The answer of this question can be given by using congruence
Answer is 20°
What is an example of congruence?
Congruent relates to anything that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
Given That:
∡DBC = 20°
DC = AD
DB is common on both triangle
As we have hypotenuse common in both triangle and 1 side equal then we can sa it is a congruent triangle by RHS
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Is y−4=3(x+1) an equation of a line through (-2, 1)? Explain.
Answer:
Yes
Step-by-step explanation:
(1)-4=3((-2)+1)
-3=3(-1)
-3=-3
The answer is yes because if you substitute x and y for -2 and 1 you can simplify the equation. Then you get the answer -3=-3 which means that the equation is equal.
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $55,000, if the total monthly fixed costs are $17,363.50 and the variable cost per chair is $52.17. $72.41 $70.80 $25.38 $20.24
Answer:
A) $72.41------------------------------
Find the total cost to produce 3575 chairs. It includes the fixed costs as well as the variable cost per chair.
17363.50 + 3575*52.17 = 203871.25Add the profit we want to have
203871.25 + 55000 = 258871.25This is the minimum amount to be made from sale.
Find minimum sales price per chair:
258871.25 / 3575 = 72.41 (rounded)This is matching the first answer choice.
A school had 1 200 students last year and only 1 080 students this year. What was the percent decrease in the number of students?
The percentage decrease in the number of students in the school was 10%.
What is the percentage?The percentage refers to the ratio or proportion of students that reduced the number of the school population for the present year in comparison to last year's.
We can compute the percentage by finding the decrease in population and taking the result as a numerator of the total number in the last year and multiplying the result by 100.
Percentages represent fractional values and are usually depicted by the percentage sign (%).
The total number of students in the school last year = 1,200
The total number of students in the school this year = 1,080
The decrease in the number of students = 120 (1,200 - 1,080)
The percentage decrease = 10% (120/1,200 x 100)
Thus, we can conclude that the school population decreased by 10%.
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find the number that is 33 greater than twice the opposite of itself
Answer:
11
Step-by-step explanation:
x = 2(-x) + 33
x = -2x + 33
x + 2x = 33
3x = 33
3/3 x = 33/3
x = 11
Starting at the beginning of the year, Kianna was able to save $215 each month. However
for the last 3 months, she increases her saving to $305 each month, and she plans to
continue saving the same amount of money for 2 more months (until end of the year).
What will be the amount of money Kianna save this year?
By using addition and multiplication, the result obtained is
Kianna saves $3020 this year
What is addition and multiplication?
Suppose there are many numbers. To get the sum total of all the numbers, addition is used
Repeated addition is called multiplication
Addition and multiplication will be used here
Amount of money Kianna saves each month for the first 7 months = $215
Total amount of money Kianna saved in the first 7 months = $215 [tex]\times[/tex] 7
= $1505
Amount of money she saves each month for the last 5 months = $305
Amount of money she saves in the last 5 months = $305 [tex]\times[/tex] 5 = $1515
Total amount of money Kianna saves this year = $(1505 + 1515)
= $3020
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Find the least common multiple of the given algebraic terms. x², 2xy, 3y
Step-by-step explanation:
common factor= x and y
remaining factor = x , 2 , 3
L.C.M = 6 x sq. y
qiang drives 15 miles at an average speed of 30 miles per hour. how many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
110 additional miles he will have to drive .
To calculate : additional miles qiang will have to drive
Let the additional no. of miles he has to drive be x .
⇒ Total Distance = 15 + x
Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )
The equation becomes ,
[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50
On simplification we get ,
15 + x = 25 + ( 10x / 11 )
x = 110
Therefore , 110 additional miles he will have to drive .
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A car is moving north at 60km/h. The driver sees a sign beside the road ahead of him. What is the velocity of the sign relative to:
a) The car
b) The ground
*Please leave an explanation*
The velocity of the sign are given as follows:
a) Relative to the car: 60 kilometers an hour.
b) Relative to the ground: 0 kilometers an hour.
What is relative speed?The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.
Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.
Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.
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A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, what is y
A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889
The general cosine function is given by
f(x)= A cos (B x -C) +D
where A= 1/3 is the amplitude,
period = 2π /B
π/3 =2π/B
B= 2/3
C= -2π is the horizontal shift and D= -3s a downward vertical shift.
If we substitute all these values into the formula we obtain;
f(x)= 1/3 cos (2/3 x +2π ) -3
if x= π then we have to calculate y
y= 1/3*0.3333 -3
y= -2.8889
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On a coordinate plane, a line goes through (0, 3) and (3, negative 1). A point is at (negative 3, 2).
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Answer:
Step-by-step explanation:
The line perpendicular to y = 4 will be a vertical line through the point (−2, 1). The equation of the vertical line is x = −2.
