Answer:
polygon has 12 sides
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
the sum of the interior angles of a polygon is
sum = 180° (n - 2 ) ← n is the number of sides
given the sum of the interior angles is 5 times sum of exterior angles, then
sum = 5 × 360° = 1800° then
180° (n - 2) = 1800 ( divide both sides by 180 )
n - 2 = 10 ( add 2 to both sides )
n = 12
Thus the polygon has 12 sides
The total number of books sold from 2010-2015 from
Amazon can be modeled by the function
3
2
f(x) = 40x + 8x + 14824x + 33000and the number of kinds
of books at Amazon from that same time period can be modeled
as g(x): =
10x + 22, where x is the number of years since
2010. What is the average number of each kind of book
Amazon sold?
Answer:
If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.
Step-by-step explanation:
Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
SSS
The triangles can be proved congruent by SAS theorem.
Properties of congruent triangles.Two or more triangles are said to be congruent if and only if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.
To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.
Therefore. in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;
It can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.
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a) What is the size of angle ABC? b) Use your answer to part a) to work out the size of reflex angle CBD. Give your answers to the nearest degree.
Answer:
a) 110
b) 250
Step-by-step explanation:
Read the top row of numbers for a. We are starting at zero and going to 110
Reflex is when two angles add up to 360
360 - 110 = 250
The table shows the approximate area
in square miles of the largest and smallest
states in the United States. What is the
difference between the areas in
square miles?
State
Area (mi?)
873
Alaska
Rhode Island
392
The difference between the areas is 481 square miles.
Given information:
Alaska is 873 sq miles in size, as well as Rhode Island, is 392 sq miles in total.
To determine the difference between the areas in square miles, the following calculation must be performed: subtract Alaska from Rhode Island square miles then we get:
Let X be the total difference:
873 - 392 = X
481 = X
Therefore, the difference in the areas in square miles is 481.
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The Burj Khalifa building in Dubai, United Arab Emirates, is one of the tallest buildings in the world at 2,722 feet tall. An American football field is 360 feet in length. Approximately how many football fields tall is the Buri Khalifa building? Round to the nearest tenth.
Answer:
7.5 which rounds to 8
Step-by-step explanation:
2,722 divided by 360 equals 7.56
check if needed <3
Find the lope of a line parallel to the line whoe equation i 6xy=-36xy=−3. Fully implify your anwer
The line parallel to 6y = -36x -3 will have the same slope which will be -6.
What is Slope of a line ?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The equation of the line is
6y = -36x -3
⇒y = -6x - 1/2
From slope intercept form of the equation we know that
equation of the line is y = mx + c
where m is the slope.
Therefore,
slope the line is -6
The line parallel to 6y = -36x -3 will have the same slope which will be -6.
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Lloyd's Llamas has $3,241.77 in liabilities and $12,457.12 in owner's equity. If the accounting equation is in balance, Lloyd's has $_______ in assets.
The number of asset is 15.698.89
How to calculate the number of asset ?
Assets = liabilities + equity
liabilities= 3,241.77
equity= 12,457.12
Assets= 3,241.77 + 12,457.12
= 15.698.89
Hence Lloyd has 15.698.89 number of assets
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Which transformation produces another triangle that has the same area as the one shown
A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.
How to plot a graph?f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.
In all options, there is a scale factor so it will change area but in option C
A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.
Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".
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The picture shows a shed. Find the length, AB, of the roof.
The length AB of the roof is 3.20 m.
What is the Pythagorean theorem.
The Pythagorean theorem is one that can be used to determine the value of the unknown side of a right triangle when given two of its sides.
The theorem states that;
/Hyp/^2 = /Adj/^2 + /Opp/^2
Considering the given picture of the shed, draw a perpendicular to B from a point C on parallel line A. So that the length of AB can be referred to as the hypotenuse of triangle ABC.
Now applying the Pythagorean theorem, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
/AB/^2 = /2/^2 + /2.5/^2
= 4 + 6.25
/AB/^2 = 10.25
AB = (10.25)^ 1/2
AB = 3.20
Thus, the length of AB of the roof is 3.20 m.
