A food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets. Should she park her truck on a perpendicular bisector, and angle bisector, a median, or an altitude

Answer:

Explanation:

The information given can be summarized as:

Interpetration of the terms in the model A = -2.3t - 7

The equation A = -2.3t - 7 is a linear function, which consists of two terms:

Thus, altitude at which Mr. Mole's burrow lie is the initial value given by the function, this is the altitude at t = 0, or the vertical intercept of the line; which, as just said is - 7. The negative sign tells that the value is below the ground (ground level is 0 meters). Then, Mr. Mole's burrow lie 7 meters below the ground.

Mr. Mole's burrow lies 7 meters below the ground which is represented by the equation  A = -2.3t - 7.

Given that:

The altitude of Mr. Mole's burrow can be calculated by determining the equation A = -2.3t - 7, where A represents the altitude in meters and t represents time in minutes.

The coefficient of t is -2.3, which shows that the altitude is decreased by 2.3 meters for every minute that passes.  At t = 0, the constant term is -7, which represents an initial altitude of -7 meters.

Since Mr. Mole is digging downward and wants to find how far below the ground his burrow lies, we will consider the absolute value of the altitude.

The absolute value of the altitude, which is the distance below the ground, is: |A| = 2.3t + 7

The distance below the ground increases by 2.3 meters for every minute that passes and there's an initial distance of 7 meters below the ground.

Therefore, Mr. Mole's burrow lies 7 meters below the ground.

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Answer:he invested $12000 in bonds and $8000 in stocks.

Step-by-step explanation:

Let x represent the amount that was invested in the bond that made 4% profit.

Let y represent the amount that was invested in the stock that made 8% profit.

Francis invested $20,000. Some was invested in bonds that made a 4% profit, and the rest was put into stocks that made an 8% profit. This means that

x + y = 20000

Profit made from the amount invested in the bond is

4/100 × x = 0.04x

Profit made from the amount invested in stock is

8/100 × y = 0.08y

if his total profit on both types of investments was $1,120, it means that

0.04x + 0.08y = 1120 - - - - - - - - - - 1

Substituting x = 20000 - y, it becomes

0.04(20000 - y) + 0.08y = 1120

800 - 0.04y + 0.08y = 1120

- 0.04y + 0.08y = 1120 - 800

0.04y = 320

y = 320/0.04 = 8000

x = 20000 - y = 20000 - 8000

x = $12000

Francis invested $12,000 in bonds.

Let's denote the amount invested in bonds as B and the amount invested in stocks as S.

We can set up a system of equations based on the given conditions:

1. B + S = 20,000  (Equation 1) - Total investment amount

2. 0.04B + 0.08S = 1,120  (Equation 2) - Total profit

We can solve this system of equations to find the amount invested in bonds B.

From Equation 1, we can express S in terms of B:

S = 20,000 - B

Now, substitute this expression for S into Equation 2:

0.04B + 0.08(20,000 - B) = 1,120

Let's solve for B:

0.04B + 1,600 - 0.08B = 1,120

-0.04B = 1,120 - 1,600

-0.04B = -480

Now, divide both sides by -0.04:

[tex]\[B = \frac{-480}{-0.04} \][/tex]

B = 12,000

So, Francis invested $12,000 in bonds.

Answer:

10in²

Step-by-step explanation:

5π/4 is 62.5% of a circle if you look at the unit circle.

So just find the area of a circle and take 62.5% of it.

A = πr²

A = π(4)²

A = 16π

16π(.625) = 10

Answer:

The answer to your question is  0.83 or 83%

Step-by-step explanation:

Data

5 red marbles

10 blue marbles

14 yellow marbles

Process

1.- Calculate the total amount of marbles

    Total amount = 5 red + 10 blue + 14 yellow

     Total amount = 29 marbles

2.- Calculate the amount of marbles that are not red

     No red marbles = 10 + 14

                                = 24 marbles

3.- Calculate the probability

Probability of not pulling a red marble = [tex]\frac{no red marble}{total amount of marbles}[/tex]

Probability of not pulling a red marble = [tex]\frac{24}{29} = 0.83 or 83%[/tex]

Answer:

Recursive formula for geometric sequence

[tex]a_{n}=a_{n-1}\times r[/tex]

is [tex]a_{n}=a_{n-1}\times 6[/tex]

and explicit formula for geometric sequence [tex]a_{n}=a_{1}^{r-1}[/tex] is

[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]

