L = √36cm, A=

The 36cm is the length, but I don’t know how to find the Area. I’ve never had a question with that little symbol on it saying it’s a length

Therefore , the solution to the problem of Right angle triangle comes ou to be true for the expression m∠R > 90°,m∠S + m∠T < 90°,m∠R > m∠T andm∠R > m∠S

Three vertices and three sides make up a triangle, which is a polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to a 180 degree angle.

Here,

A triangle is RST.

Consequently, mR+mS+mT = 180° mS+mT = 180° - mR

m∠R > m∠S + m∠T is given.

"- m∠R" "- (m∠S + m∠T)" (by multiplying-1 on both sides)

By adding 180 degrees on both sides, the formula becomes 180°-m∠R and 180°-(m∠S + m∠T).

180 degrees - (m∠S + m∠T)

By adding m∠S + m∠T on both sides, the angle is 180°.

⇒ 2(m∠S+m∠T) < 180°

⇒ m∠S+m∠T < 90°

Due to the fact that m∠R+m∠S+m∠T = 180°, m∠R > 90°.

mR > m∠S + m∠T once more.

"m∠R > m∠S" and "m∠R > m∠T"

So, the first, second, fourth, and fifth choices are right.

It should be noted that m∠S = m∠T can only occur when m∠R=90° (but it is not given)

For this reason, m∠S = m∠T is incorrect.

Additionally, there is insufficient evidence to establish that m∠S > m∠T.

For this reason, m∠S > m∠T is also false.

Therefore , the solution to the problem of Right angle triangle comes ou to be true for the expression m∠R > 90°,m∠S + m∠T < 90°,m∠R > m∠T andm∠R > m∠S

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Answer:

A: m∠R > 90°

B: m∠S + m∠T < 90°

D: m∠R > m∠T

E: m∠R > m∠S

The solution to the system of linear equations using iterative methods is X1 = 2.24, X2 = 2.17, and X3 = 4.68.

To solve this system of linear equations using iterative methods, we can use the Gauss-Seidel method. Here are the steps:

1. Rearrange the equations so that each variable is on the left side and the constants are on the right side:

X1 = (26 - 2x2 - x3)/6
X2 = (24 - 2x1 + 2x3)/8
X3 = (30 - x1 + 2x2)/6

2. Make an initial guess for X1, X2, and X3. Let's use (0, 0, 0) as our initial guess.

3. Use the equations from Step 1 and plug in the initial guess for X1, X2, and X3 to get new values.

X1 = (26 - 2(0) - (0))/6 = 4.333
X2 = (24 - 2(0) + 2(0))/8 = 3
X3 = (30 - (0) + 2(0))/6 = 5

4. Use the new values for X1, X2, and X3 in the equations from Step 1 to get newer values.

X1 = (26 - 2(3) - (5))/6 = 2.167
X2 = (24 - 2(2.167) + 2(5))/8 = 2.125
X3 = (30 - (2.167) + 2(3))/6 = 4.556

5. Keep repeating step 4 until the values for X1, X2, and X3 stop changing significantly. Let's repeat step 4 one more time.

X1 = (26 - 2(2.125) - (4.556))/6 = 2.24
X2 = (24 - 2(2.24) + 2(4.556))/8 = 2.17
X3 = (30 - (2.24) + 2(2.125))/6 = 4.68

6. We can see that the values for X1, X2, and X3 are not changing significantly anymore. Therefore, the solution to the system of linear equations using iterative methods is X1 = 2.24, X2 = 2.17, and X3 = 4.68.

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Considering the situation described in the text, we have that:

In this problem, we consider that:

At the null hypothesis, we test if both groups have the same mean score, that is, the subtraction of the means is of 0, hence:

\(H_0: \mu_F - \mu_R = 0\)

At the alternative hypothesis, we test if students that did the test in freezing cold conditions performed better, that is, the subtraction is positive, hence:

\(H_1: \mu_F - \mu_R > 0\).

We have the comparison(subtraction) of two samples, and we have the standard deviation for each sample, not for the population, hence a two-sample t-test is used.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

When a graph is reflected about the x-axis, their x-intercept(s) are invariant point(s).