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Select the correct answer from the drop-down menu. You are conducting a survey on the best beaches in the world. The group that would probably give you the most reliable data is .
A) tourists who wish to visit the beaches
B) officials who manage the beaches
C) tourists who have visited the beaches
D) friends and family
The group that would probably give you the most reliable data is tourists who have visited the beaches. Option C is the correct answer.
In order to gather information about a service, product, or process, a survey is described as an act of looking at a process or interviewing a predetermined sample of people. Surveying beachgoers who have previously been there will yield more accurate results regarding the greatest beaches because they can share their personal experiences.
Surveying those in charge of the beaches is not a smart idea since they would be prejudiced in saying that their beaches are the finest. As a result, the third choice is the best one.
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Write the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.
○ y = − 1/x + 2/1/2
O y = 2x + 4
○ y = 1/x + 1/2/2
○ y = 1/x + 1/2
The equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].
What is slope intercept form of the line?
Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.
Given:
The line passes through the points (7, 6) and (- 1, 2).
We have to find the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.
First to find the slope of the line using the formula,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1)= (7, 6), (x_2,y_2)=(-1, 2)[/tex]
Plug the values in the above formula.
[tex]m = \frac{2-6}{-1-7} = \frac{-4}{-8}=\frac{1}{2}[/tex]
Now consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)\\y-6=\frac{1}{2}(x-7) \\y-6=\frac{1}{2}x-\frac{7}{2}\\ y=\frac{1}{2}x -\frac{7}{2}+6 \\y=\frac{1}{2}x+\frac{5}{2}[/tex]
Hence, the equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].
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How can you tell if you have a perfect square trinomial or the DIFFERENCE OF SQUARES?
The value of a perfect square is either a positive number or zero. They cannot be neutral.
what is perfect square ?Perfect squares are generated when you square an integer. For instance, the number 81 is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since 12 is squared to produce it. 169 is a perfect square since 13 may be squared to obtain it. Mathematical language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the outcome is referred to as a square number, a perfect square, or simply "a square." Therefore, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
The value of a perfect square is either a positive number or zero. They cannot be neutral.
Square differences can be positive, negative, or zero depending on the order in which the numbers are obtained.
One squared term will be added to the difference of squares, and another squared term will be subtracted.
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(NEED HELP ASAP!!)
What are the coordinates of the focus of the parabola?
A: (8, 6)
B: (-8, 6)
C: (-8, 2)
D: (8, 2)
Answer:
C: (-8, 2)
Step-by-step explanation:
Given parabola:
[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]
For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.
Therefore, the x-value of the vertex of the given parabola is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]
To find the y-value of the vertex, input x = -8 into the given equation:
[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]
Therefore, the vertex (h, k) of the parabola is (-8, 4).
The focus of the parabola is (h, k+p) where:
(h, k) is the vertex[tex]p=\dfrac{1}{4a}[/tex]Therefore:
[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]
Solve the quadratic by factoring. 3x^{2}+7=-8x+3 3x 2 +7=−8x+3
The roots of the given quadratic equation are x = -2/3 and x = -2.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is a quadratic equation as follows -
3x² + 7 = - 8x + 3
The given quadratic equations are -
3x² + 7 = - 8x + 3
3x² + 8x = 3 - 7
3x² + 8x + 4 = 0
(x + 2/3)(x + 2) = 0
(x + 2/3) = 0 and (x + 2) = 0
x = -2/3 and x = -2
Therefore, the roots of the given quadratic equation are x = -2/3 and x = -2.
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Tank 1: 36 inches long, 18 inches wide, and 12 inches tall. How many gallons of water is in the tank?
I need a step-by-step explanation please
In a tank that is 36 inches long, 18 inches wide, and 12 inches tall have approximately 33 gallons of water.
How to calculate volume of a tank?The rectangular tank's volume may be calculated using the formula V = l*b* h, where "l" stands for the tank's length, "b" for its width, "h" for its height, and "V" for its volume.
