Miguel has started training for a race. The first time he trains, he runs 0. 5 mile. Each subsequent time he trains, he runs 0. 2 mile farther than he did the previous time.


a) What is the arithmetic series that represents the total distance Miguel has run after he has trained n times?


b) A marathon is 26. 2 miles. What is the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon?

Answer:

23.4 ft tall

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given: Distance from the flagpole = 14 ft

Angle of elevation θ = 74.4°

To find: Length of the flagpole

Answer:

tan(74.4°) = [tex]\frac{L}{14}[/tex]

L = 14 tan(74.4°) = 50.142 ft

So the length of the pole is 50.142 ft.

Answer:

[tex]\boxed{The \ height \ of \ the \ tabletop \ is \ 63.5 \ centimeters}[/tex]

Step-by-step explanation:

We are given that,

Length of the base = 127 centimeters

Width of the base = 85 centimeters

Area of the trapezoid shaped base = 6,731 square centimeters.

Since, we know,

[tex]\bold{Area \ of \ a\ trapezoid}=\frac{Length +Width}{2}\times Height[/tex]  

So, we get,

[tex]6731=\frac{127+85}{2}\times Height[/tex]

i.e. [tex]6731=\frac{212}{2}\times Height[/tex]

i.e. [tex]6731=106\times Height[/tex]

i.e. [tex]Height=\frac{6731}{106}[/tex]

i.e. Height = 63.5 centimeters

Hence, the height of the tabletop is 63.5 centimeters.

Yes, the ordered pair (5,6) is a solution of the system of equations {(x+y=11),(x-y=-1):}.

To check if an ordered pair is a solution of a system of equations, we can plug the values of the ordered pair into the equations and see if they are true.

For the first equation, x + y = 11, we can plug in 5 for x and 6 for y:

5 + 6 = 11

This is true, so the ordered pair satisfies the first equation.

For the second equation, x - y = -1, we can again plug in 5 for x and 6 for y:

5 - 6 = -1

This is also true, so the ordered pair satisfies the second equation.

Since the ordered pair satisfies both equations, it is a solution of the system of equations.

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For the given square, m∠OKL=45° and m∠MOL=90°.

A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).

In mathematics, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.

Angle bisector points are equally spaced from both angle lines.

Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.

In the given square,

The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.

Therefore, ∠OKL= 90/2

                  ∠OKL=45°

We know that, in a square, diagonals are equal and bisect each other at right angles.

Therefore, ∠MOL=90°

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If the ground already has an elevation of  15 degree. The degree that the ladder need to be set is 65.4 degrees.

Angle at which the ladder is set from the horizontal =  x.

Angle between the ladder and the ground =  (75 - 15 + x) degrees

Using trigonometry, we can write the equation:

tan(75 - 15 + x) = 10 / L

where:

L=  length of the ladder.

Simplifying the left-hand side using the trigonometric identity for the tangent of the difference of two angles, we get:

tan(60 + x) = 10 / L

Multiplying both sides by L, we get:

L * tan(60 + x) = 10

Dividing both sides by tan(60 + x), we get:

L = 10 / tan(60 + x)

Using a calculator, we can evaluate the right-hand side to be:

L = 10 / tan(60 + x) ≈ 5.768 / tan(x)

So, the equation we need to solve for x is:

5.768 / tan(x) = L

Substituting the value of L obtained from the previous problem, we get:

5.768 / tan(x) = 2.68

Multiplying both sides by tan(x), we get:

5.768 = 2.68 tan(x)

Dividing both sides by 2.68, we get:

tan(x) ≈ 2.153

Using a calculator, we can find the value of x that satisfies this equation by taking the inverse tangent (tan^-1) of both sides:

x ≈ 65.4 degrees

Therefore, the ladder needs to be set at an angle of approximately 65.4 degrees from the horizontal in order to reach a height of 10 feet when the ground already has an elevation of 15 degrees and the ladder is placed at a 75-degree angle with the ground.

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The complete question is:

Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75 degree  to the ground . The ground already has an elevation of  15 degree. What degree does the ladder need to be set?

Step-by-step explanation:

To find the area of the rose garden, we need to find the sum of the areas of the rectangle and the semicircle.

Area of rectangle = length x width = 22 ft x 14 ft = 308 sq ft

Area of semicircle = (1/2) x pi x radius^2, where radius = diameter/2

The diameter of the semicircle is the width of the rectangle, which is 14 ft. So the radius is 7 ft.

