In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B as reflected line equation and explained as
When a shape is reflected in a line, it means that each point on the original shape is mapped to a corresponding point on the reflected shape that is symmetrical with respect to the reflecting line.
The line of reflection can be any straight line, and in this case, the line of reflection is given by the equation x = 2. To understand how the reflection works, imagine holding a mirror along the line x = 2 and placing Shape A on the mirror. The reflected shape, Shape B, would be the image that you see in the mirror. In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B. This means that for each point on Shape A, we take its x-coordinate, subtract it from 2 to find the distance from the line of reflection, and then add that distance to 2 to find the x-coordinate of the corresponding point on Shape B. The y-coordinate remains the same.
The line of reflection acts as a dividing line between Shape A and Shape B, and the points on Shape B are exactly the same distance from the line of reflection as the points on Shape A, but on the opposite side. This means that Shape B is a perfect mirror image of Shape A, reflected across the line x = 2.
In summary, the reflection of Shape A in the line x = 2 maps each point on Shape A to a corresponding point on Shape B that is symmetrical with respect to the line of reflection. The result is a perfect mirror image of the original shape, reflected across the line.
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60. MODELING REAL LIFE You are designing an
obstacle course along a straight path. The distance
between obstacle three and obstacle seven is the
same as the distance between obstacle four and
obstacle nine. Show that the distance between
obstacle three and obstacle four is the same as the
distance between obstacle seven and obstacle nine.
By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.
What is distance?Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.
Given,
The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.
Distance of 7th obstacle = x
Let,
Distance of 9th obstacle = y
Distance of 3rd obstacle = x'
Distance of 4th obstacle = y'
Distance between obstacle 3 and 7 = x - x'
Distance between obstacle 4 and 9 = y - y'
Distance between obstacle three and obstacle four = x' - y'
Distance between obstacle seven and obstacle nine.= x - y
According to the question
x-x' = y-y'
⇒ x - y = x' - y'
Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.
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A father age is 25 years older than Son the sum of Their age is 53. find their Ages using simul- taneous equation and using elimination method
Answer: To find the father's and son's ages, we can set up two simultaneous equations:
Let's say the son's age is "x"
Then, the father's age would be x + 25
And the sum of their ages is x + (x + 25) = 53
So, 2x + 25 = 53
Solving for x, we get:
2x = 28
x = 14
Therefore, the son is 14 years old, and the father is 14 + 25 = 39 years old.
To use the elimination method, we can add the two equations:
x + (x + 25) = 53
2x + 25 = 53
Simplifying, we get:
2x = 28
x = 14
And the father's age would be x + 25 = 14 + 25 = 39 years old.
Step-by-step explanation:
which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same numb
The equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number" is 3 – (n – 1) = 1/2(3n – 4)
Let the number be n.
Gven: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"
So,
The expression "three minus the difference of a number and one" represent the equation is;
3 – (n – 1)
Also,
The expression "one-half of the difference of three times the same number and four" represent the equation is;
1/2(3n – 4)
Hence,
Complete expression represents the equation is
3 – (n – 1) = 1/2(3n – 4)
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(1 – n) – 3 = (4 – 3n)
3 – (1 – n) = (4 – 3n)
(n – 1) – 3 = (3n – 4)
3 – (n – 1) = (3n – 4)
A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
(SAT Prep) Find the value of x
PLS ASAP
The value of x is given as follows:
x = 155º.
How to obtain the value of x?For the triangle at the left, considering that the sum of the measures of the internal angles of a triangle is of 180º, the angle measures are given as follows:
90º.35º.180 - (90 + 35) = 55º.For the triangle at the right, considering the ray formed at the top, the measures are given as follows:
90º.180 - (55 + 60) = 65º.180 - (90 + 65) = 25º.An angle is supplementary with it's external angle, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:
x = 180 - 25
x = 155º.
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The distance between Dallas and Houston is about 364 kilometers. There are approximately 8 kilometers in 5 miles.
measurement is closest to the number of miles between these two towns?
Answer
A 227.5 miles
B 582.4 miles
C 40 miles
D 372 miles
kilometers in 5 miles
The measurement closest to the number of miles between the two towns is 227.5 miles.
What is cross multiplication?A method for finding the answer to linear equations in two variables is cross-multiplication. It turns out to be the quickest way to resolve two linear equations. To cross multiply two fractions, multiply the first fraction's numerator by the second's denominator and the second fraction's numerator by the first fraction's denominator.
Given that, distance between Dallas and Houston is about 364 kilometers.
