A triangle has vertices at A(-2, 3), B(2, 1), and C(1, 0). After a transformation, the image of the triangle has vertices at A'(-2, -3), B' (2, -5), and C'(1, -6). Identify the transformation.
The transformation that is applied to the ΔABC to get the ΔA'B'C' is vertical translation by 6 units downwards.
The triangle has the vertices A(-2, 3), B(2, 1), and C(1, 0)
They are transformed such that:
A(-2, 3)→A'(-2,-3)
B(2, 1)→B'(2,-5)
A(-1, 0)→A'(-2,-6)
Now if we carefully observe we can see that the y-coordinate of A' is 6 less than that of A.
Similarly for B and C the coordinates are 6 units less than that of the object, but the x-coordinate remains the same.
This proves that the graph follows a vertical transformation and since the new ordinates are 6 units smaller, so the graph is translated 6 units downwards.
A function, f, that maps to itself is known as a transformation, or f: X→X'. The pre-image X will change into the picture X' following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation.
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The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer:
A. The y-intercept represents the number of mammals when they were originally counted.
B. The line y = 0 is an asymptote of the graph.
C. The y-intercept.is 75.
D. The y-intercept is 120.
E. The asymptote indicates that the number of mammals counted when the study began was 120.
F. The asymptote indicates that as years pass, the number of mammals will approach 0.
G. The line x = 0 is an asymptote of the graph.
The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;
A. The y-intercept represents the number of mammals when they were originally counted was 120
B. The line y = 0 is an asymptote of the graph
D. The y-intercept is 120
F. The asymptote indicates that as years pass, the number of mammals will approach 0
What is an asymptote of a graph?An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.
The points on the graph of the exponential function are;
(0, 120) and (55, 17)
The rate at which the population is decreasing = -3.5%
The output of the graph, y = The number of mammals x years after counting
The key features of the exponential function are;
The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct
The coordinates of the y-intercept is (0, 120)
The y-intercept is therefore the point y = 120
Therefore, option D is correct
The general form of the growth exponential function is presented as follows;
f(x) = a·bˣ + k
r = b - 1
b = 1 + r
Therefore;
b = 1 - 0.035 = 0.965
a = The first term = 120
Plugging in the known values from the graph, we get;
f(0) = 120 = a + k
120 = 120 + k
k = 120 - 120 = 0
k = 0 = The asymptote
Therefore, an asymptote is the line y = 0 option B is therefore correct
The number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity
Therefore as the years pass the number of mammals will approach 0, option F is correct
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what is 33+900212323
Answer:
900212356
Step-by-step explanation:
An upcoming business has vowed to increase profits by 2% every year for the next decade. Initially the company started by making $100 million dollars. How much will they be making after 10 years? Keep your answer in millions rounded to a whole number.
The profit that the upcoming business would be making after 10 years is $122 million.
What is the profit in 10 years?The profit of the business in 10 years can be modelled with an exponential equation. This is because the rate of growth of profit each year would be 10% of the last year's profit.
The equation that is used to determine the profit in 10 years is:
FV = P (1 + r)^n
Where:
FV = Future value P = Present value R = interest rate N = number of yearsFV = 100 x (1 + 0.02)^10
FV = $100 million x (1.02^10) = $122 million
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(b) 12 friends travel to the festival.
5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.
The probability that they two people are chosen and travel by different transport is 47/144
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability is given as sample space / total outcome
Probability to travel by car p(C)= 5/12
Probability to travel by bus P(B)= 4/12=1/3
Probability to travel by train P(T)= 3/12= 1/4
for two people chosen at random
P(C ×B)= 5/12×1/3= 5/36
P(B×T)= 1/3×1/4= 1/12
P(C×T)= 1/4×5/12= 5/48
Therefore the probability that the two chosen travel by different car is
P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48
= 141/432
divide through by 3
= 47/144
Hence the get the required answer.
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Find the circumference of the circle to the nearest tenth. Use 3.14 for it.
Answer:
Step-by-step explanation:
157m is the answer.
A board game uses the deck of 20 cards shown to the right. Two cards are selected at a random from this deck. Calculate the probability that first card selected has a yellow bird and second cared selected has a lion both with and without replacement
The probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement is 1/40 and 1/38. respectively.
What is probability?
Probability is the likelihood of an event or more than one event occurring. It is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Probability may also be described as the likelihood of an event occurring divided by the number of expected outcomes of the event. i.e.,
P(A) = f / N
Where:
P(A) = Probability of an event (event A) occurring
f = Number of ways an event can occur (frequency)
N = Total number of outcomes possible
Here deck of 20 cards are given which implies total number of possible outcomes are 20. From these 20 cards 5 cards has lions and 5 cards has birds in which 2 are yellow and 3 are red.
