Find the vertex of the graph of the function. f(x) = (x + 4)2 - 1
a) (0,4)
b) (-1, 0)
c) (-4,-1)
d) (-1,-4)

Answer:

Scully will catch up with Mulder by 7:30 PM.

Step-by-step explanation:

Consider the provided information.

Mulder leaves the office at 9​:30a.m. averaging 57mph.

Scully leaves at 10​:00​a.m., following the same path and averaging 60 mph.

Distance covered by Mulder between 9:30 AM and 10:00 AM:

[tex]\frac{57}{2}= 28.5[/tex] miles

Let t is the time taken by Scully to catch up with​ Mulder.

After leaving office Scully needs to cover extra distance of 28.5 miles because Mulder leaves the office earlier.

Therefore total distance cover by them is:

[tex]28.5+57t=60t[/tex]

[tex]28.5=60t-57t[/tex]

[tex]28.5=3t\\t=9.5[/tex]

Hence, it would take 9 hours 30 minutes to catch up Mulder.

10 am + 9 hours 30 minutes = 7:30 pm

Therefore, Scully will catch up with Mulder by 7:30 PM.

Final answer:

Scully will catch up with Mulder at 7:30 p.m. by closing the initial 28.5 miles gap at a rate of 3 mph faster than Mulder.

Explanation:

To determine when Scully will catch up with Mulder, we need to calculate the relative speeds at which the two are traveling and how long it will take for Scully to close the gap that Mulder has created by leaving earlier. Since Mulder left at 9:30 a.m. and Scully left at 10:00 a.m., Mulder has a half-hour head start. In that half-hour, traveling at 57 mph, Mulder will have covered 28.5 miles (because 0.5 hours × 57 mph = 28.5 miles).

Scully is traveling at 60 mph, which is 3 mph faster than Mulder. So, Scully closes the gap by 3 miles every hour. To catch up 28.5 miles at a rate of 3 miles per hour, Scully will need 9.5 hours (because 28.5 miles ÷ 3 mph = 9.5 hours).

We need to add this time to Scully's departure time to find out when she will catch up. Therefore, adding 9.5 hours to 10:00 a.m. yields 7:30 p.m. So, Scully will catch up with Mulder at 7:30 p.m.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-5x -10= -20}\\\\\large\text{ADD 10 to BOTH SIDES}\\\mathsf{-5x - 10 + 10 = -20 + 10}\\\\\large\text{SIMPLIFY IT!}\\\mathsf{-5x = -20 + 10}\\\mathsf{-5x = -10}\\\\\large\text{DIVIDE -5 to BOTH SIDES}\\\mathsf{\dfrac{-5x}{-5}= \dfrac{-10}{-5}}\\\\\large\text{SIMPLIFY IT!}\\\mathsf{x = \dfrac{-10}{-5}}\\\\\mathsf{x = 2}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{Option \ A. \ 2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

In this question we are given with an equation that is -5x - 10 = -20 . And we are asked to find it's solution ( value of x ).

Solution : -

[tex] \longmapsto \qquad \: - 5x - 10 = - 20[/tex]

Step 1 : Adding 10 to both sides :

[tex] \longmapsto \qquad \: - 5x - \cancel{10 }+ \cancel{10} = - \bold{20 }+ \bold{10}[/tex]

On further calculations , We get :

[tex] \longmapsto \qquad \: - 5x = - 10[/tex]

Step 2 : Dividing with -5 on both sides :

[tex] \longmapsto \qquad \: \dfrac{ \cancel{- 5}x}{ \cancel{- 5}} = \cancel{ \dfrac{ - 10}{ - 5} }[/tex]

On further calculations , we get :

[tex] \longmapsto \qquad \: \ \: \pink{\underline{ \boxed{\frak{x = 2}}}}[/tex]

Verifying : -

Now we're verifying our answer by substituting value of x in given equation. So ,

Therefore , our answer is correct .

The answer is 1/4. Set up a proportion to solve for x. Another way is to use unit analysis.

The answer is 1/4.

The scale factor is 1:4.