Step-by-step explanation:

Given sequence is [tex]\frac{1}{2},3,18,108,648,...[/tex]

To find the recursive and explicit formula for this sequence:

Let [tex]a_{1}=\frac{1}{2},a_{2}=3,a_{3}=18,a_{4}=108,a_{5}=648,...[/tex]

To find the common ratio r:

[tex]r=\frac{a_{2}}{a_{1}}[/tex]

[tex]=\frac{3}{\frac{1}{2}}[/tex]

[tex]=3\times 2[/tex]

[tex]=6[/tex]

Therefore r=6

[tex]r=\frac{a_{3}}{a_{2}}[/tex]

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

[tex]=6[/tex]

Therefore r=6

Therefore the common ration r=6

Therefore the given sequence is geometric sequence

Recursive formula for geometric sequence is [tex]a_{n}=a_{n-1}\times r[/tex]

[tex]a_{n}=a_{n-1}\times 6[/tex]

and explicit formula is [tex]a_{n}=a_{1}^{r-1}[/tex]

[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]

[tex]=(\frac{1}{2})^{5}[/tex]

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

Therefore [tex]a_{n}=\frac{1}{32}[/tex]

Answer:

Recursive: a(n) = 6a(n-1)

Explicit: a(n) = (6^n)/12

Step-by-step explanation:

3 = 6 × ½

18 = 6 × 3

.

.

.

Recursive formula:

a(n) = 6a(n-1)

Explicit:

a(n) = a × r^(n-1)

a(n) = ½ × 6^(n-1)

a(n) = (6^n)/12

Answer:

  D:  2/4

Step-by-step explanation:

Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:

  BC : CD = 2 : 2 = 1 : 1

Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.

__

None of the segments is 3 units long, so neither of answer choices A or B makes any sense.

While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.

There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.

Answer: 1. True

Step-by-step explanation:

Given : D = {x|x is a whole number}  = { 0, 1 , 2, 3, 4, 5, ..................}

E = {x|x is a perfect square between 1 and 9} = {4 }

F = {x|x is an even number greater than or equal to 2 and less than 9} ={4 , 6 , 8}

Since intersection of sets contains all the values they have common.

Then, E ∩ F= {4}

Now , D∩ (E ∩ F) =  { 0, 1 , 2, 3, 4, 5, ..................} ∩ {4} = {4}

Hence , The number 4 is D ∩ (E ∩ F).

Thus , the given statement is 1 . true.

Answer:they would meet at 1 pm

Step-by-step explanation:

The distance between Quebec City and New York City is 520 miles.

At the point where Kate and Will meet, they would have travelled 520 miles.

Let t represent the time it takes Kate to travel a certain distance before they met.

Distance = speed × time

If Kate drives at 55mph, the distance covered would be

55 × t = 55t.will drives at 75 mph

Since Will left same that that Kate left, distance travelled by Will in t hours would be

75 × t = 75t

Since the total distance covered is 520 miles, it means that

55t +75t = 520

130t = 520

t = 520/130 = 4

9 am + 4 hours = 1 pm

Answer:

  1 pm

Step-by-step explanation:

Their combined speed is 55 + 75 = 130 miles per hour. That is the rate at which the distance between them is decreasing. The time it takes for the distance between them to become zero is found from the relation ...

  time = distance/speed

  time = (520 mi)/(130 mi/h) = 4 h

4 hours after 9 am, Kate and Will will meet. That time is 1 pm.

Answer:

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5

Step-by-step explanation:

We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use  Y for the derivative of y . Therefore, we calculate and we get

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5

Step-by-step explanation:

Say y=ax+b. It goes through (0,8) and (4,0). Therefor we can say 8=a(0)+b which gives us b=8. Then we fill in (4,0) which results in 0=a(4)+8. Given that, a=-2. so y=-2+8

Final answer:

The equation of the line that passes through points (0, 8) and (4, 0) is y = -2x + 8. The slope is calculated as -2 and the y-intercept is 8.

Explanation:

To find the equation of a line passing through two points, we can use the formula y = mx + b where m is the slope of the line and b is the y-intercept. The slope m is calculated by the change in y over the change in x, also known as rise over run. For the points (0, 8) and (4, 0), the slope is calculated as (0 - 8)/(4 - 0) which simplifies to -2. Thus, the slope m is -2.