The measurement of:
8 km = 5 miles
364 km = x miles
Using the method of cross multiplication, we have:
x = 364 (5) / 8
x = 227.5 miles
Hence, the measurement closest to the number of miles between the two towns is 227.5 miles.
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PLEASE help me understand the steps to solve this i feel like crying i dont understand
Answer:
4
Step-by-step explanation:
First:
(-2 1/2)*(-1 3/5) = 2.5*1.6
Second:
2.5*1.6=5/2*8/5
Third:
5/2*8/5=
4
I would really appreciate your help. Thank you.
Answer:
75
Step-by-step explanation:
trust me bro
I NEED HELP ON THIS ASAP!!!
Answer: Look below :)
Step-by-step explanation:
I graphed the inequality below:
from that we can see:
a. Points on the line are combinations of US/Mexico minutes he can do where all of his prepaid money will be used, For example, he could do 50 USA minutes and 80 Mexico minutes, and there would be no money left to spend
b. Points above the line are combinations of US/Mexico minutes that will cost him more than the prepaid $50.
c. Points below the line are combinations of US/Mexico minutes that will leave him with money left over from his $50.
I hope this makes sense! ask questions if you have any :)
A prize is divided in the ratio 7:5. One share is £122 more than the other what is the total amount?
a = amount given to the 1st share, ratio of 5.
a + 122 = amount given to the 2nd share, ratio of 7.
T = total amount
so the total amount is really "T", and we'll be splitting that into a 7 : 5 ratio, that is, we'll be dividing "T" by (7 + 5) and distribute accordingly.
[tex]\stackrel{\textit{total split by 7 + 5}}{\cfrac{T}{7+5}\implies \cfrac{T}{12}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{we know the 1st share is}}{a= 5\cdot \cfrac{T}{12}}\implies a=\cfrac{5T}{12} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the 2nd share is}}{a+122= 7\cdot \cfrac{T}{12}}\implies a+122=\cfrac{7T}{12}\implies \stackrel{\textit{substituting from above}}{\left( \cfrac{5T}{12} \right)+122=\cfrac{7T}{12}} \\\\\\ 122=\cfrac{7T}{12}-\cfrac{5T}{12}\implies 122=\cfrac{2T}{12}\implies 122=\cfrac{T}{6}\implies \boxed{732=T}[/tex]
Simplify the expression below:
14^2 - 24 / 3(2)
--------------------- (divided by)
|-3 + 2(6)|
Answer:
I got 20 when calculating this
PLEASE THIS IS REALLY ARGENT
Two simultaneous equations are given below, where p and q are constants.
3x-py = 4
4x-3y + q = 0
The solution to these equations is x = 1, y = 2.
Find the value of p and q.
Team % of Volume Items processed per person per hour Picking 100% 150 Packing Group A 35% 105 Packing Group B 65% 70 Shipping 100% 175 How many items will be processed by Packing Group B in order to ship a total of 168,000 units for the shift? 46 70 84,000 109,200 168,000
By using shipping volume, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift.
To solve this problem, we need to work backwards from the shipping volume and use the given processing rates to determine the required processing volumes for each stage of the process.
First, we can calculate the total number of hours of packing and shipping required to process 168,000 units:
168,000 units ÷ 175 units per person per hour = 960 hours
Next, we can determine the volume of items that need to be packed by Group B in order to ship this total volume. Since Group B processes 65% of the volume, we can set up the following equation:
0.65x = 168,000 units
where x is the total volume of items processed by all packing groups. Solving for x, we get:
x = 168,000 units ÷ 0.65 = 258,461.54 units
So the total volume of items processed by all packing groups is approximately 258,461.54 units. We can now use the given processing rates to determine the required processing volumes for each stage:
Picking: 100% of 258,461.54 units = 258,461.54 units
Packing Group A: 35% of 258,461.54 units = 90,461.54 units
Packing Group B: 65% of 258,461.54 units = 168,000 units
Therefore, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift. The answer is 168,000.
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____The given question is incorrect, the correct question is given below:
Team % of Volume Items processed per person per hour Picking 100% 150 Packing Group A 35% 105 Packing Group B 65% 70 Shipping 100% 175 How many items will be processed by Packing Group B in order to ship a total of 168,000 units for the shift?
46,
70,
84,000,
109,200,
168,000
the following frequency table represents the number of drinks someone has in a week for 40 people. what is the 70th percentile of the data?
