Final answer:
To find the difference in time, subtract the bike time from the bus time by finding a common denominator and subtracting the fractions.
Explanation:
To compare the time it took Josh to bike to work with the time it took him to take the bus, we need to subtract the bike time from the bus time.
The time it took Josh to bike to work is given as 2/5 of an hour. We can represent this as a fraction, 2/5.
The time it took Josh to take the bus is given as 5/8 of an hour. This can also be represented as a fraction, 5/8.
To find the difference, we subtract the bike time from the bus time: 5/8 - 2/5. To do this, we need a common denominator, which in this case is 40.
Multiplying the numerator and denominator of 5/8 by 5, we get 25/40. Multiplying the numerator and denominator of 2/5 by 8, we get 16/40.
Now we can subtract the fractions: 25/40 - 16/40 = 9/40.
Therefore, it took the bus 9/40 of an hour longer than it took Josh to bike to work.
Does the graph represent a function ? Why or Why Not
This does NOT represent a function.
There should only be one pair per input and output, but this graph has multiple.
A factory has three machines, A, B, and C, for producing items. Machine A makes 60% of all the widgets, and machine B makes the rest. 3% of machine A’s widgets are defective, and 8% of machine B’s widgets are defective. One of the factory’s widgets is found to be defective; what is the probability that it was made by machine?
The shark are fed three times a day during the morning feeding 2/15 of a ton. During the afternoon feeding the weight of fish fed will be 1/15 of a ton more than the fish fed during the morning if the total fish fed in a day is 1/2 of Aton how much is fed during the feeding in the night
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.
Maria and Katy each have a piece of string. When they put the two pieces of string together end to end, the total length is 84inches. Maria's string is 6 inches longer than Katy's. How long is Maria's piece of string? How long is Katy's piece of string
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
WHAT IS (13X6)+89 WITH HE SECOND POWER? PLEASE HELP WILL MAKE BRAINLIEST
(13x6)+89 with the power of 2 is 7999
A shipping conpany is loading cube shaped crates into larger cube shaped container. The smaller cubes have side lenghts of 2 1/2 feet. And the larger shipping container has side lengths of 10 feet. How many crates will it feet in the large shipping container
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.
To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you $960. One month later, you get the guitar back by paying the pawnbroker $1170. What annual interest rate did you pay?
Based on the simple interest formula, the annual interest rate paid when borrowing $960 and repaying $1170 a month later is approximately 262.5%.
Explanation: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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The graph shows how many meters above a stream, y, that a bucket on a water wheel is rotating for a given number of seconds x.
How many degrees is the bucket rotating in 10 s?
After 10 s, the bucket has rotated [tex]180^{\circ}[/tex]
Step-by-step explanation:
The motion of the bucket on the water wheel is a periodic motion, which means that it repeats itself periodically. The period of the motion is the time it takes for the bucket to returns to its original position: it can be found from the graph by looking at after how much time the graph has again the same shape.
We see that if we start from x = 0 seconds, then the graph has the same shape again (=it has completed one full cycle) at x = 20 seconds, so the period is
T = 20 s
This also means that in a time of 20 seconds, the bucket has covered a full revolution, so an angle of
[tex]\theta=360^{\circ}[/tex]
Therefore, in order to find how many degrees x the bucket has rotated in
t = 10 s
We can use the rule of three:
[tex]\frac{\theta}{T}=\frac{x}{t}[/tex]
And solving for x, we find
[tex]x=\frac{\theta t}{T}=\frac{(360)(10)}{20}=180^{\circ}[/tex]
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Mr. Davis buys 5 packages of the package a glue sticks. Ms. Wilson buys 8 package of the package b glue sticks. Use your equations to find the difference in the total number of glue sticks that each person purchased.
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.
Explanation: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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How high is a tree that casts a 2222-ftft shadow at the same time a 44-ftft postpost casts a shadow which is 77-ftft long?
Answer: The height of the tree is 12.57 ft.
Step-by-step explanation:
The height of a thing is proportional to the its shadow.
Let H = Height and S = length of shadow
Then by equation direct proportion , [tex]\dfrac{H_1}{S_1}=\dfrac{H_2}{S_2}[/tex] (i)
Given : A tree that casts a 22 ft shadow at the same time a 4 ft postpost casts a shadow which is 7-ft long.
Put [tex]S_1=22 ,\ H_2= 4,\ \ S_2=7[/tex] in (i), we get
[tex]\dfrac{H_1}{22}=\dfrac{4}{7}\\\\ H_1=\dfrac{4}{7}\times22\approx12.57[/tex]
Hence, the height of the tree is 12.57 ft.
What the user said above!
Jake shows that △ △ C B A is congruent to △ △ A D C by rotating △ 180° △ C B A 180 ° around point C so it matches up with △ △ A D C exactly. Which conclusion can be drawn from Jake's transformations?
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
A large group of people is to be checked for two common symptoms of a certain disease. Itis thought that 20% of the people possess symptomAalone, 30% posseess symptomBalone,10% possess both symptoms, and the remainder have neither symptom. For one person chosen atrandom from this group, Ønd these probabilities:
a. (2 points) that the person has neither symptom
P(A\πB)=0:20
P(πA\B)=0:30
P(A\B)=0:10
P(πA\πB)=1°P(A[B)
P(πA\πB)=1°[P(A\πB)+P(πA\B)+P(A\B)]
=1°(0:20+0:30 + 0:10)
=1°0:60
=0:40
b. (2 points) that the person has at least one symptom
P(A[B)=P(A\πB)+P(πA\B)+P(A\B)
=0:20 + 0:30+10
=0:60
or
P(A[B)=1°P(πA\πB)
=1°0:40
=0:60
c. (2 points) that the person has both symptoms, given that he has symptom
BP(AjB)=P(A\B)/P(B)
=P(A\B)P(A\B)+P(πA\B)
=0:100:10+0:30
=0:100:40
=0:25
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
A baker has 15 cups of flour. He sets aside 4 cups, and uses the rest for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make?