Since the line passes through the point (0, 8), we already know the y-intercept b; it is 8. Now, we can write the equation of the line using the slope we found and the y-intercept: y = -2x + 8.

Answer:

B. Negative 80 x + 28 y minus 56

This is equivalent to -80x + 28y - 56

C. 4 (negative 20 x + 7 y minus 14)

This is equivalent to -80x + 28y - 56

Step-by-step explanation:

Let's find out the options that are equivalent to:

8 (negative 10 x + 3.5 y minus 7)

8 ( - 10x + 3.5y - 7) =

-80x + 28y - 56

Options:

A. Negative 80 x + 24.5 y minus 56

This is not equivalent.

B. Negative 80 x + 28 y minus 56

This is equivalent to -80x + 28y - 56

C. 4 (negative 20 x + 7 y minus 14)

-80x + 28y - 56

This is equivalent to -80x + 28y - 56

D. Negative 4 (negative 20 x + 7 y minus 14)

80x - 28y + 56

This is not equivalent.

Answer:

B. Negative 80 x + 28 y minus 56

This is equivalent to -80x + 28y - 56

C. 4 (negative 20 x + 7 y minus 14)

Step-by-step explanation:

Based on the provided conditional statements, if Trisha is drinking water, then it's dinnertime. Additionally, if it's dinnertime, then Anna is drinking iced tea. Given that Trisha is drinking water, we can conclude that Anna is drinking iced tea.

The question here is dealing with conditional statements in logic. It's important to understand that if a conditional statement is true, and the first part (the condition) is true, then the second part must be true as well. In this case, Statement A states that if Trisha is drinking water, then it is dinnertime. So, if Trisha is drinking water (which is confirmed by Statement E), then it is dinnertime.

Statement C further adds to our understanding by stating that if it is dinnertime, then Anna is drinking iced tea and nothing else. Since based on Statements A and E, we know it is dinnertime, then following the logic from Statement C, we can conclude that Anna is drinking iced tea.

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Answer:

$1 coin is 23

$2 coin is 14

Step-by-step explanation:

We need to form mathematical equations that we can solve from this Long citation.

Firstly, let the numbers of $1 coins be a and that of $2 be b.

We know that there are 37 coins. Hence

a + b = 37

Now, total is 51 Canadian dollars.

a + 2b = 51

Let’s now solve this simultaneously

From 2 , a + b + b = 51

Let’s say this is 3. Now substitute 1 into 3.

37 + b = 51, b = 51 - 37 = 14

Since a + b = 37

a = 37 - 14 = 23

Answer:

The answer to your question is 32.64°

Step-by-step explanation:

Data

hypotenuse = 19

adjacent side = 16

x = ?

Process

1.- To solve this problem use trigonometric functions.

The function that relates the adjacent side and the hypotenuse is cosine.

      cos x = [tex]\frac{adjacent side}{hypotenuse}[/tex]

2.- Substitution

      cos x = [tex]\frac{16}{19}[/tex]

3.- cos x = 0.842

4.- cos ⁻¹x = x = 32.64°

Answer:

For Plato users the Answer is C

Step-by-step explanation:

Final answer:

Raymond will earn a total of $2.00 in interest over 2 years on his $10.00 savings account with a non-compounding 10% annual interest rate, as he receives the same amount of interest each year.

Explanation:

To calculate the interest Raymond earns in 2 years on his $10.00 savings at a 10% annual interest rate, where the interest is not compounded, we can follow these steps:

In 2 years, he will earn $1.00 (year 1) + $1.00 (year 2), which equals $2.00 in interest.

In conclusion, Raymond will earn $2.00 in interest over 2 years on his $10.00 savings account with a 10% annual interest rate.

Answer:

50?

Step-by-step explanation:

Answer:

Step-by-step explanation:

As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).

Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.

Final answer:

The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.

Explanation:

The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.

For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.

Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.

Answer:

B

Step-by-step explanation:

x>4

Answer:

None of the options are right. The correct answer is x < 4

Step-by-step explanation:

2(x + 1) > 3x - 2

2x + 2 > 3x - 2

2 > x - 2

4 > x

x < 4

Answer: avoid passing through the vein.