Now two cards are selected randomly.
We have to find the probability that first card selected has a yellow bird and second card selected has a lion both probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement.
Probability with replacement:
Probability that first card selected has a yellow bird = 2/20 ---(1)
Since replacement is allowed so the probability that second card selected has a lion = 5/20---(2)
So, the probability that first card selected has a yellow bird and second card selected has a lion with replacement = (1) * (2) = 2/20 * 5/20 = 1/40.
Probability without replacement:
Probability that first card selected has a yellow bird = 2/20 ---(3)
And since replacement is not allowed, the probability that second card selected has a lion = 5/19---(4)
So, the probability that first card selected has a yellow bird and second card selected has a lion without replacement = (3) * (4) = 2/20 * 5/19 = 1/38.
Therefore, the probability with and without replacement is 1/40 and 1/38. respectively.
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7/15 - 6 2/5 = need the answers
The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.
Given,
In the question:
The Fraction is given as:
7/15 - [tex]6\frac{2}{5}[/tex]
To solve the above fraction.
Now, According to the question;
Let's know
What is fraction in math?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Come to the question:
7/15 - [tex]6\frac{2}{5}[/tex]
7/15 - 32/5
Take the L.C.M
= [tex]\frac{7-96}{15}[/tex]
= -89/15
Hence, The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.
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26. Use Patterns and Structure Luis is programming
an animation for a countdown timer where
points flash in sequence, one at a time, around
in a circle. He calculates that the coordinates of
the first four points in his sequence are (6, 0),
(5.5, 2.3), (4.2, 4.2), and (2.3, 5.5). He can find
the rest of the coordinates by rotating the first
four points by 90°, 180°, and 270°. What are
the coordinates of the points that complete the
sequence around in a circle?
Answer: ?????
Step-by-step explanation:
what is the difference 5 - 3.12
Answer: There is a difference of 1.88
Step-by-step explanation: Pls brainiest.
Answer:
1.88
Step-by-step explanation:
hopethishelpsya:)
Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00. Write an expression to show how much he paid for lunch. Then find the value of the expression.
The value of the expression which shows the amount he paid for lunch is 7 dollars.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and divisions.
Given that Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00.
Now here is the expression-
1+(2x3)= 2 x 3 = $6
Cost of lunch = ($3 / hamburger) (2) + ($1 / soda) (1)
Cost of lunch = $6 + $1
Cost of Frankie's lunch = $7
Therefore, the value of the expression which shows the amount he paid for lunch is 7 dollars.
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Someone please help step by step how to solve
3(x+2)-5=13
pls
If a bar of soap cost 70p and a box of plasters cost 95p how much does buying one of each cost
The cost of buying one of each of the soap and plaster is 165p.
How to calculate the cost?From the information, the bar of soap cost 70p and a box of plasters cost 95p.
It should be noted that in order to find the total cost, we will have to add the. oat of each product.
This will be:
Total cost = Cost of soap + Cost of plaster
= 70p + 95p
= 165 p
The cost is 165p.
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Charles drew a plan for a rectangular piece of
material that he will use for a blanket. Three of the
vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).
What are the coordinates of the fourth vertex?
The fourth coordinate of rectangular piece of material is (2.8 , -2.7)
According to the question,
Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).
As we know , the opposite sides of rectangle are equal
If we locate these coordinates in our graph and join them
Length of rectangle will be = 2.8+1.4 = 4.2cm
Breadth of rectangle will be = 3.7 + 2.7 = 6.4cm
So, the fourth coordinate should lie 6.4cm far from (2.8,3.7)
Subtracting 6.4 from y-axis,
Fourth coordinate = 3.7 - 6.4
= -2.7
Therefore , The fourth side of rectangle = (2.8 , -2.7)
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juan thinks the answer is between 5 and 6 melanie says the answer is between 3 and 4 who is correct [tex]\sqrt[3]{28}[/tex]
Answer:
28
Step-by-step explanation:
4,8,12,16,20,24,28. +4 every time
7p5 · 4p3 I have no idea how to do this please help
A certain element has a half-life of approximately 15 hours. How long would it take
for 500 grams of the element to decay to 299 grams? Leave your answer as an integer
or simplified expression.
Using an exponential decay equation, we will see that after 11 hours the element will decay to 299 grams.
How long takes to decay?We know that we have an element with a half-life T, and it has a decay equation that can be written as:
f(t) = A*e^(-t*ln(2)/T)
Where A is the initial amount of the element, and f(t) is the amount of the element t hours after.