Answer:
Step-by-step explanation:
Prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders. You can only use the definition of Bk. Per the definition, Bk is formed by joining two Bk−1 trees.
We will prove that if we remove the root of a k-th order binomial tree, it results in k binomial trees of smaller orders.
Base case: If k = 1, the binomial tree consists of a single node. Removing the root node leaves an empty tree, which can be considered as a collection of 0 binomial trees of smaller orders.
Induction hypothesis: Assume that the statement is true for a k-th order binomial tree.
Induction step: We need to prove that the statement is true for a (k+1)-th order binomial tree, which is formed by joining two k-th order binomial trees.
Remove the root node of the (k+1)-th order binomial tree. This results in two trees, each of which is a k-th order binomial tree.
By the induction hypothesis, removing the root node of each of the two k-th order binomial trees results in k binomial trees of smaller orders.
Thus, removing the root node of the (k+1)-th order binomial tree results in a total of 2k binomial trees of smaller orders, which completes the proof.
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34 on april 18, 1775, paul revere set off on his midnight ride from charlestown to lexington. if he had ridden straight to lexington without stopping, he would have traveled 11 miles in 26 minutes. in such a ride, what would the average speed of his horse have b
The average speed of Paul Revere's horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.
To find the average speed of Paul Revere's horse, we can use the formula:
average speed = total distance / total time
In this case, the total distance is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).
So, the average speed of Paul Revere's horse would be:
average speed = 11 miles / 0.4333 hours
average speed ≈ 25.4 miles per hour
Therefore, the average speed of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.
Using the formula for average speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.
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The complete question is:
On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?
Zach delivers pizza and is paid by the hour. Yesterday he worked 4 hours and made $40.
Answer:
$10 / hour
Step-by-step explanation:
$40 ÷ 4 hours = 10/hour
Answer: Part A: Zach is paid $10 per hour
Part B: The equation would be p = 10h
Step-by-step explanation: Part A :Zach worked 4 hours and was paid $40. The question asks How much is Zach's paid per hour? Per hour means to find the unit rate and in order to find the unit rate in this case, you have to divide the $40 by the 4 to get how much Zach got per hour.
1.$40/4=10
Therefore, Zach is paid $10 per hour.
Part B: In the question it says Which equation shows the relationship between , h, the number of hours worked. The number of hours Zach worked was 4 hours. So, h = 4. Then for the next part of the problem, and p the amount paid. We know that Zach got paid $40. So p = 40. Now that we know our numbers, we could put the equation together.
1. P = 10h is the same as $40 = 10 x 4.
There's the answer, Hope it helps! Have a nice day!
Ashley decorates cakes and uses red icing to write a message on the cakes. she uses 10 1/2 ounces of red icing to write a message on 3 1/2 cakes . Based on this rate how many ounces of red icing are needed to write a message on one cake ?
Answer:
Step-by-step explanation: Sure! Here's a step-by-step solution to find the amount of red icing Ashley needs for one cake:
Divide the total amount of red icing by the number of cakes: 10 1/2 ÷ 3 1/2 = 3.
Simplify the result from step 1: 3 = 3 ounces of red icing per cake.
So Ashley needs 3 ounces of red icing to write a message on one cake.
Write the equation & solve: Sixteen increased by twice a number is 3 times the number decreased by 4
The equation is 16 + 2x = 3(x - 4) and the solution is x = 28
How to solve the equationFrom the question, we have the following parameters that can be used in our computation:
Sixteen increased by twice a number is 3 times the number decreased by 4
Let the variable be x
So, we have
16 + 2x = 3(x - 4)
Open the brackets
16 + 2x = 3x - 12
Evaluat the like terms
x = 28
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(the numbers are 7m and 2m)
Find the shaded area of the composite figure
Answer:
A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure
Step-by-step explanation:bc of the way u gave it im showing it to u
What is the correct equation for this word problem?
Please help me ASAP thank you!
Sophia brought some almonds from the store. She handed the cashier $15 and received $5 in change. Mr. Boone is buying an app for the class. The app costs a dollars per student and he has 32 students. He spends $96. How much is the app per student?
The cost per student for the app is $3, and can be found by dividing the total cost of $96 by the number of students, 32, which equals $3 per student.
Let x be the cost of the almonds Sophia bought and y be the cost of the app per student. Then, we have the subsequent two equations:
x + $5 = $15
32y = $96
To find the cost of the app per student, we can solve for y in the second equation:
y = $96 / 32 = $3
So the app costs $3 per student.