First, set up a proportion.
1 gallon/4 quarts=3 gallons/x quarts
Next, cross multiply to solve for x.
1/4-3/x
1x=3x4

Another way to solve the same problem is to use unit analysis.
First, write the unit conversion as a fraction.

One more framing of fractions and their relationship to multiplication and division: dividing by 8 is the same as multiplying by. Multiplying by is the same as dividing by 2. Multiplication and division are thus essentially the same, only having to flip the number or fraction upside-down into its reciprocal.

Use the quadratic equation to find x
x= -.0024, .00139
.001-.0024 is negative, which can't happen in real life so we know x actually equals .00139

Yo sup??

This question can be solved by applying the properties of similar triangles

the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 36

therefore we can say

5x/45=20/36

x=5 units

Hope this helps

Answer:

  (n -4)(n +1)^2 = n^3 -2n^2 -7n -4

Step-by-step explanation:

The least common denominator is the smallest denominator that lets you write the sum as a single fraction.

  [tex]\dfrac{n^5}{n^2+2n+1}+\dfrac{-4}{n^2-3n-4}=\dfrac{n^5}{(n+1)^2}+\dfrac{-4}{(n+1)(n-4)}\\\\=\dfrac{n^5}{(n+1)^2}\cdot\dfrac{n-4}{n-4}+\dfrac{-4}{(n+1)(n-4)}\cdot\dfrac{n+1}{n+1}=\dfrac{n^5(n-4)-4(n+1)}{(n+1)^2(n-4)}\\\\=\dfrac{n^6-4n^5-4n-4}{n^3-2n^2-7n-4}[/tex]

The least common denominator is ...

  (n-4)(n+1)^2 = n^3 -2n^2 -7n -4

Based on the simple interest formula, the annual interest rate paid when borrowing $960 and repaying $1170 a month later is approximately 262.5%.

This problem can be solved by using the formula for calculating simple interest, which is Interest = Principal (P) * Rate (R) * Time (T). In this case, the difference between what you paid and what you borrowed, $1170 - $960 = $210, is the interest you paid. Therefore, we can use the given information to set up the equation 210 = 960 * R * (1/12), because the time period T is 1 month, or 1/12 of a year. By solving this equation, we find that the annual interest rate is approximately 262.5%.

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Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let [tex]y(t)[/tex] be the depth of water in the barrel at time [tex]t[/tex],  where [tex]y[/tex] is measured in inches and [tex]t[/tex] in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

                                                 [tex]\frac{dy}{dt}=-k\sqrt{y}[/tex]

where [tex]k[/tex] is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by [tex]\frac{1}{\sqrt{y}}[/tex]

[tex]\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k[/tex]

Multiply by [tex]dt[/tex]

[tex]\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt[/tex]

Take integral

[tex]\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt[/tex]

Integrate

[tex]2\sqrt{y}=-kt+C[/tex]

Isolate [tex]y[/tex]

[tex]y(t)=(\frac{C}{2} -\frac{k}{2}t)^2[/tex]

We know that the water level starts at 36, this means [tex]y(0)=36[/tex]. We use this information to find the value of [tex]C[/tex].

[tex]36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12[/tex]

[tex]y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2[/tex]

At t = 1, y = 34

[tex]34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}[/tex]

So our formula for the depth of water in the barrel is

[tex]y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\[/tex]

To find the time, [tex]t[/tex], at which all the water leaks out of the barrel, we solve the equation

[tex]\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49[/tex]

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

The time it will take for all of the water to drain out of that barrel is 35.5 hours approx.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the considered case, let we take three variables as:

Now, when  t = 0, x = 36 inches.

and at t = 1, x = 34 inches.