In this case the given values are:
A = 500g
T = 15h
Then the exponential decay is:
f(t) = 500g*e^(-t*ln(2)/15h)
And we want to find the value of t such that f(t) = 299g, then we can solve:
299g = 500g*e^(-t*ln(2)/15h)
299/500 = e^(-t*ln(2)/15h)
If we apply the natural logarithm in both sides we get:
ln(299/500) = -t*ln(2)/15h
-ln(299/500)*15h/ln(2) = t
11 h = t
It will take 11 hours to go from 500 grams to 299 grams.
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Please help an 8th grader in needdddddddddddddddddddddddddddddddddddddddddddd
Answer:
The two points used to find the slope:
[tex]x_1,y_1[/tex]: 2,30
[tex]y_1,y_2:[/tex] 4,10
Final equation: y = -10x + 50
Step-by-step explanation:
From a fellow 8th grader <3
First, let's review the slope of a line: y = mx + b
Where m is the slope, and b the y-intercept
Let's find the slope. To do this I will select 2 points from this graph, and using the slope formula I will calculate it
Slope formula: [tex]\frac{rise}{run} =\frac{change- in- y}{change-in-x} =\frac{y^2-y^1}{x^2-x^1}[/tex]
To get the most accurate answer, I will be using the 2 points given that are directly on the line:
1 = (2, 30)
2 = (4, 10)
Slope: [tex]\frac{10-30}{4-2} =\frac{-20}{2} =-10[/tex]
m = -10
It makes sense that it is a negative, since the graph continues downwards.
Let's update our equation: y = -10x + b
We can see that the line intersects the y-axis at y = 50
Plug this into our b-value:
y = -10x + 50
Now, I would recommend using a graphing calculator (like a TI-83) or an online one (like desmos) to double check this. I have attached a screenshot of this line on desmos. From there we can see if this line matches up with the one seen on your graph.
Our answer is:
The two points used to find the slope:
[tex]x_1,y_1[/tex]: 2,30
[tex]y_1,y_2:[/tex] 4,10
Final equation: y = -10x + 50
Please let me know if this helped you, and if this was the correct answer! If it is incorrect I will do my best to revise my answer.
Answer: y intercept is (0,50) and Slope is -10.
Final equation is y= -10x+50
Step-by-step explanation:
Y-intercept is at what point the line intercepts the y-axis. It intersects at (0,50) coordinate point as you can see.
Slope is change in y divided by the change in x. When you change x by 1, y changes by -10. So it is -10/1 = -10. Slope is -10.
Since we know y intercept and slope equation is y=-10x+50
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
The center of the circle lies on the x-axis
The radius of the circle is 3 units.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The standard equation of a circle is expressed as:
x²+y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is
x²+y²-2x-8=0
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This shows that the center of the circle lies on the x-axis
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:
r² = 9
r = 3 units
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Hence we get the required answers.
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Find the range and standard deviation of the set of data.
11, 10, 5, 13, 16
The range is 11.
(Simplify your answer.)
The standard deviation is ____
(Round to the nearest hundredth as needed.)
Find the standard deviation please
The range of the set of data is 11 and the standard deviation of the set of data is 4.06
What is Standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given, set of data.
11, 10, 5, 13, 16
First of all we will arrange them
5, 10, 11, 13, 16
To find the range we have to;
Range = Biggest number - smallest number
= 16 - 5
Range = 11
Thus, the range of the given set of data is 11
Now, for standard deviation,
By first squaring the discrepancies between the observations and the mean, and then taking the square root of the sum of the squares of the differences divided by the number of observations minus 1, the standard deviation is computed.
Mean = Sum of Observations/Total Observations
Mean = (5 + 10 + 11 + 13 + 16)/5
= 55/5
= 11.
Square of the mean = 11² = 121
Now subtracting the mean from each observation and squaring it gives:
(5 - 11)² = (-6)² = 36
(10 - 11)² = (-1)² = 1
(11 - 11)² = (0)² = 0
(13 - 11)² = (2)² = 4
(16 - 11)² = (5)² = 25
Sum of squares = 36 + 1 + 0 + 4 + 25
= 66
variance = 66 / n-1
= 66 / (5 - 1)
= 66 / 4
= 16.5
Standard deviation = √variance
= √16.5
= 4.06
Thus, the Standard deviation of the set is 4.06
Hence, The range and standard deviation of the set of data is 11 and 4.06 respectively
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A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 35 ft long and 28 ft wide.
Find the area of the garden. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer
Answer:
1287.72 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area of the rectangle is length times width
a = (35)(28) = 980
Area of a circle is [tex]\pi r^{2}[/tex], but this is half of a circle so we will divide the answer by 2
a = [tex]\frac{3.14(14^{2}) }{2}[/tex] = [tex]\frac{3.14 x 196}{2}[/tex] =[tex]\frac{615.44}{2}[/tex] = 307.72
Add the half circle and the rectangle
980 + 307.72 = 1287.72
Nicola needs to put up bunting around a whole room
for a party.The room is 4m long and 3m wide.
she has lots of 70 cm lenghts of bunting.Every time she ties two pieces together she needs to use 50mm of each piece of string for the knot. How many pieces
of 70 cm long bunting does she need to go right around the room ?