For y = 2x + 3, the x-intercept is -3/2.

Also the slope of the line graph when reflected about the x-axis will change from m to -m.

Therefore the new slope is -2.

We have y = -2x + c.

When x = -3/2, y = 0.

=> (0) = -2(-3/2) + c, c = -3.

Hence the answer is y = -2x - 3. (E)

After solving the values of x are 0,-2.

Given:

f(x)=2x+1 and g(x)=x^2 and f(g(x))=g(f(x))

f(x^2) = g(2x+1)

2(x^2) + 1 = (2x+1)^2

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

2x^2 + 1 = 4x^2 + 1 + 4x

4x^2 - 2x^2 + 4x = 1-1

2x^2 + 4x = 0

2x(x+2) = 0

2x = 0 and x+2 = 0

x = 0    and x = -2

Therefore After solving the values of x are 0,-2.

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Answer:

C = 2.75

Step-by-step explanation:

it does not tell how much there for it is 1 gallon

Answer:

no it is not

Step-by-step explanation:

you would have to get a common denominator which would be 60 so 12 times 5 is 60 and 20 times 3 is 60

then you multiply 4 by 3 and thats 12 and 3 times 5 is 15 so no they arent perportional

The transformation that would produce an image with vertices B"(-2, 1), C"(3, 2), D"(0, -1) from the original vertices B(-3,0), C(2, -1), D(-1, 2) is the transformation (x,y) → (X + 1, y + 1).

By applying the transformation (x,y) → (X + 1, y + 1), each point's x-coordinate is shifted one unit to the right (X = x + 1), and each point's y-coordinate is shifted one unit upward (Y = y + 1). This results in the image with the given coordinates B"(-2, 1), C"(3, 2), D"(0, -1).

The other transformations listed do not match the given image coordinates and would not produce the desired result.

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Answer:

(x, y) → (x, −y) → (x + 1, y + 1)

Step-by-step explanation:

Reflect the vertices over the x-axis by applying the transformation (x, y) → (x, -y):

B'(-3, 0) → B'(-3, 0)

C(2, -1) → C(2, 1)

D(-1, 2) → D(-1, -2)

Translate the reflected vertices by (1, 1):

B'(-3, 0) → B″(-3 + 1, 0 + 1) → B″(-2, 1)

C(2, 1) → C″(2 + 1, 1 + 1) → C″(3, 2)

D(-1, -2) → D″(-1 + 1, -2 + 1) → D″(0, -1)

So, the correct sequence of transformations is:

(x, y) → (x, -y) → (x + 1, y + 1)

(Image provided for more proof)

Answer:

Step-by-step explanation:

100.2 the ration  

Answer:

probably cold be the second one

Answer:

The addition property of equality is used to undo subtraction. The division property of equality is used to undo multiplication. Hope this helps!

Step-by-step explanation:

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer: -1

Step-by-step explanation:

Given by your question

2(3x-1)≥4x-6

Distributive property to take off the parentheses

2×3x-2×1≥4x-6

6x-2≥4x-6

Subtract 4x on both sides (Subtractive property of equality)

6x-2-4x≥4x-6-4x

2x-2≥-6

Add 2 on both sides (Addition property of equality)

2x-2+2≥-6+2

2x≥-4

Divide 2 on both sides (Division property of equality)

2/2 x≥-4/2

x≥-2

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

Looking at the options you've provided.

-10 INCORRECT, it is not greater or equal to -2

-5 INCORRECT, it is not greater or equal to -2

-3 INCORRECT, it is not greater or equal to -2

-1 CORRECT, it is greater than -2

Hope this helps!! :)

Please let me know if you have any question

x = - 1

2(3x – 1) ≥ 4x – 6

6x - 2 ≥ 4x - 6

6x - 4x ≥ 2 - 6

2x ≥ - 4

x ≥ - 2

x ∈ [ - 2 ; + oo )

x = - 1

The dimensions that will minimize the cost of 5920

Here is the process. Volume is the volume of a cylinder plus the volume of a sphere.

The surface area of a cylinder without the top and bottom plus twice the surface area of a spherical constitutes the cost of the material.

C = 2πrh + 2(4πr2)

Put what you discovered for h in this formula.