So depth of water is function of time passed. Let x = f(t)

Also, y is negative rate of change of x with respect to t(since depth is decreasing, and draining is measuring decrement rate, thus, negative of increment rate), or

[tex]y = -\dfrac{dx}{dt}[/tex]

We're given that: "Water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time"

That means, [tex]y \propto \sqrt{x}[/tex]

Let the constant of proportionality be k, then,

[tex]y = \sqrt{x}[/tex]

Since we've [tex]y = -\dfrac{dx}{dt}[/tex], therefore,

[tex]-\dfrac{dx}{dt} = k\sqrt{x}\\\\-\dfrac{dx}{\sqrt{x}} = kdt\\\\\text{Integrating both the sides, we get}\\\\\int -\dfrac{dx}{\sqrt{x}} = \int kdt\\\\-2\sqrt{x} = kt + C[/tex]

where C is integration constant.

Since at t = 0 hours passed, x = 36 inches, and at t = 1 hour passed, x = 34 inches, we get two equations as:

[tex]-2\sqrt{x} = kt + C\\-2\sqrt{36} = -12 = C\\-2\sqrt{34} = k + C[/tex]

Putting value of C from first equation in second, we get:

[tex]k = -2\sqrt{34} + C \\k = -2\sqrt{34} - 12[/tex]

Therefore, the relationship between depth of water and time we get is:

[tex]-2\sqrt{x} = (-2\sqrt{34} - 12)t -12\\\sqrt{x} = (\sqrt{34} - 6)t + 6[/tex]

When the whole barrel gets empty, the depth of water becomes 0. The time for it is calculated using above equation as:

[tex]\sqrt{x} = (\sqrt{34} - 6)t + 6\\0 = (\sqrt{34} - 6)t + 6\\t = \dfrac{6}{6 - \sqrt{34}} \approx 35.5[/tex](in hours)

Thus, the time it will take for all of the water to drain out of that barrel is 35.5 hours approx.

Learn more about differential equations here:

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Yo sup??

we can solve this question by applying trigonometric ratios

let the angle S be x, then

sinx=2/5

x=23.6

Hope this helps.

Answer:

m∡S = 23.6 °

Step-by-step explanation:

We can see that this is a right angled triangle and therefore we can use trigonometric functions to determine an angle ∡S.

We know that:

                                              [tex]\sin \angle S = \frac{opposite}{hypotenuse}[/tex]

Therefore:

                                                   [tex]\sin \angle S = \frac{2}{5}[/tex]

It yields:

                                           [tex]\angle S = \sin^{-1} \frac{2}{5} =\sin^{-1}0.4[/tex]

Inserting that into the calculator we obtain m∡S = 23.6 degrees

Answer: Total amount invested in both accounts is $1875

Step-by-step explanation:

Let x represent the amount invested at 11%.

Let y represent the amount invested at 5%.

She invests four times as much in an account paying 11% as she does in an account paying 5%. This means that

x = 4y

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents the rate of investment

T represents the time in years.

Considering the amount invested at 11%,

I = (x × 11 × 1)/100 = 0.11x

Considering the amount invested at 5%,

I = (y × 5 × 1)/100 = 0.05y

If she earns $183.75 in interest in one year from both accounts combined, it means that

0.11x + 0.05y = 183.75 - - - - - - - - - -1

Substituting x = 4y into equation 1, it becomes

0.11 × 4y + 0.05y = 183.75

0.44y + 0.05y = 183.75

0.49y = 183.75

y = 183.75/0.49

y = 375

x = 4y = 375 × 4

x = 1500

Total amount invested in both accounts is

1500 + 375 = $1875

Amy invested a total of $1875 in both simple interest accounts. She placed $375 into the account with a 5% interest rate and $1500 into the account with an 11% interest rate to achieve the total interest income of $183.75 in one year.

Amy invests money in two simple interest accounts. One account pays 11% interest, while the other pays 5%. If she puts four times as much into the 11% account as the 5% account, we can set up the following equations to find out how much she invested altogether:

We can use the formula for simple interest which is Interest = Principal × Rate × Time, where the principal is the initial amount of money invested, the rate is the interest rate, and the time is the period of time over which the money is invested.

