The vertices of the triangle DEF after the 90º counterclockwise rotation about the point (5,2) are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)Considering the 90º counterclockwise rotation about the point (5,2), the rule is given as follows:
(x,y) -> (-y - 5, x - 2).
Hence the vertices are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
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3 /4 + 1 /6 − 2/ 3 =
Answer:
Step-by-step explanation:
Answer: 1/4
Add: 3/4 + 1/6 = 3 · 3 / 4 · 3 + 1 · 2 / 6 · 2 = 9/12 + 2/12 = 9 + 2/12 = 11/12
Subtract: 1 - 2/3 = 11/12 - 2/3 = 11/12 - 2 · 4 / 3 · 4 = 11/12 - 8/12 = 11 - 8/12 = 3/12 = 3 · 1 / 3 · 4 = 1/4
For each rhombus, find each angle measure or segment length.
Answer:34xt25
Step-by-step explanation:
Sorry for the markings but I need help ASAP. Please help!!
Answer: 72 + 2x = 180
Step-by-step explanation:
What percentage of scores must fall within 4 standard deviations of the mean according to Chebyshev's theorem?.
Percentage of scores must fall within 4 standard deviations of the mean according to Chebyshev's theorem is 93.75%
Chebyshev's theorem states that the proportion of the data set that lies between k standard deviations from the mean be calculated with the formula below.
1 − 1/k²
which in this case is,
=1 − 1/4²
= 1− 1/16
=15/16
=0.9375
which is 93.75%.
According to probability theory, Chebyshev's inequality ensures that no more than a specific percentage of values can deviate significantly from the mean given a large class of probability distributions.
The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
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An artist makes pottery. The artist earns the same amount for each piece of pottery sold
but must pay a fee to rent a booth at a local fair. After analyzing data from recent sales,
the artist finds the equation y=42x-200 models the profit, y, earned for selling x
pieces of pottery after the expense of renting the booth. Which statement is true?
a)
The slope of the equation is -200, and it represents the $200 the artist earns, on
average, for every piece of pottery sold.
b)
The slope of the equation is -200, and it represents the cost of renting the
booth.
c) The slope of the equation is 42, and it represents the $42 the artist earns, on
average, for every piece of pottery sold.
d) The slope of the equation is 42, and it represents the cost of renting the booth.
The slope of the equation is 42, and it represents the $42 the artist earns, on is true after analyzing data from recent sales.
What is sales?Sales in mathematics is the process of exchanging goods or services for money. It is a vital part of the economy and involves the transfer of ownership from the seller to the buyer. In mathematical terms, sales can be expressed as a function where the input is the amount of money paid for goods or services and the output is the goods or services received. Sales can also be expressed as an equation in which the variables are the cost of goods or services, the number of goods or services sold, and the total sale amount.
The slope of the equation is 42, and it represents the $42 the artist earns, on average, for every piece of pottery sold.
The constant -200 represents the cost of renting the booth.
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if point A is (2,0) and point B is (2,12) What point divides the directed line segment AB¯¯¯¯¯ into a 3:1 ratio?
The coordinates of the point dividing the segment in the ratio 3:1 will be ( 38 / 4, 6 / 4).
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that point A is (2,0) and point B is (2,12) and the line is divided in the ratio of 3:1. the coordinate of the point will be calculated as,
Point = { ( mx₂ + nx₁ ) / ( m + n ) }, { ( my₂ + ny₁ ) / ( m + n ) }
Point = { ( 3 x 12 0 + ( 1 x 2 ) / ( 3 + 1 )], { ( 3 x 2 ) + 0 ) / ( 3 + 1) }
Point = { 38 / 4, 6 / 4 }
Hence, the coordinates of the point dividing the segment by a factor of three will be (38 / 4, 6 / 4).
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i need answer by today
what is 2 and 2/13 of 52
Answer:
the answer 112
Step-by-step explanation:
hope this helps
Please help me I am struggling ;((((
Answer:
X
[tex] \frac{y2 - y1}{x2 - x1} - \frac{y - y1}{x - x1} [/tex]
Step-by-step explanation:
in every point given put one as (x1, y1) and the other is (x2, y2)
simplify the formula and you'll get you linear equation
don’t really understand can someone help me. how do you turn this into radical form
Answer :
The first one
Step-by-step explanation:
A cube root is a number that, when cubed, is equal to the given number.
