Sin * (x - y) , if sin x = 8/17 cos y = 12/37

The type of Function shown in the graph

Step-by-step explanation:

1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.

2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.

3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.

Answer:

y= 1/2 csc (x)

Step-by-step explanation:

probably

Answer:

  a) linear. Cost per minute is a constant.

  b) f(x) = 40 -0.15x

  d) f(100) = 25. The remaining value is $25 after using 100 minutes.

Step-by-step explanation:

a) Since the cost per minute is a constant, the remaining dollar value of the phone decreases by the same amount for each minute used. The cost as a function of minutes used is a linear function with a constant rate of change.

__

b) The value starts at $40 and decreases by $0.15 for each increment of x (minutes used). The function can be written as ...

  f(x) = 40 -0.15x

__

d) Put 100 where x is in the function definition and do the arithmetic.

  f(100) = 40 -0.15×100 = 40 -15

  f(100) = 25

According to the variable and function definitions, x=100 means 100 minutes have been used; f(x) = 25 means the remaining value of the phone is 25 dollars.

  f(100) = 25 means the phone's remaining value is $25 when 100 minutes have been used.

Answer:

1. f₁(x)=-x²+2x-2

2. f₂(x)=-x²+6x-10

3. f₃(x)=-x²-2  

4. f₄(x)=-x²+10x-26

5. f₅(x)=-x²-2x-2

6. f₆(x)=-x²

Step-by-step explanation:

1. we have that f(x) is translated right by 1 unit , also

according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2

2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)

y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10

3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)

y+2 = -(x)² ⇒ y=-x²-2  

4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)

y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26

5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)

y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2

6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)

y+0 = -(x+0)² ⇒ y=-x²

Answer:

a. E(F)=0.875

b. 99.9976%

c. P(X=2)=0.1683

Step-by-step explanation:

a. We notice that this is a binomial distribution with the probability of success;

[tex]p=\frac{5}{40}=0.125[/tex]

#We are given the sample size, n=7. The Expected value is calculated as:

[tex]E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875[/tex]

Hence the expectation, E(F)=0.875

b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;

[tex]P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%[/tex]

Hence, the range of F is 99.9976%

c. The probability that F=2 is calculated  using the binomial distribution function as:

[tex]P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683[/tex]

Hence, the probability of F=2 is 0.1683

Using the hypergeometric distribution, it is found that:

a) E(F) = 0.875

b) The range is {0, 1, 2, 3, 4, 5}

c) 0.1741 = 17.41% probability that F = 2.

The computers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item a:

The expected value of the hypergeometric distribution is:

[tex]E(F) =  \frac{nk}{N}[/tex]

Hence:

[tex]E(F) = \frac{35}{40} = 0.875[/tex]

Item b:

The range is the possible values that F can assume, which is from 0 to k, hence 0 to 5.

Item c:

The probability is P(X = 2), applying the hypergeometric distribution.

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,40,7,5) = \frac{C_{5,2}C_{35, 5}}{C_{40,7}} = 0.1741[/tex]

0.1741 = 17.41% probability that F = 2.

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Answer:

4 Km behind.

Step-by-step explanation:

1. Draw a graph

2. make Dave Edith and Foley

3. 8-0 is 8 and 12-8 is 4

The speed is the distance covered by an object at a particular time. When Edith finishes the race, the distance by which Foley is behind is 6 km.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Let the time in which Dave finishes the race be represented by t. Therefore, in time t Dave completed 24 km.

Given that When Dave finishes the race, Edith is 8 km behind. Therefore the distance that Edith will cover in time t is 16 km. Now, the speed of Edith will be,

Speed of Edith = 16 km /t

Also, When Dave finishes the race, Foley is 12 km behind. Therefore the distance that Edith will cover in time t is 12 km. Now, the speed of Edith will be,

Speed of Edith = 12 km /t

Now, the time it will take for Dave to finish the rest of 8 km distance is,

Time = 8 km / (16 km/t)

        = 0.5 t

Further, the distance that Edith will cover in time 0.5t is,

Distance = 0.5t × 12km/t

               = 6 km

Therefore, the distance that will be left for Foley is 6 km.