The pieces of long bunting is 22.
From the question, we have
The room is 4m long and 3m wide.
perimeter of room = 2×(4+3)
=14 m = 1400 cm
she has lots of 70 cm lenghts of bunting.
1400 cm/70 cm = 20
she needs to use 50mm =5 cm of each piece of string for the knot.
20×5 = 100
100/70 ≈2
pieces of 70 cm long bunting = 20+2 =22
Divide:
Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.
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x + y is greater than or equal to 4
Answer:
I am going sujshsbeba170
Triangles F G H and J K L are shown. Angles G F H and K J L are congruent and angles F H G and J L K are congruent.
To show that ΔFGH ≅ ΔJKL by SAS, what additional information is needed? Check all that apply.
FH ≅ JL and FG ≅ JK
FH ≅ JL and HG ≅ LK
∠G ≅ ∠K and FH ≅ JL
∠G ≅ ∠K and GH ≅ KL
∠G ≅ ∠K and FG ≅ JK
Any of the following information can be used to show that ΔFGH is congruent to ΔJKL by SAS.
How to Show that Two Triangles are Congruent by SAS?The criteria for proving that two triangles are congruent to each other by the SAS congruence postulate are:
The two corresponding sides of both triangles must be congruent to each other.One pair of included corresponding angles in both triangles must also be congruent to each other.In the image given that shows triangle FGH and triangle JKL, we are given the following:
∠F ≅ ∠J and ∠H ≅ ∠L [two pairs of congruent angles]
No two congruent sides are marked in the triangles. Therefore, the additional information that may be needed to prove the triangles are congruent by SAS can be:
a. FH ≅ JL and FG ≅ JK
b. FH ≅ JL and HG ≅ LK
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Lamar buys candy that costs $5 per pound. He will buy at most 12 pounds of candy. What are the possible amounts he will spend on candy
Use C for the amount (in dollars) Lamar will spend on candy.
Write your answer as an inequality solved for C.
Answer:
He will spend $60 on candy
Step-by-step explanation:
If the cost for one pound is $5, then just multiply.
12 x $5 = $60
Answer: C=7
Step-by-step explanation: C=12+5
the answer is c=7
Determine which answer in the solution set will make the equation true.
5f − 14 = 4f − 16
S: {−16, −2, 2, 4}
−16
−2
2
4
a) What are the coordinates of A?
b) What are the coordinates of B?
Answer:
coordinates of A are (-4.5, 2)
coordinates of B are (0, -3.5)
Solve for X
(9x+1)°
789
(17x - 3)
Type your answer...
The value of x in the given triangle is x = 4
Calculating the value of x in a triangleFrom the question, we are to determine the value of x.
From the given triangle,
We can write that
(9x+ 1)° + 78° + (17x - 3)° = 180° (Sum of angles in a triangle)
Now, we will solve for x
(9x+ 1)° + 78° + (17x - 3)° = 180°
9x° + 1° + 78° + 17x° - 3° = 180°
Collect like terms
9x° + 17x° = 180° - 1° + 3° - 78°
26x° = 104°
x = 104/26
x = 4
Hence, the value of x is 4
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For triangle XYZ, m∠X = (3g + 19)° and the exterior angle to ∠X measures (6g + 53)°. Find the measure of ∠X and its exterior angle
Check the picture below.
Estimate the product. 17 × 1.68
Answer:
34
Step-by-step explanation:
When estimating the product of an integer and a decimal, first round the decimal to its nearest whole number.
If the digit in the tenth place is less than 5, round down to the nearest whole number.If the digit in the tenth place is 5 or more, round up to the nearest whole number.Therefore,
1.68 ≈ 2So an estimate of the product is:
[tex]\implies 17 \times 1.68 \approx 17 \times 2[/tex]
Partition 17 into tens and units:
[tex]\implies17 \times 2= (10+7) \times 2[/tex]
Apply the distributive property of multiplication over addition:
[tex]\begin{aligned}\implies (10+7) \times 2&=(10 \times 2)+(7 \times 2)\\&=20+14\\&=34\end{aligned}[/tex]
Therefore:
[tex]\boxed{17 \times 1.68 \approx 34}[/tex]
Answer:
≈ 34
Step-by-step explanation:
The estimate value of 1.68,
→ 17 ≈ 17
→ 1.68 ≈ 2
Then the estimated product is,
→ 17 × 1.68
→ 17 × 2 = 34
Therefore, the product is 34.