Area of semicircle = (1/2) x 3.14 x 7^2 = 3.14 x 24.5 = 77.03 sq ft

Total area of rose garden = area of rectangle + area of semicircle

= 308 sq ft + 77.03 sq ft

= 385.03 sq ft

Therefore, the area of the rose garden is 385.03 square feet.

Three rational expressions that simplify to (x)/(x+1) are:

1) (x+2-2)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1)
3) (3x+5-5-2x)/(x+2+1-2)

To simplify these expressions, we can combine like terms in the numerator and denominator:

1) (x+2-2)/(x+1) = (x)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1) = (-x+3)/(-x+3) = (x)/(x+1)
3) (3x+5-5-2x)/(x+2+1-2) = (x)/(x+1)

As shown, all three expressions simplify to (x)/(x+1), fulfilling the requirements of the question.

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To find the determinant of the given 5x5 matrix A, we need to convert it into an upper triangular form.

This means that all the values below the diagonal elements should be 0. Once we have the upper triangular form, we can find the determinant by taking the product of the diagonal elements.

To convert the given matrix into an upper triangular form, we can use elementary row operations. We can subtract multiples of the first row from the other rows to make the values below the first element 0. Then we can do the same for the second row, third row, and so on until we have an upper triangular matrix.

Once we have the upper triangular matrix, we can find the determinant by taking the product of the diagonal elements. The determinant of the given matrix A is the product of the diagonal elements of the upper triangular matrix.

So the steps to find the determinant of the given matrix A are:
1. Convert the given matrix into an upper triangular form using elementary row operations.
2. Take the product of the diagonal elements of the upper triangular matrix to find the determinant.

By following these steps, we can find the determinant of the given 5x5 matrix A.

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The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.

Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.

Therefore, the correct answer is option b. Ordinal data.

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By algebra properties, the factor form of polynomials are listed below:

In this problem we need to factor 13 cases of polynomials, whose results must be derived by algebra properties. The factor form of the polynomial is:

Case 1:

a² - b²

(a + b) · (a - b)

Case 2:

a³ + b³

(a + b) · (a² - a · b + b²)

Case 3:

a³ - b³

(a - b) · (a² + a · b + b²)

Case 4:

x⁴ - 36

(x² + 6) · (x² - 6)

(x² + 6) · (x + √6) · (x - √6)

Case 5:

64 · c³ + 1

(4 · c + 1) · (16 · c² - 4 · c + 1)

Case 6:

k³ - 27

(k - 3) · (k² + 3 · k + 9)

Case 7:

54 · x³ + 250 · y³

(∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²]

Case 8:

3 · m⁴ - 48 · n²

(√3 · m² - 4√3 · n) · (√3 · m² + 4√3 · n)

3 · (m² - 4 · n) · (m² + 4 · n)

3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n)

Case 9:

a⁷ · b² - a · b²

a · b² · (a⁶ - 1)

a · b² · (a³ + 1) · (a³ - 1)

a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1)

Case 10:

x³ · y² - 343 · y⁵

y² · (x³ - 343 · y³)

y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²)

Case 11:

9 · y⁷ - 144 · y

y · (9 · y⁶ - 144)

y · (3 · y³ - 12) · (3 · y³ + 12)

9 · y · (y³ - 4) · (y³ + 4)

9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²]

Case 12:

w² - 13 · w + 36

(w - 4) · (w - 9)

Case 13:

p³ + 5 · p² - 84 · p

p · (p² + 5 · p - 84)

p · (p + 12) · (p - 7)

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Therefore, the distance from the center of the circle to the crossing point of the two strings is 40sqrt(2) cm, or approximately 56.57 cm to two decimal places.

The Pythagorean theorem can be used to calculate the distance between the circle's centre and where the two strings cross. Let A and B represent the spots where the threads converge, with O serving as the circle's centre. Next, we have:

OA2 plus OB2 equals AB2.

The circle's radius being equal to half the separation between the two strings, we get:

The equation OA = OB = sqrt((560/2)2 + (640/2)2) (156800)

And because the circle's diameter is twice its radius, we get the following equation: AB = 2 * radius = 2 * 360 = 720.

Now that we have the values, we can calculate:

2 * (156800) = AB2 => 2 * (156800) = 7202 => 313600 = 518400 - 2 * OA2 => OA2 = 102400 / 2 => OA = sqrt(51200) => OA = 40sqrt (2)

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Measure of angles ∠Q,∠T,∠R are 98°, 98°, 82° respectively.