So, the total interest earned from both accounts is:

Interest from 5% account + Interest from 11% account = $183.75

(x × 0.05 × 1) + (4x × 0.11 × 1) = $183.75

0.05x + 0.44x = $183.75

0.49x = $183.75

Now, solve for x:

0.49x = $183.75

x = $183.75 / 0.49

x = $375

Since x represents the amount invested at 5%, Amy invested $375 in the 5% account. To find the total investment:

Total investment = x + 4x

Total investment = $375 + 4(×$375)

Total investment = $375 + $1500

Total investment = $1875

Answer:

  64

Step-by-step explanation:

10 ft is 4 times 2 1/2 ft, so the larger container has dimensions of 4 crates in every direction. That is, it will hold 4^3 crates, or 64 crates.

Answer: the length of Maria's piece of string is 45 inches.

the length of Katy's piece of string is 39 inches

Step-by-step explanation:

Let x represent the length of Maria's piece of string.

Let y represent the length of Katy's piece of string.

When they put the two pieces of string together end to end, the total length is 84inches. This means that

x + y = 84 - - - - - - - - - - - -1

Maria's string is 6 inches longer than Katy's. This means that

x = y + 6

Substituting x = y + 6 into equation 1, it becomes

y + 6 + y = 84

2y + 6 = 84

2y = 84 - 6 = 78

y = 78/2 = 39

x = y + 6 = 39 + 6

x = 45

Answer:

a) Mean = 1

b) Variance = 0.9      

Step-by-step explanation:

We are given the following in the question:

P(Success of exploration) = 0.1

Then the number of adults follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

All the explorations are independent.

where n is the total number of observations, x is the number of success, p is the probability of success.

Here n = 10, p = 0.1

a) Mean number of successful explorations

[tex]\mu = np = 10(0.1) = 1[/tex]

b) Variance number of successful explorations

[tex]\sigma^2 = np(1-p) = (10)(0.1)(1-0.1) = 0.9[/tex]

Answer: d. 25

Step-by-step explanation:

Let x be the total number of students in the class.

As per given :

Number of students want ice cream party = 20% of x= 0.20x

[we divide percent by 100 to convert it into decimal.]

Actual number of students want ice cream party =5

⇒  0.20x=5

Divide both sides by 0.20 , we get

⇒ x=  [tex]\dfrac{5}{0.20}=\dfrac{500}{20}=25[/tex]

Hence, the total number of students in the class.= 25

Thus , the correct answer is d. 25

The temperature at 10 pm was -1 degree.

To find the temperature at 10 pm, we need to start with the temperature at 8am. Since the temperature was 3 degrees below zero at 8 am, we can add the rise of 14 degrees by 1 am to get the temperature at 1 am. Then, we need to subtract the 12 degree drop by 10 pm to find the temperature at that time.

Starting with 8 am: -3 degrees

Add 14 degrees: -3 + 14 = 11 degrees at 1 am

Subtract 12 degrees: 11 - 12 = -1 degree at 10 pm

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(13x6)+89 with the power of 2 is 7999

Answer:

The shark are fed [tex]\frac16 \ ton[/tex] of fish during the night.

Step-by-step explanation:

Given:

Weight of fish fed in the morning = [tex]\frac{2}{15}\ ton[/tex]

Also Given:

During the afternoon feeding the weight of fish fed will be 1/15 of a ton more than the fish fed during the morning.

Weight of fish fed in the afternoon = [tex]\frac{2}{15}+\frac{1}{15}=\frac{2+1}{15}=\frac{3}{15}\ ton[/tex]

Total fish fed in whole day = [tex]\frac12 \ ton[/tex]

We need to find the Weight of fish fed in the night.

Solution:

Now we can say that;

Weight of fish fed in the night can be calculated by by subtracting Weight of fish fed in the morning and Weight of fish fed in the afternoon from Total fish fed in whole day .

framing in equation form we get;

Weight of fish fed in the night = [tex]\frac{1}{2}-\frac{2}{15}-\frac{3}{15}= \frac{1}{2}-(\frac{2}{15}+\frac{3}{15})=\frac{1}{2}-\frac{2+3}{15}= \frac{1}{2}-\frac{5}{15} = \frac{1}{2}-\frac{1}{3}[/tex]

Now we will use LCM for making the denominator common we get;

Weight of fish fed in the night = [tex]\frac{1\times3}{2\times3}-\frac{1\times2}{3\times2} = \frac{3}{6}-\frac{2}{6}[/tex]

Now denominator are common so we will solve the numerators.