It is denoted with an exponent of "1/3".
Example, the cube root of 27 is 27^1/3 = 3.
Now,
[tex]24^{ \frac{1}{3} } \: is \: the \: same \: as \: \sqrt[3]{24} [/tex]
From there, we can simplify
[tex] \sqrt[3]{24} \\ \sqrt[3]{2 \times 2 \times 2 \times 3} \\ \sqrt[3]{ {2}^{3} \times 3} \\ 2 \sqrt[3]{3} [/tex]
I need help please. I would like someone to make sure I have the right answer .
How do you use the 3 4 5 triangle method?.
To get the sides of the right-angle triangle, we employ the 3 4 5 triangle method.
A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.
The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.
Therefore, to determine the sides of the right-angle triangle, we employ the 3 4 5 triangle method.
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The ratio of consonants to vowels in a word is 7:5.Are there more vowels or consonants in the word?
Answer:
constants because
7 > 57>5
There u go
If consonants to vowels has a ratio of 7:5, this means there are 7 consonants for every 5 vowels. There are more consonants in the word.
Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded monthly. How much money will be in her account at the end
of the 12 years? (Remember to round your answer to the nearest cent.)
A-$ type your answer.....
Answer:$917.58.
Step-by-step explanation:
The formula for compound interest is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial deposit is $500, the annual interest rate is 4%, the number of times compounded per year is 12 (monthly), and the number of years is 12.
So, we can plug in the values into the formula:
A = $500(1 + 0.04/12)^(12*12) = $500(1.003333333)^(144) = $500(1.835170816) = $917.585
The final amount in her account after 12 years is $917.58
To round to the nearest cent, we can use the following method:
If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.
If the digit in the thousandths place is greater than 5, we round up the hundredths digit.
In this case the digit in the thousandths is 5 so, we have to round up the hundredths digit of $917.58.
So, the final amount in her account after 12 years is $917.59.
Answer: $800.516
Step-by-step explanation:
We use the equation
A = P(1 + )^nt
P = principal
r = rate of interest
t = times
Now let's solve
P = $500
r = 4% = 0.04
t = 12 years
A = $500(1 +[tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516
Write a sentence describing a situation that could be represented by the equation.
4 ÷ 1 1/3
The sentence which describes a situation which can be represented by the equation 4 ÷ 1 1/3 is, "4 divided by the fraction number 11 by 3"
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation,
⇒ 4 ÷ 1 1/3
Mathematically, it represents that,
4 is divided by fraction number 11 by 3
or
Product of 4 and reciprocal of 11 divided by 3
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Dylan is hosting a party she buys pumpkins 20 dollars each and balloons 2 dollars each she has a budget of 250 if x represents pumpkins and y represents balloons write an inequality that represents all possible ways she could buy a pumpkin and balloons what is the max number of ballons she could buy
Answer:
Dylan's budget is $250, and she is buying pumpkins for $20 each and balloons for $2 each. We can represent the total cost of the pumpkins as 20x and the total cost of the balloons as 2y. The inequality that represents all possible ways she could buy pumpkins and balloons within her budget is:
20x + 2y <= 250
To find the maximum number of balloons she could buy, we can use the equation above and set x = 0, and then solve for y.
20(0) + 2y <= 250
2y <= 250
y <= 125
The maximum number of balloons she could buy is 125.
Geometry
A jar contains 5 red balls and 3 white balls. A ball is selected and its color is noted, then the ball is replaced. A second ball is selected and its color is noted. Find the probability of each of the following.
a. What is the probability of selecting 2 red balls?
b. What is the probability of selecting 1 red ball and then 1 white ball?
Answer:awnsers below
Step-by-step explanation:
a. The probability of selecting 2 red balls is (5/8) * (5/8) = 25/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a red ball on the second draw is also 5/8, since the ball is replaced after each draw.
b. The probability of selecting 1 red ball and then 1 white ball is (5/8) * (3/8) = 15/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a white ball on the second draw is 3/8, since the ball is replaced after each draw.