Step-by-step explanation:

Answer:

Convenience  Sampling

Step-by-step explanation:

The given situation indicates the non-probability sampling because the sampling units are not selected at random and every unit in population has unequal chance of being selected. Convenience sampling is a type of non-probability sampling in which the sampling unit close to interviewer are selected. In the situation statistics student interviews the individual that resides in his building, so it is a convenience sampling.

Final answer:

The statistics student used convenience sampling, a non-probability method, by interviewing individuals in his apartment building to determine cell phone ownership. This method is subject to sampling bias and does not provide generalizable results.

Explanation:

The type of sampling used in the scenario where a statistics student interviews everyone in his apartment building to determine who owns a cell phone is called convenience sampling. This non-probability sampling method involves choosing participants because they are convenient to the researcher, not because they are randomly selected or necessarily representative of the larger population. Therefore, while it is easy and cost-effective, the results of convenience sampling cannot be reliably generalized to the wider population due to potential sampling bias.

The phytoplankton population will be double the foraminifera population at the end of the first day. It'll take approximately 6.44 days for the phytoplankton population to be 1000 times the foraminifera population.

To solve this problem, we'll need to figure out the exponential growth rate for each organism. As per the question, phytoplankton doubles its population twice a day and the foraminifera doubles every five days.

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Final answer:

To find when the phytoplankton population is double that of the foraminifera, we solve the equation 2^(t/5) = 2^(2t-1), yielding approximately 1.67 days. To find when the phytoplankton population is 1000 times the foraminifera population, we solve 1000 × 2^(t/5) = 2^(2t), resulting in approximately 5.95 days.

Explanation:

To solve this problem, we use the formula for exponential growth: N(t) = N_0 × 2^(t/T), where N(t) is the population at time t, N_0 is the initial population, and T is the doubling time. For phytoplankton with a doubling time of 0.5 days, we have N_p(t) = N_0 × 2^(2t), because they double twice a day. For foraminifera, which double every 5 days, we have N_f(t) = N_0 × 2^(t/5).

Part A

To find when the phytoplankton population is double the foraminifera population, we set 2N_f(t) = N_p(t) and solve for t. This gives us 2 × N_0 × 2^(t/5) = N_0 × 2^(2t). Canceling N_0 and dividing by 2, we get 2^(t/5) = 2^(2t-1), thus t/5 = 2t-1. Solving for t gives us t = 5/3 days, or approximately 1.67 days.

Part B

To determine when the phytoplankton population is 1000 times the foraminifera population, we set 1000N_f(t) = N_p(t). Solving for t in 1000 × N_0 × 2^(t/5) = N_0 × 2^(2t) and simplifying, we find that t = 5 × log2(1000)/3, which is about 5.95 days.

Answer:

C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.

Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.

Step-by-step explanation:

The sample mean obtained was :

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}= 144.3[/tex]

A. The given value is a parameter parameter for the year year because the data collected represent a population population.

False. The data colected represent a sample of the population of interest, so for this case is not a parameter because we don't have the information about all the population of interest.

B. The given value is a parameter parameter for the year year because the data collected represent a sample sample.

False. First the sample average is not a parameter, and second the population mean is not equal to the sample mean most of the times.

C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.

Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.

D. The given value is a statistic statistic for the year year because the data collected represent a population.

False. If is an statistic can't represent the population, since the parameter represent the population not the statistic.

In this exercise we have to use the knowledge of statistics to be able to identify the correct statement, so I can say that it is:

The letter  C

So knowing the statistics topics we can recognize the true alternative:

A. False. The information in visible form colected show a sample of the inhabitants of a place of interest, so for this case exist not a limit cause we forbiddance bear the facts about all the inhabitants of a place of interest.

B. False. First the sample average exist not a limit, and second the inhabitants of a place mean happen inadequate the average value most of the opportunity.

C. Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.

D. False. If exist an detail of action can't represent the inhabitants of a place, because the limit represent the inhabitants of a place not the detail of action.

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Answer:

{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)

Step-by-step explanation:

Sample space is the set of all possible outcomes of an experiment.

Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.

As a result person can choose

oatmeal as  meal and coffee as drink

oatmeal as meal and tea for drink

eggs for meal tea for drink

eggs for meal coffee for drink

pancakes for meal tea for drink finally

pancakes for meal and coffee for drink

The sample space of a distribution is the list of possible options.