To find the cost of the app per student, we need to find the total cost of the app and then divide it by the number of students. Mr. Boone spent $96 on the app for 32 students, so the cost per student would be $96 / 32 = $3. This means that each student paid $3 for the app.
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A candle burns 2 inches per hour. After burning for 2 hours, the candle was 5 inches
long. If one the candle has been burning for 240 minutes, how long is the candle?
Write an equation that models the situation.
The length of the candle that has been burning for the total of 240 minutes would be = 9 inches.
How to calculate the length of the candle?The rate at which a candle burns = 2 in/ 2 hours
That is,
2 in = 2 hour; 2 inches = 120 minutes
X in = 240 minutes
Make X the subject of formula;
X = 2×240/120
X= 480/120
X = 4+5
X = 9 inches
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Groundhog Day predictions have a 39% accuracy. How baby times should we expect to be correct over the next 38 years? *PLEASE HELP*
It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.
What is the expected value?The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.
Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.
To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),
39% * 38 = 14.82
So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.
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What does the following rule describe?
(x, y) → (x-2, y+5)
The transformation represents a horizontal of 2 units to the right and a vertical of 5 units up
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the initial coordinates of the point be represented as P
Now , the coordinates of P = P ( x , y )
And , the transformed point be represented as Q
Now , the coordinates of Q = Q ( x - 2 , y + 5 )
when x → ( x - 2 )
The graph is moved 2 units to the right
And , when y → ( y + 5 )
The graph is moved 5 units up
Substituting the values in the equation , we get
The transformation is 2 units to the right and 5 units up
Hence , the transformation is 2 units to the right and 5 units up
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pls help due now!!!!!!!!!!!!!!!!!!!
Answer:
B.
The equation you can use to find the area of a sphere when given radius is:
V = 4/3πr 3
Fitting 5 into the equation:
V = 4/3π5 3
V = 523.598776
Therefore, B is the correct answer.
Find b and then solve the equation
2x^2+bx-10=0 if one of its roots is 5
well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the remainder theorem we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then
[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]
Consider the sequence 7, 3, –1, –5, –9, ... a. What kind of sequence is it? Explain how you know. b. Write a rule t(n) for each term in the sequence, where n is the term number.
The sequence is an arithmetic sequence.
A rule for each term is t(n) = 7 - 4(n - 1).
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence is 7, 3, –1, –5, –9, ....
First term = 7
Second term = 7 + -4 = 3
Third term = 7 + (-4 × 2) = -1
....................
Here each term is getting by adding -4 to the preceding term.
So -4 is the common difference.
nth term of the sequence is t(n) = 7 - 4(n - 1).
Hence the sequence is arithmetic sequence and any term of the sequence is t(n) = 7 - 4(n - 1).
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Write the linear equation given slope is -1/3 and the point (-9,-1)
The Linear Equation for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4 .
We use the point slope form of a linear equation to write the equation of a line with its slope and a point on the line.
The point-slope form is ⇒ y - y₁ = m(x - x₁) ;
Where m is = slope of line, and (x₁, y₁) is a point on line.
The Slope (m) of line is = -1/3 and point on line (x₁, y₁) is = (-9, -1),
Now , we substitute these values ;
we get ;
⇒ y - (-1) = (-1/3)(x - (-9)) ;
⇒ y + 1 = (-1/3)(x + 9) ;
Simplifying further ,
we get ;
⇒ y + 1 = (-1/3)x - 9/3 ;
Subtracting 1 from both sides, we get:
⇒ y = (-1/3)x - 4
Therefore, the equation of the line is y = (-1/3)x - 4 .
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if you want to wear 4 of your 10 bow ties next week (monday through sunday), how many ways can this be accomplished?
There are 10/4 ways ( [tex]\frac{10}{4}[/tex] ) to accomplish the given task by wearing the ties for a week according to the permutations and combinations.
Given if you wear tie for a week, where one need t wear 4 of his ties from the 10 of total. The number of ways to wear the ties will be equal to the value. So there are many ways to wear a tie of different types and also to remove the tie there are different ways. Now we will see the ways to wear a tie accordingly.
According to the permutations and combination rules the formula will be:
Number of ways: (Number of ties want to wear) / (Number of Total ties)
Therefore total number of ways to wear ties = 10/4
Number of ways this can be accomplished is 10/4
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A recipe calls for 6 cups of flour to make 24 pancakes. How many pancakes
can be made with a single cup of flour?
On the double number line below, fill in the given values, then use
multiplication or division to find the missing value:
cups of flour
pancakes
