The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 18 , 27 , . . . Find the 8th term.

The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.

The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.

Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.

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Answer:

[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]

A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.

The area of the figure is 51 cm², which is option C.

In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.

To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.

Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.

Using the given information, we can calculate the longer base:

longer base = 4 cm + 6.2 cm = 10.2 cm

Now we can use the formula for the area of a trapezoid to find the area of the figure:

A = (1/2)h(b₁ + b₂)

where h is the height, b₁ is the shorter base, and b₂ is the longer base.

Plugging in the given values, we get:

A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²

Therefore, the area of the figure is 51 cm² , which is option C.

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Complete Question:

A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?

Jackson's total cost after the discount and before tax would be $24.67.

When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.

To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).

Here we have

Jackson has a 10% discount at his local hardware store.

Let 'x' be the cost before tax

After a 10% discount,

The amount that Jackson could pay 90% of the cost

Given that he wants to buy $ 27.40  

The cost of items after discount = 90% of 27.40

= [ 90/100 ] × 27.40

= [ 0.9 ] × 27.40

= 24.66

Therefore,

Jackson's total cost after the discount and before tax would be $24.67.

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Answer:

Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

On Thursday, she practiced for 5 minutes according to the table.

On Friday, she practiced for 9 minutes according to the table.

Adding these two times together, we get:

5 minutes + 9 minutes = 14 minutes

Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.

When expanding a binomial expression in the form of (a + b)ⁿ, the middle term can be found using the following formula:

Middle term coefficient = nC(k), where k = (n+1)/2 if n is odd, and k = n/2 or (n/2 + 1) if n is even. The middle term coefficient is then multiplied by the product of a raised to the power of (n-k) and b raised to the power of k.

The difference of squares pattern is a special algebraic pattern that arises when we factor a polynomial that is the difference between two perfect squares. For example,

x² - y² = (x+y)(x-y)

When we apply this pattern to the expression w - 121, we can rewrite it as:

w² - 11²

And, we can use the difference of squares pattern to factor it as:

(w + 11)(w - 11)

Notice that there is no middle term with a variable in this factorization. This is because when we multiply (w + 11)(w - 11), the middle term cancels out.

To see why this happens, let's expand the product:

(w + 11)(w - 11) = w² - 11w + 11w - 121

The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.

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Answer: 104%

Step-by-step explanation: 26% times 4 years

Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Answer:

s/3

Step-by-step explanation:

since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.

Answer:

K = √-6k

i did the math and got this answer and it was right

Answer:

In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.

If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:

an = a1 + (n-1)d

where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.

If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:

a1 = 3

a2 = 8

a3 = 13

a4 = 18

and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:

a129 = a1 + (129-1)d

a129 = 3 + 128(5)

a129 = 643

Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.

Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

We are given two equations:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x + d

and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:

y = 4(-4)² - 3(-4) + 3 = 49

y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d

So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:

49 = 60 + d

Solving for d, we get:

d = -11

Therefore, the two equations become:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x - 11

We can now set them equal to each other:

4x² - 3x + 3 = x³ + 7x² - 3x - 11

Simplifying and rearranging, we get:

x³ + 3x² - 8x - 14 = 0

We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:

2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10

Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:

(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4

This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:

(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6

This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:

x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)

The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:

x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2

= [ -1 ± 3√(7) ] / 2

Therefore, the three intersection points are:

(-2, 0)

( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )

( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

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Briana and her mother will need to measure and cut the fabric for the quilt. They will need to decide on a pattern and color scheme for the quilt. They will need to sew the pieces of fabric together to create the quilt top. They will need to layer the quilt top with batting and backing fabric and then quilt the layers together. Finally, they will need to bind the edges of the quilt.

It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to√(0.861(1.0.861)/410) = 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

What is a proportion?

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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Step-by-step explanation:

6^2 / 6^1   x    6^12 / 6^8   =

6^(2-1)      x    6^(12-8)   =

6^1          x    6^4   =

6^(1+4)  =   6^5     or  = 7776

63% of people Surveyed shop at a local grocery store.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.

For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.

In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.

The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;

it is frequently stated as a fraction.

For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.

An assertion of equality between two ratios is a proportion.

For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,

hence the sentence "3/5 = 6/10" is a proportion.

Analysis: -

people surveyed at store = 45

total no. of people = 72

the

Percent of peopla = 45/72  x100

= 0.625 × 100

= 62.5 %

= 63 %

63% of people Surveyed shop at a local grocery store.

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If each person drove at a constant rate,than Laura drove the fastest

Displacement is the measurement of  the how far an object is out of place,therefore distance refers to  the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.

The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.

to compute who drove the quickest by Using this   formula

speed=Distance /time,

first of all the convert times into hours:

Hank: 3.2 hours x 3 hours and 12 minutes.

Laura: 2.5 hours is 2 hours and 30 minutes.

Nathan: 2.25 hours is 2 hours and 15 minutes.

Raquel: 4 hours plus 24 minutes equals 4.4 hours.

now to calculate the speed by above formula

Hank: 55 miles per hour for 176 miles in 3.2 hours.

