water.

Volume is the measure of the amount of space occupied by an object or substance. It is often represented by the symbol 'V' and is typically measured in units such as liters (L), cubic meters (m^3), or gallons (gal). In three-dimensional space, the volume of an object is calculated by multiplying its length, width, and height (or depth). In two-dimensional space, the area of an object can be calculated by multiplying its length and width.

The volume of the metal bar is 3 cm x 3 cm x 2 cm = 18 [tex]cm^3[/tex]. The density of water is 1 g/[tex]cm^3[/tex]. To find the volume of water displaced, we need to convert the volume of the bar from cubic centimeters to liters.

1L = 1000[tex]cm^3[/tex]

So the volume of water displaced would be 18 [tex]cm^3[/tex] / 1000 = 0.018 L.

In summary, the metal bar would displace 0.018 liters of water.

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The required two-column proof that the triangles are congruent is explained below.

A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.

When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).

The two-column proof required in the question is given below:

       STATEMENT                                     JUSTIFICATION

1. <WXZ ≅ <YXZ                               Property of an angle bisector.

2. <XZW  ≅ <XZY                             Definition of a perpendicular bisector.

3. WX ≅ YX                                       Congruent sides of a triangle.

4. WZ ≅ YZ                                        Definition of a midpoint.

Therefore,

ΔWXZ ≅  ΔYXZ                                  Angle-Angle-Side theorem

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Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

The length of the straw placed inside the rectangular box is [tex]\sqrt{73}[/tex] inches.

A quadrilateral with parallel sides equal to one another and four equivalent vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel. The area of a rectangle is given as the product of the length and breadth of the rectangle.

The given parameters are:

The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

[tex]s=\sqrt{l^{2}+w^{2}+h^{2} }\\[/tex]

The equation becomes:

[tex]s=\sqrt{6^{2}+6^{2}+1^{2} }\\[/tex]

Evaluate the exponents:

[tex]s=\sqrt{73}[/tex] inches

=> s≈8.544 inches

Hence, the length of the straw is 8.544 inches.

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The correct statement is (A) the points on the line would indeed be a part of the equation y = 0.5x.

Relationships between two variables that are proportional occur when their ratios are equal.

Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value.

The "constant of proportionality" is the name of this constant.

Observing the graph, the line traverses (0, 0). We obtain y=0.5(0)=0 if x=0.

Since this is the point's y-coordinate, it passes through this.

Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form equation for this line.

m=0.5 and b=0 in this equation.

This indicates that the slope is 0.5 or 1/2; as slope = rise/run, this indicates that the line rises one for every increase in the horizontal dimension of two.

This implies that starting from (0, 0), we would climb 1 and cross 2 to make the spot (2, 1).

When examining the graph, the line passes through this location.

We would then ascend 1 and cross over 2 once more to (4, 2). Once more, the line passes through this spot.

Therefore, the correct statement is (A) the points on the line would indeed be a part of the equation y = 0.5x.

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Complete question:

Which statement best explains if the graph correctly represents the proportional relationship y = 0.5x?

A. Yes, the points shown on the line would be part of y = 0.5x

B. Yes, all proportions can be shown on a graph of this line

C. No, the points shown would not be part of y = 0.5x

D. No, proportions cannot be represented on a graph

Therefore , the solution of the given problem of graphs comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.

Graphs are used by mathematicians to rationally represent or chart facts or values. Typically, a graph tip will show a connection amongst two or more objects. A graph is a type of non-linear data structure that is made up of nodes, and vertices, and edges. affix the nodes, also referred as as vertices. This graph includes elements E=3,2,14,5 , having (2.5) and vertex V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistics charting (bar charts, charts, line charts, etc.). the form of a triangle-shaped logarithmic graph

Here,

If she is first driving toward the gas station, then the graph will be declining.

She fills up her tank at the gas station, which causes the graph to move upward.

After that, the graph will start to decline as she approaches the market.

From the information,

we can simply deduce that the graph will initially start out declining, then quickly increase, and finally have a continuous reduction until we achieve our target.

Therefore , the solution of the given problem of graph comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.

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By using the given formula and solving we get, the original value of the vase is 5000 pounds.

A percentage is a way to express a number as a fraction of 100. It is often denoted by the symbol "%". For example, 25% means 25/100 or 0.25. Percentages are often used to express rates of change or proportions.

A rate is a ratio that compares two quantities of different units, such as distance and time, or weight and volume. It is often represented as a fraction or a decimal and can be converted to a percentage by multiplying by 100.

The given formula tells us how the value of the vase changes over time, with the value increasing by a factor of 1.28 (28% increase) every year.

To find the original value of the vase, we need to know the value of the vase when n = 0.

Substituting n = 0 into the formula, we get:

value in pounds = 5000*1.28^0

When n = 0, 1.28^0 = 1, so the original value of the vase is:

value in pounds = 5000*1 = 5000 pounds

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The value of x is equal to 9 for the two-variable equation -2x - 7y = 17 when y is equal to -5.

A two-variable equation is an equation that has 2 variables, typically x and y

For the two-variable equation;

-2x - 7y = 17

we shall evaluate for the value of x when y = -5 as follows:

-2x - 7(-5) = 17

-2x + 35 = 17

subtract 35 from both sides of the equation

-2x = 17 - 35

-2x = -18

divide through by -2

x = -18/-2

x = 9

Therefore, 9 is the value of x when y is equal to -5 for the two-variable equation -2x - 7(-5) = 17.