Define volume.The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume = length*width*height
V=36*18*12
V=7776 inches^3
which is approximately 33 gallons.
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Mr. Nunez brought 2 1/2 cake to chool for her cla. If there are 15 people in the cla ,including Mr. Nine, how much of the cake will each peron receive
Each person present in Mrs. Nunez's class is going to receive 1/6th part of the cake when they get it cut.
Mr. Nunez brought 2 ½ cakes for 15 people which means, 2 ½ cakes will be equally divided into 15 pieces and distributed to each person. Since 2 ½ is a mixed fraction we have to convert it into a regular fraction which will be equal to 5/2. So, the amount of cake a person will receive is equal to (5/2)/15 which is 1/6, which is roughly 0.167 part of the whole cake.
The given problem has been solved by using the properties of fractions.
The complete question that you might be looking for is-
Mrs. Nunez brought 2 1/2 cake to school for her class. If there are 15 people in the class, including Mr. Nine, how much of the cake will each person receive?
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hat is the product of the least common multiple and the greatest common factor of $22$ and $48$?
Answer:
1056
Step-by-step explanation:
You want the product of the LCM and the GCF of 22 and 48.
ProductOne way to find the LCM of two numbers is to start with their product, then divide out the extra factor:
LCM(A, B) = (A×B)/GCF(A, B)
Since we want the product of the LCM and the GCF, we can start with this and multiply by the GCF:
LCM(A, B) · GCF(A, B) = ((A×B)/GCF(A, B)) · GCF(A, B)
LCM(A, B) · GCF(A, B) = A×B
Using this for the given numbers, we get ...
LCM(22, 48)·GCF(22, 48) = 22·48 = 1056
__
Additional comment
If you want to go to the trouble of finding the LCM and GCF, you get ...
22 = 2·11
48 = 2·24
LCM(22, 48) = 2·11·24 = 528
GCF(22, 48) = 2
LCM·GCF = 2·528 = 1056
Simplify:-
[tex]x {}^{2} - 5x + 6 \div x {}^{2} +3x - 10 \\ [/tex]
Guys help me please.
Step-by-step explanation:
[tex] = {x}^{2} \div {x}^{2} + 3x - 5x + 6 - 10 \\ = 1 - 2x - 4 \\ = - 2x - 4 + 1 \\ = - 2x - 3 \\ = - 1(2x + 3)[/tex]
HI,HOPE THAT IS HELPFUL.
help. pls.
-photo attached !
Find the measures of the numbered angles.
(the angles i need to find)
<1 _?
<2 _?
<3 _?
<4 _?
<5 _?
<6 _?
<7 _?
<8 _?
Answer:
<1=75°[corresponding angles are equal]
<2=180-<1=(180-75)°=105°[sum of st.angles is supplementary]
<3=<2=105°[Vertically opposite angles are equal]
<4=75°[Alternate angles are equal]
<6=<2=105°[Corresponding angles are equal]
<7=<6=105°[Vertically opposite angles are equal]
<8=75°[Vertically opposite angles are equal]
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somebody help please
Answer:
Step-by-step explanation:
because HA⊥HR, HR⊥DR, so HA ║ DR, then we know ∠DHR=∠ARH,
we konw, AR=HD, They have a common segment HR, as well as the same angle，so HRA≅RHD
You have an ant farm with 22 ants . The population of ants in your farm will double every 3 months
The number of ants in 6 months will be 88 ants.
How to calculate the value?The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this situation, in an ant farm with 22 ants and the population of ants in your farm will double every 3 months.
The number of ants in 6 months will be:
= 22 × (6/3)²
= 22 × 2²
= 88 ants
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Complete question
You have an ant farm with 22 ants . The population of ants in your farm will double every 3 months. What is the number of ants in 6 months.
what are the conditions for using the normal approximation for a sampling distribution of proportions g
The normal approximation for sampling distributions of proportions can be used when the sample size is large enough.