Consider Cost's derivative with regard to r. After that, zero out the derivative and find r.

Utilize the radius, r, value once you have it to solve for the height, h.

now,

V = πr2h + (4/3)πr3 = 5920

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Value of x for the given equation ( 1 / x) + ( 1 / 3x) = 4 is equal to x = 1/ 3.

As given in the question,

Given equation is equal to

( 1 / x) + ( 1 / 3x) = 4

Simplify the given equation to get the value of x

Take least common multiple of x and 3x

Least common multiple of x and 3x = 3x

( 3 + 1 ) / 3x = 4

⇒ 4 / 3x =4

Take like terms on the same side we get,

3x = 4 / 4

⇒ 3x = 1

⇒ x = 1 / 3

Therefore,  value of x for the given equation ( 1 / x) + ( 1 / 3x) = 4 is equal to x = 1/ 3.

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Lex will need approximately 18.96 units of tile to surround his pool. The perimeter of the quadrilateral is the sum of these lengths.

To find the number of units of tile Lex will need to surround his pool, we can calculate the perimeter of the quadrilateral ABCD.
Given the coordinates of the vertices on the coordinate plane, we can calculate the lengths of the sides:
AB = \(\sqrt((3-0)^2 + (5-4)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
BC = \(\sqrt((5-3)^2 + (-1-5)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
CD = \(\sqrt((2-5)^2 + (-2+1)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
DA = \(\sqrt((2-0)^2 + (-2-4)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
The perimeter of the quadrilateral is the sum of these lengths:
Perimeter = AB + BC + CD + DA = 3.16 + 6.32 + 3.16 + 6.32 = 18.96 units (rounded to the nearest hundredth)
Therefore, Lex will need approximately 18.96 units of tile to surround his pool.

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Lex will need approximately 20.46 units of tile to surround his pool. To find the number of units of tile needed to surround the pool, we need to calculate the perimeter of the pool.

Given the coordinates of the four vertices of the pool:
    A(0, 4)
    B(3, 5)
    C(5, -1)
    D(2, -2)

We can find the length of segment AB using the distance formula:
    \(AB = \sqrt{(3-0)^2 + (5-4)^2} = \sqrt{9 + 1} = \sqrt{10} = 3.16\)units (rounded to the nearest hundredth).

The length of diagonal BD can also be found using the distance formula:
    \(BD = \sqrt{(2-3)^2 + (-2-5)^2} = \sqrt{1 + 49} = \sqrt{50} = 7.07\) units (rounded to the nearest hundredth).

Since angles A and C are right angles, we know that the opposite sides AB and CD are parallel. Similarly, the opposite sides AD and BC are parallel.

The perimeter of the pool is the sum of the lengths of all four sides:
    Perimeter = AB + BC + CD + AD
                      = 3.16 + BD + 3.16 + BD
                      = 6.32 + 7.07 + 7.07
                      = 20.46 units (rounded to the nearest hundredth).

Therefore, Lex will need approximately 20.46 units of tile to surround his pool.

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Answer:

\(x = \pm 2\sqrt3\)

Step-by-step explanation:

Hello!

Let's use the square root property to solve this question

Solve:

The answer is option A: x = ±2√3

The probabilities are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of students in the problem is given as follows:

17 + 25 + 21 + 37 = 100.

Hence the probabilities are given as follows:

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a. the costs of non-compliance, enforcement, prevention and evaluation are -75 d/p, -$7500, $17500 and $5000 respectively

b. The percentage of effort devoted to each component is:

a) To calculate the costs of non-compliance, enforcement, prevention, and evaluation, we need to determine the deviations in effort for each component and multiply them by the corresponding cost per person-day.