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The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.

Answer:

2(3b+6) =78 : b=11

-2(6c-3) = -72 : c=6.5

Step-by-step explanation:

They are correct

The x and y-intercepts of the given equation of line 8x - 5y = -11 are (-11/8,0) and (0,11/5) respectively.

Given the equation of line in the question;

8x - 5y = -11

To find the x-intercept, substitute in 0 for y  and solve for x.

8x - 5y = -11

8x - 5(0) = -11

8x - 0 = -11

8x = -11

x = -11/8

Hence, the x-intercept is (-11/8,0)

To find the y-intercept, substitute in 0 for x  and solve for y.

8(0) - 5y = -11

0 - 5y = -11

-5y = -11

y = -11 / -5

y = 11/5

Hence, the y-intercept is (0,11/5).

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The constant of proportionality is 12. The equation to represent the relationship is :  b = 12p.

Constant proportional:

A constant of proportionality is a constant value for the ratio of two proportional quantities. If the ratio or product is constant, the two variables are proportional. The value of the constant of proportionality depends on the type of relationship between the two given quantities (positive versus inverse variation).

According to the question:

From the above mentioned , the individual ratio of number of birdhouse (b) cans of paints is:

Now,

For 1st  pair,

   b/ p = 3/ 1/4

⇒ b / p = 3 ×4 /1

⇒ b/ p = 12

Again,

For 2nd pair,

   b /p = 9/0.75

⇒ b /p = 12

For 3rd pair,

 b /p = 18/3/2

⇒ b /p = 18× 2/3

⇒ b/ p = 12

Finally,

For 4th Pair =

⇒ b/ p = 20/2.5

⇒ b/ p = 12

As all the ratios are equivalent, the relationship between number of birdhouse (b) and cans of paints (p) is proportional. The constant of proportionality is 12. The equation to represent the relationship is :  

                                            b = 12p.

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The quadratic pattern with value of p and q has been proved.

A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word for square, is where the word "quadratic" originates.

Here,

Given : 1st difference

p−4;

11−p;

q−11;

22−q;

2nd difference−2p+15;

q+p−22;

33−2q−2p+15=1−2p=−14p

=733−2q

=1q+p−22

=1−2q=−32or/of

q+7−22=1

q=16

Therefore , the solution of the given problem of quadratic comes out to be q =16

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Answer:

Two possible ways Arvin can complete his training plan are:

Biking 35 miles a week, 3 days a week, biking 11.67 miles per day.

Biking 41 miles a week, 4 days a week, biking 10.25 miles per day.

In the first option, Arvin bikes 35 miles a week, 3 days a week, which means he bikes 11.67 miles per day to achieve his goal.

In the second option, Arvin bikes 41 miles a week, 4 days a week, which means he bikes 10.25 miles per day to achieve his goal.

It is important to note that these are just examples, and there could be other options that Arvin can consider, as long as it meets his requirement of biking between 35 and 41 miles a week, either 3 or 4 days a week, and the same number of miles each day.

Step-by-step explanation:

Therefore ,as a result, the  solution of the given problem of equation is  left side of the line's run is taken into consideration because the slope is positive.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two variable on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.

Here,

provided: y + 1= (x-4)

The slope in this case turns out to be =>

=>y = x -5

We obtain m = 1 and an intercept of c = -5 when comparing with the equation y= mx + c.

As a result, the left side of the line's run is taken into consideration because the slope is positive.

We can swap the point for plot the graph by bringing the piece down by -5.

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Step-by-step explanation:

[tex]volume \: of \: cylinder = \pi \: {r}^{2} h \\ volume = 3.14 \times {7}^{2} \times 19 \\ = 2923.34 \: millimetres[/tex]

Hana can put 4 fruits in each bowl. We can solve the given problem by finding the highest common factor using prime factorization.

The Highest Common Factor (HCF) of two numbers is the largest possible number that divides both numbers equally.

There are various methods for calculating the highest common factor between two numbers. The prime factorization method can be used to quickly determine the HCF of two or more numbers.

Examine the many attributes and components of HCF to learn more about it. Find the solutions to questions like what is the highest common factor for a collection of integers, how to quickly calculate the highest common factor, how to compute HCF using the prime factorization, and more to learn more fascinating details about them.

We found that the Highest common factor is 4

then 8 melons can be placed in 2 bowl having 4 melons in each bowl

12 pears can be placed in 3 bowls having 4 pears in each bowl

and lastly, 24 apples can be placed in 6 bowls having 4 apples in each bowl.

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Answer:

2

Step-by-step explanation:

The equation of the relationship between the price of oranges last week and this week is y = 1.2x

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

Price last week = x

Rate of increment = 20%

Price this week = y

Using the above as a guide, we have the following:

Price this week = Price last week * (1 + Rate of increment)

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

y = x * (1 + 20%)

Express as decimal

y = x * (1 + 0.2)

Evaluate the sum

y = x * 1.2

So, we have

y = 1.2x

Hence, the equation is y = 1.2x

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Answer:

not enough info

Step-by-step explanation:

Let h = number of history books.

Let m = number of math books.

"The number of history textbooks sold was three times the number of math textbooks sold."

h = 3m

"A textbook store sold a combined total of history and math textbooks in a week."

h + m = t

t = total number of books sold.

We have a system of equations:

h = 3m

h + m = t

Since we do not have a value for t, and we have a system of 2 equations in 3 variables, we cannot find the numbers of history or math books sold.