Hence, When Edith finishes the race, the distance by which Foley is behind is 6 km.

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Answer:

Rolling case achieves greater height than sliding case

Step-by-step explanation:

For sliding ball:

- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.

- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.

- The ball slides it only has translational kinetic energy as follows:

                                   ΔK.E = ΔP.E

                                   0.5*m*v^2 = m*g*h

                                    h = 0.5v^2 / g

For rolling ball:

- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:

                                  ΔK.E = ΔP.E

                                  0.5*m*v^2 + 0.5*I*w^2 = m*g*h

- Where I: moment of inertia of spherical ball = 2/5 *m*r^2

             w: Angular speed = v / r

                               0.5*m*v^2 + 0.2*m*v^2 = m*g*h

                               0.7v^2 = g*h

                               h = 0.7v^2 / g

- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.

A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle.

A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle. This is because, when the ball slides up, it gains potential energy which is then converted to kinetic energy as it rolls up the second ramp. The ball will reach a greater height because it retains some of the initial energy it gained from sliding up the first ramp.

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Answer:

Step-by-step explanation:

Please find the attached photo for your reference how to draw the rectangle.

1. From on point E and draw a segment 2 units long because the height is 2 units and be vertical.

2. Draw horizontally a line 4 units long (the length) to the right

3. Draw a line upwards 2 units long, at that point it must be at the same height than point E.

4. Draw a 4-units line to the left, and you will be back on point E, the rectangle done.

Answer:

Over here

Step-by-step explanation:

Answer:

Investments in order by least risk to greatest risk: A, C, E, D, F, B.

Step-by-step explanation:

Answer:

18 days

Step-by-step explanation:

Let x represent number of days.

We have been given that Brandy's watch falls 1 second every day. So Brandy's watch will fall [tex]1x[/tex] seconds behind in x days.

We are also told that Brandy set her watch 4 seconds behind, so Brady's watch will be behind by total [tex]x+4[/tex] seconds in x days.

Since Brady's watch is 22 seconds behind, so we will equate [tex]x+4[/tex] by 22 to solve for x as:

[tex]x+4=22[/tex]

[tex]x+4-4=22-4[/tex]

[tex]x=18[/tex]

Therefore, Brandy set her watch 18 days ago.

Answer:

Its been 19 days since brandy last set her watch as the watch is 22 seconds behind.      

Step-by-step explanation:

We are given the following in the question:

Brandy set her watch 4 seconds behind and it falls behind another 1 second every day.

Thus, this forms an arithmetic progression.

4, 5, 6, 7, ...

First term, a = 4

Common difference, d = 1

The [tex]n^{th}[/tex] terms is 22. We have to find the value of n.

The  [tex]n^{th}[/tex] terms of A.P is given by

[tex]a_n = a + (n-1)d[/tex]

Putting values, we get,

[tex]22 = 4 + (n-1)1\\18 = n-1\\n = 19[/tex]

Thus, its been 19 days since brandy last set her watch as the watch is 22 seconds behind.

Answer:

The mean of the sampling distribution of the sample mean for the three observations each day is 132.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 132

Standard Deviation, σ = 5

Each observation behaves as a random sample.

a) Mean of the sampling distribution

[tex]\bar{x} = \mu = 132[/tex]

b) Standard deviation of the sampling distribution

Sample size,n = 3

[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{5}{\sqrt{3}} = 2.887[/tex]

Thus, the mean of the sampling distribution of the sample mean for the three observations each day is 132.

Answer:

One cubic foot of the stone weigh 10 tons.

Step-by-step explanation:

There is a mistake in the question, thus it is corrected:

A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone and how much did it one cubic foot of the stone weigh?

Now, to find the volume of average stone and how much one cubic foot of stone weigh.

Dimension of rectangular prism:

Length = 5 feet.

Height = 5 feet.

Width = 6 feet.

Now, to get the volume of stone which was a rectangular prism we put formula:

[tex]Volume=length\times width\times height[/tex]

[tex]Volume=5\times 6\times 5[/tex]

[tex]Volume=150\ cubic\ feet.[/tex]

The volume of the average stone was = 150 cubic feet.