Weight of fish fed in the night = [tex]\frac{3-2}{6}=\frac16 \ ton[/tex]

Hence The shark are fed [tex]\frac16 \ ton[/tex] of fish during the night.

Answer:

The population of interest is all the residents of the state.

Step-by-step explanation:

The term 'population of interest' is defined as the population under study from which the sample is drawn to make conclusions about the said population.

For instance, if a school principal wants to know the average SAT score for the students of his school, then his population of interest will be all the students of the school.

In this scenario a poll is conducted to determine which candidate, running for the governor's seat, has more support.

The sample of 500 registered voters are selected from the state for the poll.

This implies that the population under study consists of all the people of the state.

Thus, the population of interest in this case are all the residents of the state.

The correct option is: all the residents of the state.

Answer:

The higher you go in the good chain the lower the population.

Explanation:

In the food web, there are only a few sharks since in the food chain they are higher. Just 10% energy is retained in the tissues once the energy is moved from one trophic level to another, and the leftover power is emitted as metabolic energy.

If an animal is high up the energy ladder, the individual has less resources; thus, a few of the highest predators are present in an ecosystem.

Answer:

because there are more sharks than seals in the area

Step-by-step explanation:

Answer: It is not possible that two triangles that are similar and not congruent in spherical geometry.

Step-by-step explanation:

For instance, taking a circle on the sphere whose diameter is equal to the diameter of the sphere and inside is an equilateral triangle, because the sphere is perfect, if we draw a circle (longitudinal or latitudinal lines) to form a circle encompassing an equally shaped triangle at different points of the sphere will definately yield equal size.

in other words, triangles formed in a sphere must be congruent and also similar meaning having the same shape and must definately have the same size.

Therefore, it is not possible for two triangles in a sphere that are similar but not congruent.

Two triangles in sphere that are similar must be congruent.

Final answer:

By substituting x with 14 in each option, it is determined that option D, which is f(x) = x + 9, is the correct function where f(14) equals 23.

Explanation:

The student is asking to find the function for which f(14)=23. To answer this, we substitute x with 14 in each of the given options and see which one results in f(x) being equal to 23.

Substitute x=14 in f(x)=12x−20: f(14)=12(14)−20=168−20=148, which is not 23.

Substitute x=14 in f(x)=14x+23: f(14)=14(14)+23=196+23=219, which is not 23.

Substitute x=14 in f(x)=3x−7: f(14)=3(14)−7=42−7=35, which is not 23.

Substitute x=14 in f(x)=x+9: f(14)=14+9=23, which is the correct answer.

The correct function is D. f(x)=x+9.

Answer:

(a) and (b) are correct but (c) is not correct

Step-by-step explanation: (c) P(nA)*P(nB) + P(nA/nB)

0.20*0.30 + 0.10 = 0.060 + 0.10 = 0.160

Answer:

Reflection about either the x- axis or y- axis.

Step-by-step explanation:

It is likely that the triangle shows a mirror image when it has been rotated at point C so that it matches ΔADC.

The triangles are congruent if the sides and angles are equal. The only way to effect the change is through a rotation.

In fact, two objects are said to be congruent if they can be transformed into another shape by translation, rotation, and reflection.

The resulting image is a distinct figure that can fit and match the other completely.

In this case, the triangle is rotated through 180⁰ so the resulting image is a reflection or mirror image.

Answer:

If two pairs of angles and the included side are congruent, the triangles are congruent.

Step-by-step explanation:

itsLearning

Answer:

So, 22 batches of cookies can the baker make.

Step-by-step explanation:

A baker has 15 cups of flour.

He sets aside 4 cups.

So, the remaining cups = 15 - 4 = 11

A cookie recipe that calls for 1/2 cup of flour.