An isosceles trapezoid can be defined as a trapezoid whose non-parallel sides and base angles have the same measure. That is, if the two opposite sides (bases) of a trapezoid are parallel and the two non-parallel sides are of equal length, it is an isosceles trapezoid.

Given,

Isosceles trapezoid QRST

m∠S = 82°

Base angles are equal in Isosceles trapezoid

m∠R = m∠S

m∠R = 82°

and

m∠Q = m∠T

Sum of all interior angles of a quadrilateral is 360°

m∠Q + m∠T + m∠R + m∠S = 360°

m∠Q + m∠Q + 82° + 82° = 360°

2 m∠Q = 360° - 164°

2 m∠Q = 196°

m∠Q = 98°

m∠T = 98°

Hence, 98°, 98°, 82° are measure of angles ∠Q,∠T,∠R respectively.

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-14w + 35  is the  simplified answer of  (2w-5)(-7).

The distributive property states that for two numbers a and b, a(b+c) = ab + ac. This means that multiplying a number by a sum is the same as multiplying each number in the sum by the original number.

To simplify the expression (2w-5)(-7) using the distributive property, we need to multiply each term inside the parentheses by -7.

The distributive property states that a(b + c) = ab + ac. In this case, a = -7, b = 2w, and c = -5.

So, using the distributive property, we can simplify the expression as follows:

(2w-5)(-7) = (-7)(2w) + (-7)(-5)

= -14w + 35

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Answer:

the first one:  1:39

the second one: 7:12

the third one: 10:24

Step-by-step explanation:

the short hand points to the hour and the long hand points to the minutes. when the long hand is at 1, that's 5 minutes and when it's at 2, that's 10 minutes and so on and so forth. and each of the little dash marks in between the numbers is 1 minute.

i hope this was correct, i'm not great with time

Question 1:

Question 2:

Question 3:

Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.

To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:

There were n1 squirrels in the first group.

Second sample's fox count is equal to n2.

Second sample's total number of labelled squirrels is m2.

The following provides the Lincoln-Petersen index:

=> n1 * n2 / m2

Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.

=> n1 * n2 / m2 = 100 * 200 / 20 = 1000

Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.

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A \times B \times C = \left[\begin{array}{ll} -40 & -60 \\ -68 & 70 \\ 6 & 0 \end{array}\right]

To find the product of the matrices A, B and C, we can use the following equation:



$$A \times B \times C = \left[\begin{array}{lll} (A \times B)_{11} & (A \times B)_{12} & (A \times B)_{13} \\ (A \times B)_{21} & (A \times B)_{22} & (A \times B)_{23} \\ (A \times B)_{31} & (A \times B)_{32} & (A \times B)_{33} \end{array}\right] \times C = \left[\begin{array}{ll} (A \times B \times C)_{11} & (A \times B \times C)_{12} \\ (A \times B \times C)_{21} & (A \times B \times C)_{22} \\ (A \times B \times C)_{31} & (A \times B \times C)_{32} \end{array}\right]$$



To find each element of the product, we use the following equation:



$$(A \times B \times C)_{ij} = \sum_{k=1}^{3} A_{ik} \times B_{kj} \times C_{ij}$$



Where $i$ and $j$ represent the row and column numbers respectively. For example, to find the element $(A \times B \times C)_{11}$, we have:



$$(A \times B \times C)_{11} = \sum_{k=1}^{3} A_{1k} \times B_{k1} \times C_{11} = (-5 \times -8 \times -4) + (1 \times 7 \times -4) + (-7 \times 5 \times -4) = -40$$



Therefore, the product of A, B and C is:



$$A \times B \times C = \left[\begin{array}{ll} -40 & -60 \\ -68 & 70 \\ 6 & 0 \end{array}\right]$$

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Answer:

Step-by-step explanation:

Ratio of corresponding sides are equal.

[tex]\tt \cfrac{BD}{FD} =\cfrac{AC}{EC}[/tex]

[tex]\tt \cfrac{BC}{30} =\cfrac{16}{40}[/tex]

[tex]\tt BD=30\left(\frac{2}{5}\right)[/tex]

[tex]\tt BC=6\cdot \:2[/tex]

[tex]\tt BD =12[/tex]

Therefore, the length of BD is 12.

___________________________

Hope this helps! :)

Answer:

1/  24 bottle of water for $3 is a better buy

2/ $0.045

Step-by-step explanation:

12 bottles of water for $2

2 / 12 =$0.17

So, it costs $0.17 for each bottle of water.