The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)

From the question, the meals are:

Meals: Oatmeal, Eggs, Pancakes

And the beverages are:

Beverages: Coffee, Tea

This means that, the available selections are:

Hence, the sample space is (a)

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Answer:

i think it is 18 or something

Step-by-step explanation:

Answer:

Side length B is 17.

Step-by-step explanation:

Use the Pythagorean Theorem a^2 + b^2 = c^2. if one of the legs is 8, and another is 15, the hypotenuse will be 17.

For this case we have the following equation:

[tex]T = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

We must solve the equation for the variable "h":

We subtract [tex]2 \pi * r ^ 2[/tex] from both sides of the equation:

[tex]T-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]

We divide by [tex]2 \pi * r[/tex] on both sides of the equation:

[tex]\frac {T-2 \pi * r ^ 2} {2 \pi * r} = h\\h = \frac {T} {2 \pi * r} - \frac {2 \pi * r ^ 2} {2 \pi * r}\\h = \frac {T} {2 \pi * r} -r[/tex]

Answer:

[tex]h = \frac {T} {2 \pi * r} -r[/tex]

Answer:the speed of the barge in still water is 11 mph

the speed of the current is 3 mph

Step-by-step explanation:

Let x represent the speed of the barge in still water.

Let y represent the speed of the current.

Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be

x - y mph

Distance = speed × time

Therefore,

56 = 7(x - y)

8 = x - y - - - - - - - - - - - -1

Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be

x + y mph

Therefore,

56 = 4(x + y)

14 = x + y - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

22 = 2x

x = 22/2 = 11

Substituting x = 11 into equation 2, it becomes

14 = 11 + y

y = 14 - 11 = 3

Answer:

b. {-9, 3}.

Step-by-step explanation:

x^2 + 6x - 27 = 0

We need 2 numbers whose product is -27 and whose sum is + 6.

These are + 9 and - 3. So the factors are:

(x - 3)(x + 9) = 0

(x - 3) = 0 or (x + 9) = 0

x = 3 or -9.

Answer: option b is the correct answer.

Step-by-step explanation:

The given quadratic equation is expressed as

x^2+6x-27=0

In order to solve the equation by factorization, the first step is to find two numbers such that their sum or difference is 6x and their product is

- 27x^2. The two numbers are 9x and - 3x. Therefore,

x^2 + 9x - 3x - 27 = 0

x(x + 9) - 3(x + 9) = 0

x - 3 = 0 or x + 9 = 0

x = 3 or x = - 9

Answer:

Cookie monster needs to steal at least 6 cookies more.

Step-by-step explanation:

Given:

Number of cookies already stole = 4

Total number of cookies he wants to steal [tex]\geq 10[/tex]

We need to find how many cookie he needs to steal more.

Solution:

Let number of cookies he needs to steal more be 'x'.

Now we can say that;

Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal

framing in equation form we get;

[tex]4+x\geq 10[/tex]

Now using Subtraction property of Inequality we will subtract both side by 4 we get;

[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]

Hence Cookie monster needs to steal at least 6 cookies more.

The Cookie Monster needs to steal at least 6 more cookies after getting caught.

The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.

Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.

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Step-by-step explanation:

Before we start, let's look at what we're trying to prove: that two triangles are congruent.  There are a few ways we can do that: SSS, SAS, ASA, or AAS.  Whichever we choose, we'll need to show that at least one pair of sides is congruent.  We can do that, since we know that H is the midpoint of LM.  So we'll either use ASA or AAS.

1. LG || JM, H is the midpoint of LM

Given

2. LH ≅ HM

Definition of midpoint

3. ∠GLH ≅ ∠JMH

Alternate interior angles theorem

(∠GLH and ∠JMH are alternate interior angles.  Since LG and JM are parallel, the alternate interior angles are congruent.)

4. ∠LHG ≅ ∠MHJ

Vertical angles theorem

(∠LHG and ∠MHJ are vertical angles, which are always congruent.)

5. ΔLGH ≅ ΔMJH

ASA

(We have two pairs of congruent angles, and a pair of congruent sides between them.)

Now, I chose to use ASA.  However, you could use AAS.  Instead of using vertical angles in step 4, we could have used alternate interior angles theorem to show that ∠LGH ≅ ∠MJH.