So, x batches of cookies can the baker make with 11 cups

Use the ratio and proportional

1 : 1/2 = x : 11   ⇒ multiply both sides by 2

2 : 1 = 2x : 22

solve for x

2x = 2 * 22

x = 22

So, 22 batches of cookies can the baker make.

She can make 22 batches of cookies.

Given that there are 15 cups of flour. The baker sets aside 4 cups.

So remaining (15 - 4) = 11 cups.

Let she can make x batches.

Given each batch takes 1/2 cup.

That means she will need [tex]x\cdot\frac{1}{2}=\frac{x}{2}[/tex] cups.

According to the question:

[tex]\frac{x}{2}=11\\x=22[/tex]

So she can make 22 batches of cookies.

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Answer:

[tex]A = 5 {x}^{2} + 6x + 1[/tex]

Step-by-step explanation:

[tex]A = \frac{(a + b)h}{2} = \frac{(6x - 5 + 4x + 7)(x + 1)}{2} = \frac{(10x + 2)(x + 1)}{2} = \frac{2(5x + 1)(x + 1)}{2} = 5 {x}^{2} + 6x + 1[/tex]

Answer: 15

Step-by-step explanation:Do 27-12 and you get 15

Answer:

15 students don't have a home computer

Step-by-step explanation:

Take the total amount of students, which is 27 and take the amount that do have home computers, which is 12, and subtract.

So, 27 - 12 = 15

To find the difference in the total number of glue sticks that Mr. Davis and Ms. Wilson purchased, subtract the number of glue sticks each person bought from one another.

To find the difference in the total number of glue sticks that Mr. Davis and Ms. Wilson purchased, we can subtract the number of glue sticks each person bought from one another.

Mr. Davis bought 5 packages of glue sticks, and each package has a certain number of glue sticks in it.

Ms. Wilson bought 8 packages of glue sticks, and each package also has a certain number of glue sticks in it.

To find the difference, subtract the total number of glue sticks from Mr. Davis from the total number of glue sticks from Ms. Wilson.

For example, if each package of glue sticks contains 4 glue sticks, Mr. Davis purchased 5 x 4 = 20 glue sticks. Ms. Wilson purchased 8 x 4 = 32 glue sticks. The difference is 32 - 20 = 12 glue sticks.

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Answer:

Step-by-step explanation:

Since angle ABD is 133 degrees and the sum of the angles in a triangle is 180 degrees, it means that

m∠ DAB + 133 + 22 = 180

m∠ DAB = 180 - 155 = 25 degrees

Also, ∆ ADC is an isosceles triangle because two of its sides are equal. It also means that the base angles are equal. Thus,

m∠ A = m∠ B

Therefore,

m∠ A + m∠ B + angle D = 180

m∠ A + m∠ B = 180 - 22 × 2

m∠ A + m∠ B = 180 - 44 = 136

m∠ A = m∠ B = 136/2 = 68 degrees

m∠ CAB + m∠ DAB = m∠ A

Therefore,

m∠ CAB = 68 - 25 = 43 degrees

Since ∆ ABC is isosceles, then

m∠ CAB = m∠ ACB

m∠ ACB = 43 degrees

m∠ ABC = 180 - (43 × 2) = 180 - 86

m∠ ABC = 94 degrees

m∠ BCD = 68 - m∠ ACB

m∠ BCD = 68 - 43 = 25 degrees

Answer: the rate of the wind is 6.2 mph

Step-by-step explanation:

Let x represent the rate of the wind.

Joe traveled against the wind in a small plane for 3hours. If the speed of the plane in still air is 180 mph, then the total speed with which the plane flew is

(180 - x) mph

Distance = speed × time

Therefore, distance travelled against the wind is

3(180 - x)

= 540 - 3x - - - - - - - - - - - - - -1

The return trip with the wind took 2.8 hours.

the total speed with which the plane flew is

(180 + x) mph

Therefore, distance travelled with the wind is

2.8(180 + x)

= 504 + 2.8x - - - - - - - - - - - - - -2

Since the distance is the same, then

540 - 3x = 504 + 2.8x

540 - 504 = 2.8x + 3x

5.8x = 36

x = 36/5.8 = 6.2