In triangle ABC, m∠B = (4x − 15)° and the measure of the exterior angle to ∠B is (14x − 21)°. Find m∠B.
12°
32°
33°
36°
Applying the definition of exterior angle, the measure of angle B is: c. 33°
What is the Exterior Angle of a Triangle?When a side of a triangle is extended through an interior angle, the angle formed is called the exterior angle of a triangle.
The angle to the exterior angle of the triangle, when added to the exterior angle will have a sum of 180 degrees, which means their supplementary angles.
Therefore:
4x - 15 + 14x - 21 = 180
4x + 14x - 15 - 21 = 180
18x - 36 = 180
18x = 180 + 36
18x = 216
18x/18 = 216/18
x = 12
m∠B = 4x - 15 = 4(12) - 15 = 33°
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Answer:
its B. 33
Step-by-step explanation:
HELP
At a Junk Yard a study was conducted using 48 cars and found that the average mileage on a car before it was junked was 164,000 and the population standard deviation is known to be approximately 28,000. Construct a 99% confidence interval of what the actual average mileage is for a car before it is junked.
A 99% confidence interval of what the actual average mileage is for a car before it is junked is; (153589, 174411)
How to find the confidence Interval?The formula for confidence interval is;
CI = x' ± z(s/√n)
where;
x' is sample mean
s is standard deviation
n is sample size
z is critical value at confidence level
We are given;
x' = 164000
n = 48
s = 28000
CL = 99%
z-score at confidence level of 99% is 2.576
Thus;
CI = 164000 ± 2.576(28000/√48)
CI = 164000 ± 10410.78
CI = (164000 - 10410.78), (164000 + 10410.78)
CI = (153589, 174411)
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A rectangular garden must have a perimeter of 540 feet and and area of at least
12,000 square feet. Describe the possible lengths of the garden. round to the nearest
whole number
I need help please!
The length of the garden is: l ≥ 6225ft.
Area = L multiplied by W. Since you measure the area in square feet, your final number should reflect that.
What is a Rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Let l serve as a symbol for the garden's length.
Let w be the symbol for the garden's width.
The perimeter is 540 feet.
The rectangle's circumference is equal to
2(l + w)2(l + w) = 540 l + w = 270. (1)
The rectangle's area is equal to its length times its width, which equals 12000. (2)
Make the variable w the subject of the following equation:
w = 270 - l. (3)
Substitute equation (3) into equation (2)
(270 - l)(l) ≤ 12000
270l - l² ≤ 12000
0 ≤ l² - 270l + 12000
l² - 270l + 1200 ≥ 0
Solving the quadratic inequality above:
l ≥ 6225
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The Venn diagam represents the
information from the following sets.
= {Prime numbers less than 38}
R = {2, 3, 5, 17, 19, 37}
S = {3, 5, 7, 11, 13, 37}
R
17 5
2
19 37
3/13
S
11
231 23
Find P(RUS)
P(RUS) =
=======================================================
Explanation:
The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.
R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 17, 19, 37, 3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}
This list of values consist of items in set R, set S, or both.
There are 9 items in set R U S.
This is out of 12 items total in the universal set rectangle.
The probability of randomly selecting something from set R U S is 9/12 = 3/4
In the given figure, l ∥ m and n are a transversal. If ∠1=80° and ∠5=100°,
find the measure of <2 , ∠3, ∠4.
Please give brief explanation
The value of angle ∠5 will be equal to 120°.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines.
A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.
Given that In the given figure, l ∥ m and n are transversal and the angles are ∠1=80° and ∠5=100°.
First, calculate angle 2,
∠1 = ∠2 = 80 ( By alternate interior angles)
Calculate the angle ∠4,
∠4 = 180 - 80 - 40
∠4 = 180 - 120
∠4 = 60°
Calculate the angle ∠5,
∠5 = 180 - 60
∠5 = 120
Therefore, the value of angle ∠5 will be equal to 120°.
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Write the equation for the line that passes through the point (-6, 2)
The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .
In the question ,
two points are given as (-6 , 2) and (-4 , -1) .
we need to find the equation of the line passing through the given points .
to find the equation First we need to find the slope ,
slope = (-1-2)/(-4-(-6))
slope = -3/(-4 + 6)
slope = -3/2
So , the equation of the line passing through the point (-6 , 2) with slope -3/2 is
(y - 2) = (-3/2)(x - (-6))
y - 2 = (-3/2)(x + 6)
y - 2 = (-3/2)x - 9
y = (-3/2)x - 9 + 2
y = (-3/2)x - 7
2y = -3x - 14
3x + 2y = -14
Therefore , The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .
The given question is incomplete , the complete question is
Write the equation for the line that passes through the point (-6, 2) and (-4,-1) , write the answer in fully reduced form .