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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Write a polynomial expression that represents the area of the trapezoid. (A=1/2h(b1+b2))
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]
I need ASAP!!
Find CU. If necessary, round answers to 4 decimal places
Answer:
The correct answer for this equational ratio is x = 5
Step-by-step explanation:
In order to calculate for x, we must create the necessary ratios
[tex]\frac{16}{20} = \frac{45-5x}{5x}[/tex]
Cross multiply to get
900 - 100x = 80x
900 = 180x
x = 5
Consider the matrices A = 2 1 2 2 2 −2 3 1 1 and x = x1 x2 x3
(a) Show that the equation Ax = x can be rewritten as (A − I)x = 0 and use this result to solve Ax = x for x.
(b) Solve Ax = 4
Answer:
94
Step-by-step explanation:
Jen has
there are 27 students in mrs. Yean's homeroom. 12 of them have home computers how many students don't have a home computer?
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
Find the least common denominator please
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
Joe traveled against the wind in a small plane for 3hours. The return trip with the wind took 2.8 hours. Find the speed of the wind to the nearest tenth if the speed of the plane in still air is 180 mph.
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
At 8am the temperature was 3 degrees below zero by 1 am the temperature rose 14 degrees and by 10 pm dropped 12 degrees what was the temperature at 10 pm
The temperature at 10 pm was -1 degree.
Explanation: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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Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want an ice cream party, 7 want a movie party, 10 want a costume party, and the rest are undecided. If 20 percent want an ice cream party, how many students are in the class?a. 23
b. 200
c. 5d. 25
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
in massaschusetts a team of scientists studying great white sharks estimate that a population of 15000 seals support fewer than 100 sharks. why are there so few top level consumers in this system?
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:
Amy invests money in two simple interest accounts. She invests four times as much in an account paying 11% as she does in an account paying 5%. If she earns $183.75 in interest in one year from both accounts combined, how much did she invest altogether?
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.
Explanation: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:
Let x represent the amount invested at 5%.Then 4x will represent the amount invested at 11%.The total interest from both accounts is $183.75 for one year.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
Do you expect δhsoln to be a large positive number, a large negative number, or close to zero? do you expect to be a large positive number, a large negative number, or close to zero? δhsoln is a large positive number. δhsoln is a large negative number. δhsoln is close to zero.
Answer:
δhsoln will be close to zero.
Step-by-step explanation:
In calculus, the symbol d represents a large or significant increment in a value. For example, say the change in the volume of a liquid in a tank depends upon the change of the height h.
The above statement can be written like this:
dV/dh
This means that the volume of the tank (V) depends with a significant change in the height of the liquid (h).
It is also possible to compute small changes in physical quantities. The symbol δ simply presents a small increment or small change. Using the same expression above, if a very large tank was to have a very very small leak, the change would be: δV/δh
In other words, the change in the volume will be almost negligible and will be close to zero.
what is -5x -10= -20
a.2
b.3
c.7
d.6
[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:
Option a ( 2 ) is the answerStep-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]
Henceforth , value of x is 2 that means option a is correct .Verifying : -
Now we're verifying our answer by substituting value of x in given equation. So ,
-5x - 10 = -20-5 ( 2 ) - 10 = -20-10 - 10 = -20-20 = -20L.H.S = R.H.SHence , Verified .Therefore , our answer is correct .
#Keep LearningFor which function does f(14)=23?
A. (x)=12x−20
B. f(x)=14x+23
C. f(x)=3x−7
D. f(x)=x+9
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.
A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective in killing roaches. Seventy-nine percent of the respondents agreed that the roach disk would be effective. The number 79% is a(n) ________.a. population. b. statistic. c. parameter. d. sample.
The latest online craze is a new game, Khan on Seven. You get 100100100 points for playing the game. In addition, you get 505050 points for each seven-letter word you make with the ten letters you receive. Sal wants to break the record, and he needs 18{,}00018,00018, comma, 000 or more points to do so. Write an inequality to determine the number of seven-letter words, www, Sal could make to break the record.
Answer:
[tex]50w+100 \ge 18000[/tex]
Step-by-step explanation:
Each seven-letter word is worth 50 points. [tex]w[/tex] words are then worth [tex]w\times50=50w[/tex].
Since Sal gets 100 points for playing the game, his points total after [tex]w[/tex] words is [tex]50w +100[/tex]. If he wants to break the record, he must get, at least, 18000 points. "At least" in inequality means [tex]\ge[/tex] (just as "at most" means [tex]\le[/tex]). Then the required inequality is
[tex]50w+100 \ge 18000[/tex].
Note that the question says "18000 or more", which is why we used the [tex]\ge[/tex] symbol. If the phrase had been "more than 18000", we would have used [tex]>[/tex].
Please help!! I don't know what to do :(
Find the value of x. Show all your work for full credit.
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
I'm need help a question and I'm confuse.
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