Laura: 60 miles per hour equals 150 miles in 2.5 hours.

Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.

Raquel: 65 miles for 286 miles in 4.4 hours.

As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.

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The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is

Substituting the values in the equation, we get

Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A

Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil

And , number of cups of vegetable oil used by Colin to make 8 cakes A =

A = 8 x number of cups of vegetable oil used by Colin to make 1 cake

On simplifying the equation, we get

[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]

[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]

Therefore, the value of A is 5 1/3 cups

Hence, the number of cups of vegetable oil required is 5 1/3 cups

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Complete question is-

Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.

If Colin made 8 cakes, how much oil did Colin use in all?

A. 5 1/3 cups

B. 7 1/3 cups

C. 8 2/3 cups

D. 16 1/3 cups​

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

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Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.

Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).

Given data:

Principal P = $1500

Amount after interest A = $1600

Rate of simple interest R = 6.49%

Time  = T years

The formula for the simple interest:

SI = PRT/100

A = P + SI

A = P + PRT/100

PRT/100 = A - P

1500*6.49*T/100 = 1600 - 1500

1500*6.49*T = 100 *100

T = 10000 / 9735

T = 1.027 years

Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

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Answer: 30 and 5

Step-by-step explanation:

The exponential function is y=5.[tex]2^x[/tex].

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here the exponential function is [tex]y=ab^x[/tex]

Since (-3,5/8) is on the graph, -[tex]\frac{5}{8}[/tex]=[tex]ab^{-3}[/tex] -----> 1

Since (3, 40) is on the graph, 40=[tex]ab^3[/tex] ------> 2

So, [tex]\frac{ab^3}{ab^{-3}}=\frac{40}{\frac{-5}{8}}[/tex]

=> [tex]b^{3+3}=8\times8[/tex]

=> [tex]b^6=2^6[/tex]

=> b = 2

put b=2 into 2 then,

=> 40= [tex]a\times2^3[/tex]

=> 8a=40

=> a =5

Then the exponential function is y=5.[tex]2^x[/tex].

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The absolute value equation is:

|x - 15| = 0

We want an absolute value equation that only has the solution x = 15.

So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)

So the equation will be something like:

|x - a| = 0

And the solution is 15, so:

|15 - a | = 0

then a = 15

The equation is:

|x - 15| = 0

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subtract 3 from both sides to get

4x > 27

divide both sides by 4 to get

x > 27/4 or 6 3/4

We can use the procedures below to calculate what proportion of the original principal the overall amount of interest represents. This total amount of interest received corresponds to about 5.34% of the initial investment.

Divide the principal even by rate of interest, the time period, and other factors to arrive at simple interest. Simple return Equal principal + interests + hours is the marketing formula.The most typical technique to figure out interest is to use a portion of the principal sum. He would only pay his share of the 100% interest, for example, if somebody borrows $100 from the a partner and pledges to repay the loan with 5% interest. $x (0.05) = $5. When, you must pay interest.when you lend money after borrowing it and adding interest. Interest is often determined as an indicator of the overall of the loan total. The interest rate of the loan is the name given to this percentage.

Determine the total interest that was earned in Step 1.

It states that $33.75 was earned in interest overall.

Step 2: Determine the interest generated before to taxes.

The sum of the interest earned after tax can be determined by dividing the entire sum of the interest by (1 + rate of taxation), where the rate of tax is given as a decimal. Daniela was subject to a tax of 15% on the investment earnings. The tax rate in this instance is 15%, which really is equal to 0.15.

Interest gained before taxes is equal as $33.75 / (1 Plus 0.15), that results in a value of $29.35.

3. Determine the initial principal.

The $550 that Daniela first put into the CD is referred to as the original primary.

Compute the proportion of the initial principle in step four.

By dividing the sum of interest generated after tax by the original principal and multiplying the result by 100 as express it as a percentage, one can determine what proportion of the original principal the entire amount of interest represents.

(Interest paid before taxation / Original principal) / 100 equals the percentage of the original principal.

= ($possess / $550) w x 100

≈ 5.34%

Hence, the total interest earned is equivalent to roughly 5.34% of the initial capital.

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The value of x from the given figure is given as follows:

144º.

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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The given information and the transitive property of inequalities, we can prove that [tex]AC[/tex] is greater than [tex]EF[/tex] .

Statement Reason

[tex]BC = EF[/tex] Given

Betweenness Given

[tex]AC > BC[/tex] Given

[tex]AC > EF[/tex] Transitive property [tex](3, 1)[/tex]

Explanation:

[tex]BC = EF[/tex] Given: Given statement that BC is equal to EF.

Betweenness Given: Given statement that states the concept of betweenness, where BC is between AC and EF.

AC > BC Given: Given statement that  [tex]AC[/tex] is greater than BC.

[tex]AC > EF[/tex] Transitive property: Using the transitive property, we can conclude that  [tex]AC[/tex] is greater than EF (based on statement 3 and 1).

Therefore, using the given information and the transitive property of inequalities, we can prove that AC is greater than [tex]EF[/tex]  .

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