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One motorcycle travels 80 mph and the second motorcycle travels 60 mph. if the faster motorcycle travels 1 hr longer than the slower motorcycle and it also travels twice the distance of the slower motorcycle, what distance does each motorcycle travel?
Each motorcycle travel a distance of 240 miles for the faster motorcycle and 120 miles for the slower motorcycle.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = time it took the faster motorcycle to travel
If the faster motorcycle travels 1 hr longer than the slower motorcycle, then the slower motorcycle travels x - 1 hours.
The product of the rate of speed and time is equal to the distance.
Hence, the distance traveled by the faster motorcycle is 80x, while the distance traveled by the slower motorcycle is 60(x - 1).
If the faster motorcycle travels twice the distance of the slower motorcycle, then the distance traveled by the slower motorcycle is 80x/2.
60(x - 1) = 80x/2
Simplify and solve for x.
60(x - 1) = 80x/2
60x - 60 = 40x
20x = 60
x = 3
distance traveled by the faster motorcycle = 80x = 80(3) = 240 miles
distance traveled by the slower motorcycle = 80x/2 = (80)(3)/2 = 120 miles
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Let's find
11
6
- Im
First, write the addition so the fractions have denominator 6.
Then add.
1 1
6
1
3 6
0 0
6
The required addition of the given fraction is given as 7/6.
Given that, a mixed fraction is given 1 1 /6 we have to determine the simplified fraction.
Fraction is defined as the number of compositions that constitutes the Whole.
Here,
Given fraction = 1 1 /6
This fraction is written as 1 + 1/6
Simplifying the fraction by multiplying the one with 6 and adding the product to the 1 in the numerator,
= [1×6 + 1]/6
= 7/6
Thus, the required addition of the given fraction is given as 7/6.
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What are the advantages of bankruptcy? a. Exempted items are allowed. b. Certain incomes are unaffected. c. Debts are erased. d. "Exempted items are allowed" and "An automatic stay is enacted". e. All of these choices are correct. f. An automatic stay is enacted.
The advantages of bankruptcy include the following: e. All of these choices are correct.
What is bankruptcy?In Financial accounting, bankruptcy can be defined as a legal process that is initiated when an individual or business organization (debtors) is relieved of the responsibility to pay their debts, honor its financial obligations to creditors, or protect them while they are trying to repay their debt.
The advantages of bankruptcy.Generally speaking, there are several advantages of bankruptcy and these include the following:
Some certain incomes are unaffected by bankruptcy.All of the debts are erased.An automatic stay would be enacted.Exempted assets such as unemployment benefits and retirement accounts are retained or allowed.In conclusion, we can reasonably infer and logically deduce that bankruptcy is generally considered as both a friend and foe (enemy).
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In a paragraph, explain the difference between an opinion piece of writing and an informational/informative piece of writing. What are the fundamental differences between the two? What do you write about in each? What do they have in common? I ONLY HAVE THIRTY MINUTES
The main difference between opinion based and informational essay is that in opinion based you have to share your own opinion reading any topic or something but in case of informative essay to have to provide particular information about the subject.
What is essay?Generally speaking, an essay is a bit of writing in which the author presents their own arguments; nevertheless, this definition seems ambiguous and includes elements of letters, papers, articles, pamphlets, and short story collections. Essays are divided into two categories: formally and informally. Formal writings are distinguished by their "serious aim, dignity, logical arrangement, and length," whilst informal papers are distinguished by their "personal element."
To express your opinions on a subject and persuade the reader of your point of view, you must write an opinions essay. To accomplish it, you must first present the subject and express your viewpoint. Following that, you should provide three arguments in favor of your viewpoint. Finally, create a closing in which you summarize your case and restate your viewpoint in a new way.
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Write a function rule for the table. x ƒ(x) –3 –6 –2 –4 –1 –2 0 0 ƒ(x) = x + 2 ƒ(x) = –2x ƒ(x) = x – 2 ƒ(x) = 2x
A function rule for the table: f(x) = 2x
In this question, we have been given a table.