Answer:
Step-by-step explanation:
a)
P(Red)=5/8
(5/8)^2=25/64
b)
P(Red)=5/8 P(White)=3/8
5/8*3/8=15/64
What is 7 8 equivalent to in fractions?.
Equivalent 7/8 is equals to 56/64 in fractions.
In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.
The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.
= 7/8 is equivalent to:
= 7/8 * 8/8
= 56/64
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Correct Question:
What is 7/8 equivalent to in fractions?.
Can a linear system only have 2 solutions?.
Most linear systems will have exactly one solution. Nevertheless, it is possible that there are no solutions or infinitely many. (but It is not possible that there are exactly two solutions of a linear system.)
Let's assume a system of two linear equations, then, there are three possibilities of solutions.
The possibilities are:
Two parallel lines
e.g. y = 3x + 1
y = 3x − 2 (with the same slope, different intercepts)
Two (distinct) intersecting lines
As we know two straight lines cannot meet at two points. Two points determine only one line (not two lines).
e.g. y = 3x + 1
y = 5x − 2 (different slopes)
These equations have the same line as their graphs
If two lines do have two points in common, then "the lines coincide" (which really means "there is only one line".) In this case, we say, "the two lines are the same".
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Is the solution of the equation 2x y 5 and 3x 2y 11 *?.
The value of x=3 and y=1 is the solution.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
given equations are,
2x-y=5 and 3x+2y=11
Let 2x-y=5 ----[1]
, 3x+2y=11 ----[2]
Now, solving [1] and [2] by substitution method,
Substitute the value of x from [1] in [2],
x= [tex](\frac{5+y}{2})[/tex]
3x+2y=11
3[tex](\frac{5+y}{2})[/tex] + 2y = 11
[tex](\frac{15+3y}{2})[/tex] + 2y = 11
[tex](\frac{15+3y+4y}{2})[/tex] = 11
15 + 7y = 22
7y = 22 - 15
7y = 7
y = 1
Substitute the value of y=1 in [1],
2x - y = 5
2x - 1 = 5
2x = 6
x = 6 / 2
x = 3
Therefore, The value of x=3 and y=1.
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What is range in math class 8?.
The range in statistics for a given data set is the difference between the highest and lowest values.
As a result, the range can also be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.
To find the range in statistics, we need to arrange the given values or set of data or set of observations in ascending order.
For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, The range in statistics for a given data set is the difference between the highest and lowest values.
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How do you change the base of a logarithm?.
To change the base of a logarithm, for example from base a to base c, we use the formula [tex]log_{a} (b)[/tex] = [tex]log_{c} (b)[/tex] / [tex]log_{c} (a)[/tex].
In order to change the base of a logarithm the following basic formula is used,
[tex]log_{a} (b)[/tex] = [tex]log_{c} (b)[/tex] / [tex]log_{c} (a)[/tex]
For example,
If we have to change the base of log₃(81) to base 5,
It will be written as
log₃(81) = log₅(81) / log₅(3)
The change of base rule is able to covert a logarithm in a given base to a logarithm in a new base. The result will be a quotient, which is a fraction, with the new logarithm as both the numerator as well as a denominator.
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Jackie’s pizzeria made 50 pizzas. 3 of the pizzas had thin crust and the rest had thick crust. What is the ratio of the number of thick-crust pizzas to the number of thin-crust pizza?
Answer:
47:3
Step-by-step explanation:
47 pizzas had thick crust and 3 had thin crust
You're planning on making 7 meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. How many canisters do you need to buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
You will need ___ canisters.
Give your answer accurate to at least one decimal place (You can only buy whole canisters, but this way you'll know how much you'll have left over)
You will need 2.8 canisters.
To determine this, you need to know the quantity of breadcrumbs required for one meatloaf and how many meatloafs you are planning to make. Since the breadcrumbs are sold by the canister, you will also need to know the quantity of breadcrumbs in one canister. With this information, you can calculate the total quantity of breadcrumbs required for all the meatloafs and divide it by the quantity of breadcrumbs in one canister to find out how many canisters you need to buy.