Non-compliance cost:

Non-compliance cost = Actual effort - Predicted effort

To calculate the actual effort, we need to sum up the effort for each component mentioned:

Actual effort = Plan development + Software development + Reviews + Tests + Training + Methodology

Actual effort = 25 + 75 + 20 + 30 + 20 + 5 = 175 d/p

Non-compliance cost = Actual effort - Predicted effort = 175 - 250 = -75 d/p

Enforcement cost:

Enforcement cost = Non-compliance cost * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the enforcement cost:

Enforcement cost = -75 * $100 = -$7500 (negative value indicates a cost reduction due to underestimation)

Prevention cost:

Prevention cost = Predicted effort * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the prevention cost for each component:

Plan development prevention cost = 25 * $100 = $2500

Software development prevention cost = 75 * $100 = $7500

Reviews prevention cost = 20 * $100 = $2000

Tests prevention cost = 30 * $100 = $3000

Training prevention cost = 20 * $100 = $2000

Methodology prevention cost = 5 * $100 = $500

Total prevention cost = Sum of prevention costs = $2500 + $7500 + $2000 + $3000 + $2000 + $500 = $17500

Evaluation cost:

Evaluation cost = Total project cost - Prevention cost - Enforcement cost

Evaluation cost = $25000 - $17500 - (-$7500) = $5000

b) To calculate the percentage of effort devoted to each component out of the total cost, we can use the following formula:

Percentage of effort = (Effort for a component / Total project cost) * 100

Percentage of effort for each component:

Plan development = (25 / 250) * 100 = 10%

Software development = (75 / 250) * 100 = 30%

Reviews = (20 / 250) * 100 = 8%

Tests = (30 / 250) * 100 = 12%

Training = (20 / 250) * 100 = 8%

Methodology = (5 / 250) * 100 = 2%

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The explanatory variables spread out is desirable when testing hypotheses or constructing confidence intervals about β1 because it promotes the fulfillment of statistical assumptions, reduces multicollinearity issues, improves precision and reliability of estimates, and provides a more comprehensive understanding of the relationship between the explanatory variables and the response variable.

Desirability of spread out explanatory variables for testing hypotheses or constructing confidence intervals about β1:

It is desirable to have the explanatory variables spread out when testing a hypothesis regarding β1 or constructing confidence intervals about β1 in order to ensure the reliability and accuracy of the statistical analysis. A spread out distribution of explanatory variables helps to satisfy the assumptions of the statistical model and provides more information for estimating the slope coefficient (β1) with greater precision.

When testing a hypothesis or constructing confidence intervals about β1, one of the key assumptions is that the explanatory variables are not perfectly correlated with each other. This assumption is known as the assumption of multicollinearity. If the explanatory variables are highly correlated or too close together, it can lead to multicollinearity issues. Multicollinearity makes it difficult to isolate the individual effects of the variables and can result in unstable and unreliable estimates of β1.

By having the explanatory variables spread out, it helps to reduce the correlation among them and minimize the risk of multicollinearity. This improves the precision of the estimates and makes the hypothesis testing and confidence interval construction more reliable. When the explanatory variables are spread out, they provide a wider range of values, allowing for a better understanding of their relationship with the response variable and a more accurate estimation of β1.

Moreover, a spread out distribution of explanatory variables helps to capture a more comprehensive representation of the data and reduces the potential for bias in the estimation of β1. It provides a diverse set of observations that covers different ranges of the explanatory variables, enabling a more robust analysis and reducing the impact of outliers or extreme values.

In summary, having the explanatory variables spread out is desirable when testing hypotheses or constructing confidence intervals about β1 because it promotes the fulfillment of statistical assumptions, reduces multicollinearity issues, improves precision and reliability of estimates, and provides a more comprehensive understanding of the relationship between the explanatory variables and the response variable.

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five couples have reserved seats in a row for a concert, 3840 different ways can they be seated. So, using the concept of combination formula we get -

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

The formula becomes: \(^nC_r\)

Where n = total number of objects in the set.

r = number of choosing objects from the set

Given that,

there are five couples

These couples have reserved seats in a row for a concert.

So, arrangements of 5 couples can be done in 5! × 2⁵= 3840 ways.

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We assume that the population standard deviation are known, the samples from each population are independent, the population is normally distributed if we use t test of two samples.

Given T test of significance has been used.

T test is a statistical test that is like z test. Z test is used when n>30 and t test is used when n<30. It is used in hypothesis testing.

We know that there are many test which can be used to test a hypothesis.

The requirements to perform a two sample t procedure are as follows:

1)The two samples have equal variance. Hence the variance should be known.

2) The samples for which the two sample t procedure is performed must be independent.