24 bottles of water for $3

3 / 24 = $0.125

So, it costs $0.125 for each bottle of water.

0.17 - 0.125 = $0.045

So, 24 bottles of water for $3 is a better buy by $0.045

Vοlume οf the Pyramid is 21 cm³

A prism is a sοlid shape with twο identical parallel bases and flat sides that cοnnect the bases. The sides οf a prism are usually rectangles, but they can alsο be triangles οr οther pοlygοns.

A pyramid is a sοlid shape with a pοlygοnal base and triangular sides that meet at a single pοint called the apex.

When a prism have same base area and height as that οf a pyramid the vοlume οf the prism is three times that οf the pyramid.

=> Vοlume οf prism = 3 Vοlume οf pyramid

Here we have

The prism and pyramid abοve have the same width, length, and height.  

The vοlume οf the prism is 63 cm³  

As we knοw,

Vοlume οf prism = 3 Vοlume οf pyramid

The vοlume οf the Pyramid = [ Vοlume οf prism ]/ 3

= [ 63 cm³]/3 = 21 cm³  

Therefοre,

Vοlume οf the Pyramid is 21 cm³

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The probability of choosing the lists of students from the class is given by combinations C = 2400 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the total ways of choosing the students from the class be C

Now , the total number of boys = 12 boys

The total number of girls = 10 girls

And , the lists are in the order

A = { boy , girl , boy }

B = { girl , boy , girl }

The total number of ways C = A + B

From the combination of selecting boys and girls , we get

The total number of selecting A = 12 x 10 x 11 = 1320 ways

The total number of selecting B = 10 x 12 x 9 = 1080 ways

So , the total number of selecting the lists C = 2400 ways

Hence , the probability of choosing the lists of students from the class is given by C = 2400 ways

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Benito and his family will save $1,315 by the move to Oakland.

Savings in house = $1200 - $565

                               = $635

Savings in food = $655 - $545

                          = $110

Saving in health care = $495 - $245

                                   = $250

Saving in taxes  = $625 - $450

                          = $175

Saving in necessities = $495 - $350

                                   = $145

Total saving = $635 + $110 + $250 + $175 + $145

                    = $1,315.

Hence, Benito and his family will save $1,315 by the move to Oakland.

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Your question is incomplete, the complete question is:

Benito's family is thinking of relocating from Los Angeles to Oakland to save money. They set up a budget comparing the cost of living for both cities.

Oakland     Los Angeles  

Cost Housing       $565        $1200

Food                     $545        $655

Health Care         $245        $495

Taxes                    $450         $625

Other Necessities $350        $495

How much money will they save monthly by the move to Oakland? $1315, $1560, $1665, or $1765?

The division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials is 400 tons ÷ (1,000 tons + 400 tons + 200 tons) = 25%.

The total weight of the bridge's materials is the sum of the weight of concrete, steel structure, glass, and granite, which is:

1,000 tons + 400 tons + 200 tons = 1,600 tons

Simplifying the expression by dividing both numerator and denominator by 400 tons gives:

Weight of steel structure / Total weight of bridge's materials = [tex]\frac{1}{4}[/tex]

Weight of steel structure / Total weight of bridge's materials

[tex]= \frac{400 tons}{1,000 tons + 400 tons + 200 tons}[/tex]

[tex]= \frac{400 tons}{1,600 tons}[/tex] = 0.25

Therefore, the weight of the steel structure is one-fourth (or 25%) of the total weight of the bridge's materials.

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The complete question is:

Write a division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials. Concrete weighs 1,000 tons, Steel structure weighs 400 tons and glass and granite weighs 200 tons.

Because it only covers those who are entering the sports centre, the survey will be prejudiced.

This means that the survey will only reflect the opinions of those who are likely to have positive perceptions of the sports facilities and who are interested in using them. It does not include the viewpoints of those who do not use or hold a poor opinion of the sporting facilities.

Those who don't use the facilities, for instance, could have bad perceptions of the sports centre if it is renowned for being pricey or challenging to get to. The survey will miss important information if it simply polls visitors to the sports centre.

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The percentage that is less than the average number of shoppers in the original store at any time is 60%.

Little's law is a fundamental principle in queueing theory that relates the average number of customers in a stable system to the average time that a customer spends in the system.

The law states that the average number of customers N in the system is equal to the average rate of customer arrivals r multiplied by the average time W that a customer spends in the system:

Here we have

For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes.