Weight of stone = 15 tons.

Now, to get one cubic foot of the stone weigh we divide the volume of the average stone by weight of stone:

The volume of the average stone ÷ weight of stone

[tex]150\div 15[/tex]

[tex]=10\ tons.[/tex]

Therefore, one cubic foot of the stone weigh 10 tons.

Answer:

cluster sampling

Step-by-step explanation:

ideal groups of objects are naturally chaos arranged in groups, and randomly selected. Unlike class sampling, with homogeneously arranged groups and only a few randomly selected objects from each group, in cluster sampling, each group is allocated in a chaotic and all objects in the group become part of the sample.

Answer:

X = 1 - (1/4) - 2 * (1/4)

Step-by-step explanation:

The equation to be raised must take into account what is painted on Monday and Tuesday. First consider the wall as a unit, that is to say painting the entire wall (100%) is equivalent to 1. Therefore the equation would be the following:

Let X be the unpainted part:

X = 1 - (1/4) - 2 * (1/4)

X = 1 - (1/4) - (1/2)

Now, if we solve this, we have that 0.25, therefore 25% or 1/4 is left to be painted on the wall.

Answer:

yes

Step-by-step explanation:

It depends on how accurate you want your answer to be, but basically yes, imagine we set our numerator to be x, and our denominator to be 2x, if we built our fraction we will get that:

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

If the denominator of a fraction is exactly twice the numerator, then the fraction will be simplified to 1/2 or 0.5.

Now, the greater the denominator is, the closer the fraction will get to zero.

Take for example I had an fraction like this:

[tex]\frac{3}{6}=0.5[/tex]

which approximates to 0. If we made the denominator bigger, let's say 7, we would get:

[tex]\frac{3}{7}=0.43[/tex]

notice the answer is closer to 0 this time, so it's valid to round it to zero. If we made the denominator greater, let's say 25, we would get:

[tex]\frac{3}{25}=0.12[/tex]

and so on. So it is true that if the denominator of a fraction is greater than twice the numerator, we can always replace the fraction with a 0 (depending on how accurate you want your answer to be).

If the denominator is more than twice the numerator, the number is therefore less than halve, 1/2 but cannot always be replaced with a 0.

An example;

Suppose we have a numerator, 2.

Then, we have a denominator which is more than twice the numerator; say 5

The resulting fraction is therefore;

The fraction 2/5 is definitely less than 1/2 but cannot always be replaced with a 0.

Read more on fractions:

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Answer:

Oliver read in two months = 945 minutes

Step-by-step explanation:

Oliver read in this month = 450 minutes

Goal for the next month = 10 % more than this month = [tex]\frac{110}{100}[/tex] × 450

⇒ Oliver read in next month = 495 minute

⇒ Oliver total  read in two months = 450 + 495  = 945 minutes

Thus Oliver read in two months = 945 minutes

Answer:

Oliver will read 945 minutes in 2 months.

Step-by-step explanation:

Given:

Number of minutes read this month = 450 mins

Percent of minutes to read next month = 10%

We need to find the number of minutes he read in two months.

Solution:

First we will find the number of minutes he read in next month.

number of minutes he read in next month is equal to Number of minutes read this month plus Percent of minutes to read next month multiplied by Number of minutes read this month.

framing in equation form we get;

number of minutes he read in next month = [tex]450+\frac{10}{100}\times 450 =450+45 =495\ mins[/tex]

Now  number of minutes he read in two months is equal to sum of Number of minutes read this month and number of minutes he read in next month.

framing in equation form we get;

number of minutes he read in two months = [tex]450+495 = 945\ mins[/tex]

Hence Oliver will read 945 minutes in 2 months.

Answer:

The correct answer to the question is

a. variable interval

Step-by-step explanation:

In a variable interval, the time at which reinforcement or reward is gained occurs at an unpredictable time. That is the animal gets a reinforcement on the grounds of an unpredictable time period.

An example of a variable interval is the catching of fish whereby the fisher catches fishes at an unpredictable time throughout the day.

The result of a variable interval is a controlled but stable response rate. In the case in the question, constant monitoring of the fishing device is important

The reinforcement schedule described is a variable interval schedule where the reinforcement occurs at unpredictable intervals of time.