3) The data are in alignment with the normal distribution probability.

4) The sample are random samples taken from different respective population.

Hence when two sample t procedure is performed we have to assume population standard deviation is known and population is normally distributed.

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The value of R100−L100, which is the difference of the Right Riemann sum and the Left Riemann sum using 100 rectangles to estimate the (signed) area under the function f(x)=7x on [0, 10], is 70.

To find the value of R100−L100, we need to calculate the Right Riemann sum and the Left Riemann sum separately and then take their difference.

The width of each rectangle is given by Δx = (b-a)/n = (10-0)/100 = 0.1, where n is the number of rectangles used.

The height of each rectangle for the Right Riemann sum is given by the value of f(x) at the right endpoint of the subinterval, which is x_i+1 = a + (i+1)Δx, where i = 0, 1, 2, ..., n-1.

Thus, the Right Riemann sum is given by:

R100 = f(x1)Δx + f(x2)Δx + ... + f(x100)Δx

= 7(0.1) + 7(0.2) + ... + 7(10)

= 7(0.1 + 0.2 + ... + 10)

= 7(0.1)(1 + 2 + ... + 100)

= 7(0.1)(5050)

= 3535

Similarly, the height of each rectangle for the Left Riemann sum is given by the value of f(x) at the left endpoint of the subinterval, which is x_i = a + iΔx, where i = 0, 1, 2, ..., n-1.

Thus, the Left Riemann sum is given by:

L100 = f(x0)Δx + f(x1)Δx + ... + f(x99)Δx

= 7(0) + 7(0.1) + ... + 7(9.9)

= 7(0 + 0.1 + ... + 9.9)

= 7(0.1)(0 + 1 + ... + 99)

= 7(0.1)(4950)

= 3465

Therefore, the difference between the Right Riemann sum and the Left Riemann sum is:

R100−L100 = 3535 - 3465 = 70

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Only the First Graph is a Graph of a Function

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

(i) Yes the 1st Graph is a graph of a function

Because, for every value of x there is an unique value of y

(ii) No the 2nd Graph is not a graph of a function

Because, there are two values of y associated with single value of x

(iii) No the 3rd Graph is not a graph of a function

Because, there are two values of y associated with single value of x

(iv) No the 4th Graph is not a graph of a function

Because, there are two values of y associated with single value of x

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Answer:

aₙ = 6aₙ - 18

Step-by-step explanation:

a₃ = 0, a₄ = 6, a₅ = 12, a₆ = 18, a₇ = 24...

aₙ = 6aₙ - 18

a₃ = (6 × 3) - 18 = 0

a₄ = (6 × 4) - 18 = 6

a₅ = (6 × 5) - 18 = 12

a₆ = (6 × 6) - 18 = 18

a₇ = (6 × 7) - 18 = 24

I hope this helps!

Answer:

7

Step-by-step explanation:

The ∠G and ∠J are congruent because they are bisector  angles.

ΔGHI and ΔJKL are congruent because of the similar triangle theorem.

When two lines in a plane do not cross at any point, they are said to be parallel. Thus, lines that never cross each other's paths and do not have a common junction point are said to be parallel.

From the given information, segments GH and JK are parallel and congruent and segments GL, LI, and IJ are congruent.

If we see the figure according to the statements,

The ∠G and ∠J are congruent because they are bisector  angles.

ΔGHI and ΔJKL are congruent because of the similar triangle theorem.

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Answer:

y = 0 , x = 1

Step-by-step explanation:

jdbdjdajhsbsbs

Answer:

Step-by-step explanation:

The graph has both a vertical and horizontal asymptote to which the value

of the function approaches as the y-values and x-values approaches

infinity respectively.

Reasons:

The horizontal asymptote is the horizontal line that the function's graph

tends towards as the value of the input variable approaches infinity.

The horizontal line that the graph of the function approaches is y = 0

Therefore;

Similarly, the vertical asymptote is the vertical line that the graph of the

function approaches but never meets.

Therefore;

The graph of the function on the bottom left approaches the line x = 1 from

the left, while the graph of the function with the domain 0 < x < ∞,

approaches the line x = 1 from the right.

Therefore;

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