What prerequisites must be met for a sampling distribution of proportions g in order to use the normal approximation?The conditions for using the normal approximation for a sampling distribution of proportions are as follows: The sample size (n) must be sufficiently large (usually 30 or more). The sample proportion (p) should not be close to 0 or 1. The population distribution should be normally distributed.The general rule is that if the sample size (n) is greater than or equal to 30, then the normal approximation can be used. When using the normal approximation for a sampling distribution of proportions, the sample size must be greater than or equal to 30 and the population proportion (p) must be between 5% and 95%. Furthermore, the sample size must be large enough that the expected number of successes (np) and expected number of failures (nq) are both greater than or equal to 10. Finally, the sampling distribution should be approximately normal and the sample should be randomly selected from the population. The normal approximation is a useful tool for estimating confidence intervals and the probability of extreme values, as well as for hypothesis testing. It can be used to estimate the probability of success in a given sample of proportions, which can be helpful when making decisions about a population or understanding the behavior of a system.To learn more about distribution of proportions refer to:
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City Fitness, a popular gym, currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of
1
4
each year.
Write an exponential equation in the form y=a(b)x that can model the number of members, y, in x years.
The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.
The expression can be written as,
[tex]y = 840(1.25)^x[/tex].
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A container has cups of milk in it. The container is 1/3 full. How many cups does the container hold? Explain or show your reasoning.
Answer:
Step-by-step explanation:
2 or 6 i think im probaly wrong
Answer:
The container can hold 6 cups.
Step-by-step explanation:
Since the container is 1/3 full, and it currently has 2 cups, we know that it can only hold 6 cups as 3 × 2 is equal to 6.
Questions with Bounds:
1) Andy Mann is building a garden fence out of planks. The planks are 10cm wide to the nearest cm. He needs to make 75 m of fencing altogether, correct to the nearest meter. How many planks does he need to order to make sure he has enough to complete the fence?
A total of 785 planks Andy Mann needs to order to make sure he has enough to complete the fence.
As the planks are 10cm wide to the nearest cm.
The total length of the fencing is = 75 m
From above, we can conclude that,
Range of the planks' lengths: 9.5 cm <= Plank's length < 10.5 cm
Range of fencing needed: 74.5 m <= Fence length < 75.5 m
We should consider the worst-case scenario where all the planks are 9.5 cm.
To complete the job, he only needs 74.5 m in total.
So, the total number of planks needed for completing the Job will be
= (74.5 * 100) / 9.5 = (7.84210*100) = 784.210
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Mrs. Hanover borrows $1,413 at a
rate of 5% per year. How much
Simple Interest will she owe if it
takes her 9 months to repay the
loan? Round your answer to the
nearest cent
well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99[/tex]
11c+ 8) (-9c - 1)
Help plssss
Answer:
Step-by-step explanation: (11c + 8) (-9c - 1)
Then expand
which would be 11c ( -9c - 1) + 8 ( -9c - 1)
-99c^2 -11c - 72c - 8
It becomes -99c^2 - 83c -8
I hope this was helpful
What are the 3 steps to solving a two step equation?
Answer:
Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes
1.3584655000
2.85760000
3.146737000
4.5555627000
5.7777000
please help
Step-by-step explanation:
1. Eliminate any constant that is on the same side as the variable.
2. Use inverse operations to isolate the variable by itself.
3. Whatever you do to one side you do to the other.
Find the value of x in the figure
Answer:
x=40º
Step-by-step explanation:
A straight line is 180º
180-40=140º
180-140=40º
x=40º
Hope this helps :)
What is another word for undecidable?
Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.
Clarify algorithm.A calculation or problem-solving procedure is known as an computation or algorithm. Algorithms serve as a thorough set of instructions that direct hardware- or software-based routines through a sequence of planned actions step by step. In all areas of IT, algorithms are commonly employed.
Here,
If it is impossible to develop an algorithm that reliably returns a true or false result for each input value, the problem is said to be undecidable.
The category of inherently unknowable questions, a subtype of insoluble problems, only includes questions that ought to receive a yes-or-no response .
Thus ,incomputable. is another word for undecidable.
Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.
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