The reinforcement schedule described in the question is a variable interval schedule.

Variable interval refers to a schedule in which the reinforcement (in this case, catching fish) occurs at unpredictable intervals of time. Harold catches fish throughout the day, but the intervals between catching fish are inconsistent and unpredictable.

Examples of variable interval schedules include waiting for a bus that arrives at different times or checking your phone for new messages throughout the day.

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To find out how many packs of construction paper Ms. Perkins will need, divide the total number of pieces needed by the number of pieces in each pack. Using long division, we find that she will need at least 16 packs of construction paper.

To find out how many packs of construction paper Ms. Perkins will need, we can divide the total number of pieces she needs (8,000) by the number of pieces in each pack (495). This will give us the number of packs required.

Using long division, we divide 8,000 by 495:

Since the remainder is less than 495, we stop here. Therefore, Ms. Perkins will need at least 16 packs of construction paper.

Answer:

The answer to your question is  7y - 19 = 0

Step-by-step explanation:

Data

Equation l         x  + 4y - 12 = 0

Equation ll        x = 3y - 7

Process

1.- Substitute equation ll in equation l

                    3y - 7 + 4y - 12 = 0

2.- Group like terms

                   (3y + 4y) + (-7 - 12) = 0

3.- Simplify like terms

                           7y - 19 = 0

4.- Result

                    7y - 19 = 0

Step-by-step explanation:

Below is an attachment containing the solution.

Answer:

(A) 0.15625

(B) 0.1875

(C) Can't be computed

Step-by-step explanation:

We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let X = Amount of time taken by student to complete a statistics quiz

So,   X ~ U(32 , 64)

The PDF of uniform distribution is given by;

    f(X) = [tex]\frac{1}{b-a}[/tex] ,  a < X < b      where a = 32 and b = 64

The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]

(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)

   P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625

(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43)  = P(X <= 43) - P(X < 37)

    P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375

    P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625

    P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) Probability that student complete the quiz in exactly 44.74 minutes

     = P(X = 44.74)

The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.

Answer:

All values are identical.

Step-by-step explanation:

We are given the following in the question:

If the standard deviation of a set of data is zero.

Then, all the values in data are identical.

This can be shown as:

Let all the terms in data be x.

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{nx}{n} = x[/tex]

Sum of squares of differences =

[tex]\displaystyle\sum (x_i - x)^2 = 0[/tex]

[tex]\sigma = \sqrt{\frac{0}{n}} = 0[/tex]

Thus, the correct answer is

All values are identical.

The correct conclusion about the set of values when the standard deviation is zero is that all values are identical.

The standard deviation is a measure of the amount of variation or dispersion in a set of values. A standard deviation equal to zero means that there is no variation at all in the data set. This can only occur if all the values in the set are exactly the same.

To understand why this is the case, let's consider the formula for standard deviation (for a population):

[tex]\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \][/tex]

Here, [tex]\( \sigma \)[/tex]  is the standard deviation, [tex]\( x_i \)[/tex] represents each value in the data set, [tex]\( \mu \)[/tex] is the mean of the data set, and [tex]\( N \)[/tex] is the number of values in the data set.

Now, let's address the other options:

Answer:

Each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.

Step-by-step explanation:

We are given the following in the question:

Number of guests at Sara's party = 15

Amount of liquid soap bubble used by 15 guest =

[tex]\dfrac{3}{5}\text{ of a gallon}[/tex]

Fraction of liquid soap bubble available for each guest =

[tex]=\dfrac{\text{Liquid soap bubble used by 15 guest}}{\text{Number of guest}}\\\\=\dfrac{\frac{3}{5}}{15}\\\\=\dfrac{1}{25}[/tex]

Thus, each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.

Answer:

1/25 of the gallon each person will get

Step-by-step explanation:

The two problems are almost identical: you have to set up a system, and then solve it.

In the first case, let [tex]g[/tex] and [tex]b[/tex] be, respectively, the number of girls and boys.

We know that [tex]g=2b+4[/tex] (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that [tex]g+b=61[/tex] (there are 61 students in total).