We need to write a function rule for the table.
x ƒ(x)
-3 -6
-2 -4
-1 -2
0 0
We can observe that f(x) = 2x
Therefore, a function rule for the table: f(x) = 2x
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sin(2x)cos(7x) - cos(2x)sin(7x) = 0.1
Answer:
x≈-0.0200335+2kπ/5
x≈-0.648352+2kπ/5
Step-by-step explanation:
sin(-5x)=0.1
-sin(5x)=0.1
sin(5x)=-0.1
sin(5x)=1/10
5x=arcsin(- 1/10)
5x=π-arcsin(- 1/10)
5x=π-arcsin(- 1/10)
5x=π-arcsin(- 1/10)+2kπ
5x=π-arcsin(- 1/10)+2kπ
x=arcsin (1/10)/5 + 2kπ/5
x=arcsin (1/10)/5 + 2kπ/5
x≈-0.0200335+2kπ/5
x≈-0.648352+2kπ/5
Convert Decimal to Percent
1.56 =
0.31 =
Convert Percent to Decimal
62%=
94% =
Convert Decimal to Fraction
1.12 =
12
100
0.223 =
223
1000
0.728=
1.67 =
91.8% =
36.2 % =
0.57 =
0.67=
0.7 =
0.783=
148 % =
32.6% =
0.393 =
0.28=
100-
25
Answer: Your question is too long for me to answer
Step-by-step explanation:
2) Find the slope of the line passing through the points (5, 5) and (2, -3).
the answer is 1 but it could be a I took the test
Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Letters2go
Pack of 25 envelopes for £3.19
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
Using mathematical operations, Betsie should buy the 250 envelopes from Letters2go Shop at a total cost of £319.
How is the total cost determined?To determine the total cost, we first determine the unit cost of an envelope at each shop.
The unit cost is multiplied by the number of envelopes required less the cost of free envelopes at Value World.
The mathematical operations used include division and multiplication.
Deals:
Letters2go
Pack of 25 envelopes for £3.19
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go Value World
Cost per pack £3.19 £1.99
Cost per envelope £0.1276 £0.199
The number of envelopes 250 250
The number of packs 10 (250/25) 25 (250/10)
Cost of free envelopes £24.875 (25/2 x £1.99)
Total cost of envelopes £319 (£3.19 x 10) £472.63 (£1.99 x 250 - $24.875)
Thus, using mathematical operations, the total cost of 250 envelopes at Letter2go is less than the total cost at Value World.
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Suppose that y varies directly with .x, and y=-8 when x=2.
(a) Write a direct variation equation that relates x and y.
Equation:
(b) Find y when x = 5.
OC
Answer:
A. y = -4x
B. y = 20
Step-by-step explanation:
A. y = xk
Where k is constant
Substitute y for -8 and x for 2
-8 = 2k
Divide both sides by 2
-8/2 = 2k/2
-4 = k
k = -4
y = x(-4)
y = -4x
B. y when x = 5
y = 5(-4)
y = 20
Solve 6/k= cos 46°
Give your answer to 2 d.p.
n is an integer greater than 1
Prove algebraically that 10 + [tex]n^{2}[/tex] - (n-2)[tex]^{2}[/tex] is always an even number.
Your final line must have, "always even" as part of the line.
The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))
How to prove algebraically that 10+ n² - (n - 2)² is always an even number?To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer
Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically
10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² ) (factorize difference of two squares)
= 10+(n-(n-2))(n+(n-2))
= 10+(n-n+2)(n+n-2) (simplify)
= 10+(2)(2n-2) (factorize)
= 2(5+(2n-2))
Therefore, due to the factor of 2, the given expression is always even for integer n
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two cars are traveling in the same direction along the same route. the red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. if the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
Balck car can overtake the red car in 2 hrs
Relationship between Speed, Distance and Time:
The Relationship between Speed, Distance & Time can be understood by the following formulas
Speed = Distance/Time
Time = Distance / Speed
Distance = Speed X Time
Constant speed:
Constant speed is also called the uniform rate which involves something traveling at a fixed and steady pace or something moving at some average speed.
Here we have
Two cars are traveling in the same direction along the same route.
The speed of the Red car = 40 miles per hr
The speed of the Black car = 50 miles per hr
From above data
The difference between speeds of cars = 50 - 40 = 10 miles per hr
Which means the Black car is chasing the Red car at 10 miles per hr
Given that distance between two cars = 20 miles
The time taken by the Black car to cover 20 miles
=> Distance/ speed = 20/10 = 2hrs
Balck car can overtake the red car in 2 hrs
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Quetion
The elevation of a unken hip i −120 feet. Your elevation i 58 of the hip’ elevation. What i your elevation?
Quetion
The elevation of a unken hip i −120 feet. Your elevation i 58 of the hip’ elevation. What i your elevation?
Our elevation is 178 feet when the elevation of a sunken ship is 120 feet.
Given, The elevation of a sunken ship is 120 feet.
Your elevation is 58 of the ship elevation.
as it is given that the elevation of a sunken ship is 120 feet and our elevation is 58 of the ship elevation.
So, on using the concept of application of trigonometry we can conclude that our elevation is 58.
As, it is given that our elevation is 58 of the ship elevation.
So, our elevation is 120 + 58 = 178 feet.
Hence, our elevation is 178 feet when the elevation of a sunken ship is 120 feet.
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