=> Number of shoppers per minute = 1.5    

=> Rate of shoppers per minute = 1.5

The manager estimates that each shopper stays in the store for an average of 12 minutes.

Hence, by Little’s law, the number of shoppers N = r × t

=> Number of shoppers = (1.5) × 12 = 18  

Let the estimated average number of shoppers in the original store at any time be 45.    

So, the number of shoppers is (45 - 18) less than the original i.e 27

Percentage  [ 27/45 ] × 100 = 60%  

Therefore,

The percentage that is less than the average number of shoppers in the original store at any time is 60%.

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The average percentage of time spent studying is 8.64%.

To find the average percentage of time spent studying, we need to first add up the total hours and total percentage of all the students. Then, we can divide the total percentage by the total hours to find the average percentage of time spent studying.

Total hours = 18 + 10 + 2 + 6 + 8 = 44 hours
Total percentage = 100% + 80% + 50% + 70% + 80% = 380%

Average percentage = Total percentage / Total hours = 380% / 44 hours = 8.64%
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Complete question

Find the average percentage of time spent on studying. data. Nina: 18 hours, 100%; Johannes: 10 hours, 80%; Al-Rahim: 2 hours, 50%; Caroline: 6 hours, 70%; Saul: 8 hours, 80%

Given that there was no test this week (X0 = 0), the probability that there is a test in two weeks time (X2 = 1 or X2 = 2) is given by the sum of the probabilities of the two possible states in the two-step transition probability matrix:
P(X2 = 1 or X2 = 2|X0 = 0) = P^2[0][1] + P^2[0][2] = 0.36 + 0.12 = 0.48

To compute P(X5 = 2|X3 = 1, X1 = 0), we can use the formula for conditional probability:
P(X5 = 2|X3 = 1, X1 = 0) = P(X5 = 2, X3 = 1, X1 = 0)/P(X3 = 1, X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)*P(X1 = 0)/P(X3 = 1|X1 = 0)*P(X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)/P(X3 = 1|X1 = 0)
= P(X5 = 2|X3 = 1)
= P²[1][2]
= 0.12

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The solutions for the equation 6x²-11x-7=0 are x = -1/2 and x = 7/3

It is important to note that quadratic equations are defined as equations having the highest degree of x as 2.

From the information given, we have that the quadratic equation is given as;

6x²-11x-7=0

Now, multiply the coefficient of x squared with the constant value, then find the pair factors of the product that adds up to given the coefficient of x = -11

We have;

6x² - 14x + 3x - 7 =0

Group the expression in pairs

(6x² - 14x) + (3x - 7) = 0

Factor the expressions

2x(3x - 7) + 1(3x - 7) = 0

Then, we have;

(2x + 1) and (3x - 7) = 0

x = -1/2

x = 7/3

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If FG = 8, EH = x - 1: EG = x + 1​

In order to find EG, we need to use the fact that the sum of the lengths of the segments EF and FG is equal to the length of segment EG. That is,

EF + FG = EG

We are given that FG = 8, and we know that EH + HF = EF. Therefore,

EF = EH + HF

Putting this all together, we get:

EF + FG = EG

(EH + HF) + 8 = x + 1

EH + HF = x - 7

But we also know that EH = x - 1, so we can substitute that in:

x - 1 + HF = x - 7

Simplifying this equation, we get:

HF = -6

Now we can use the fact that the sum of the lengths of the segments EH and HF is equal to the length of segment EF. That is,

EH + HF = EF

(x - 1) + (-6) = EF

x - 7 = EF

Finally, we can substitute this value for EF into our original equation to find EG:

EF + FG = EG

(x - 7) + 8 = EG

x + 1 = EG

Therefore, EG = x + 1.

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Answer:

Yes, the triangle is right-angled since one of the angles is 90°

Step-by-step explanation:

The sum of the three angles of a triangle must add up to 180°

Here the three angles are 3x – 7, 4x – 1, and 5x + 20.

Adding them up gives

3x – 7 + 4x – 1 + 5x + 20 = 180

Grouping like terms:
3x + 4x + 5x - 7 - 1 + 20 = 180

12x + 12 = 180

12x = 180 - 12 = 168

x = 168/12 = 14

Substituting this value of x into each of the expressions:
3x – 7  = 3(14) - 7 = 42 - 7 = 35°

4x – 1 = 4(14) - 1 = 56 - 1 = 55°

5x + 20 = 5(14) + 20 = 70 + 20 = 90°

Since one of the angles is 90° it is indeed a right angled triangle