So, we have the system

[tex]\begin{cases}g=2b+4\\g+b=61\end{cases}[/tex]

We can use the first equation to substitute in the second

[tex]g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19[/tex]

And then solve for [tex]g[/tex]:

[tex]g=2b+4=2\cdot 19+4=38+4=42[/tex]

For the second problem, let [tex]c[/tex] and [tex]j[/tex] be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system

[tex]\begin{cases}c=j+12\\c+j=230\end{cases}[/tex]

And you can solve it in the very same way we solved the previous one.

Answer:

So if the parameter 's value  is 7 or 803 or 141 the function returns true . But if the parameter 's value  is -22 or -57, or 0, the function returns false .

My Code:

bool is Positive ( int x ) {  

if ( x > 0 )  

{  

 return true;  

}  

else {  

 return false ;  

}  

}

Length of side BM is 30 yd

Step-by-step explanation:

⇒ ∠B + ∠M + ∠S = 180°

⇒ 35° + 102° + ∠S = 180°

∴ ∠S = 180° - 137° = 43°

Law of sines ⇒ a/sin A = b/sin B = c/sin C

Here, let BM be a then, sin A = sin S = sin 43° = -0.83

Also, b = 18 yd, then sin B = sin 35° = -0.43

⇒ BM/-0.83 = 18/-0.43

⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)

Answer:

Step-by-step explanation:

Looking at the triangle, to determine BM, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. From the triangle, m∠S = 180 - (102 + 35) = 43°

Therefore, applying the rule,it becomes

18/Sin35 = BM/Sin43

Cross multiplying, it becomes

BM × Sin 35 = 18 × Sin 43

BM × 0.5736 = 18 × 0.6820

0.5736BM = 12.276

Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes

0.5736BM/0.5736 = 12.276/0.5736

BM = 21.4

Answer:

The answer to your question is x = 64; y = 20

Step-by-step explanation:

Angles    2x + 2  and 130° are vertical angles so they measure the same.

                           2x + 2 = 130

- Solve for x

                           2x = 130 - 2

                           2x = 128

                             x = 128/2

                             x = 64

Angles  3y - 10 and 50° are vertical angles, so they measure the same.

                           3y - 10 = 50

                           3y = 50 + 10

                           3y = 60

                             y = 60/3

                            y = 20

Answer:

70

Step-by-step explanation:

Answer: x = 35

Step-by-step explanation:

In a parallelogram, the opposite sides and the opposite angles are equal and parallel.

Also, the consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.

Angle (2x - 10) and angle (2x + 50) are consecutive angles. Therefore,

2x - 10 + 2x + 50 = 180

2x + 2x - 10 + 50 = 180

4x + 40 = 180

4x = 180 - 40 = 140

x = 140/4

x = 35

Answer:

Step-by-step explanation:

Two train traveling in opposite direction

Distance apart the train is 120miles

Train A

Speed =30mph

Train B

90mph

What is common to the train is the same time, they will meet at the same time

Let assume they meet at distance x from from Washington

Then A has travelled x mile distance

Then, B has travelled 120-x mile distance

Time for train A to get to x,, = time for train B to get 120-x

Time=distance/speed

da/Sa=db/Sb

Let da be distance of train A

And db be distance of train B

Sa be speed of train A

Sb be speed of train B

Then,

da/Sa=db/Sb

x/30=120-x/90

Cross multiply

90x=3600-30x

90x+30x=3600

120x=3600

Then, x=3600/120

x=30miles

Then will meet at 30miles from Washington

Second part of the questions

Train B is faster than train A

Train B has already travelled 90miles while train B travels 30 miles

This shows that train A will not get to Baltimore before train B catch up

Then, let train A travel y distance

Then B will have to complete the 30 miles and then with another 30 miles that A has travel and then y

Total distance B travel will be

db=30+30+y

db=60+y

And da=y

Therefore,

da/Sa=db/Sb

y/30=60+y/60

Cross multiply

60y=1800+30y

60y-30y=1800

30y=1800

Then, y=1800/30

y=60miles

That means they will meet at 60miles from both Washington and Baltimore, or they are at mid points