Divide 1 hour in the ratio 1:5
Answer: ratio of 1: 10mins
ratio of 5: 50mins
Step-by-step explanation:
The ratio of 1:
[tex]\frac{1}{6}[/tex] x 60 (hours should be converted to minutes therefore it is 60 mins and
the denominator seen here is taken by adding the two values in the
given ratio and since we're still finding 1 you should divide 1 by the
added denominator and the same applies when finding the ratio 5)
Answer= 10mins
The ratio of 5:
[tex]\frac{5}{6}[/tex] x 60 (refer to the underlined explanation above)
answer= 50mins
so if you want to verify you add the two values you got to see if you got 60 as 60mins in hours was divided in ratio so when you add it will be 60 which means your answer is correct!
Answer: 12:60
Step-by-step explanation: To find the ratio, we must take 1 h and turn it into minutes. So as we know, it's 60 minutes. So next, we shall change the ratio into fraction form (don't worry it's the same basic format)
[tex]\frac{1}{5} = \frac{?}{60}[/tex]
So with that given information, we know that 60 would be our denominator. So, we need to divide both denominators, and then whatever we get from that, multiply that by the given numerator. So, we would do:
60 / 5
= 12
12 * 1
= 12
Therefore we now know that 1/5 = 12/60 as a ratio. I hope this helped :)
(Attachment included)
What is the product of X+ a and x b )?.
The product of expressions ( x + a ) and (x + b ) is equals to the x² + (a - b)x - ab.
Product is an important arithmetic operation. The multiplication or product of algebraic expressions is a method of multiplying two expressions consisting of variables and constants. The product of two factors with the same signs will be positive, and the outcome of multiplying two terms with two, unlike signs, will be negative. We have two algebraic expressions as ( x + a) and ( x - b) and we have to calculate their product.
=> (x + a) ( x - b) = x( x- b) + a(x - b)
=> (x + a) ( x - b) = x² - xb + ax - ab
=> (x + a) ( x - b) = x² + (a - b)x - ab
Hence, required product is x² + (a - b)x - ab .
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Complete question:
What is the product of (x + a )and (x - b )?.
In 3 1/2 hours a car moving at 40 miles per hours (mph) will travel
miles
Answer: 140 mph
Step-by-step explanation:
3 1/2+40=140 mph
The number of miles traveled in 3(1/2) hours is 140 miles.
We have,
Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula of speed is used.
Speed = Distance / Time
From the given statement, make an expression.
1 hour = 40 miles
Multiply 3(1/2) on both sides.
3(1/2) hours = 3(1/2) x 40 miles
Simplify the mix fraction.
3(1/2) hours = 7/2 x 40 miles
Simplify the fraction.
3(1/2) hours = 7 x 20 miles
3(1/2) hours = 140 miles
Thus,
The number of miles traveled in 3(1/2) hours is 140 miles.
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9x2+4y÷z 9 x 2 + 4 y ÷ z when x=23, x = 2 3 , y=3, y = 3 , and z=6?
The solution of the given expression 9x² + ( 4y / z ) will be 4763.
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.
Given that the expression is 9x² + ( 4y / z ) and the values are x=23, y=3, and z=6.
The expression will be solved as below,
E = 9x² + ( 4y / z )
E = 9 x ( 23 ²) + ( 4 x 3 ) / ( 6 )
E = 4761 + 2
E = 4763
Hence, the solution will be 4763.
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Is linear equations in two variables easy class 10?.
Linear equations in two variables can be relatively easy to understand and work with, as they represent straight lines in the xy-plane. The slope-intercept form of a linear equation, y = mx + b, is a simple way to represent a line with a specific slope and y-intercept.
Graphing linear equations is also straightforward, as you can find the x-intercept and y-intercept and plot the line using these points.
However, solving linear equations in two variables can become more challenging when the equations involve multiple terms or are presented in a different form. Also, understanding the concept of slope, y-intercept, and how to graph the line can be challenging for some students.
Overall, linear equations in two variables can be considered as a fundamental concept in algebra and mathematics and it requires practice to gain mastery over it.
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[Real world example] A sewage treatment centre fills a cylindrical silo with waste. The diameter is 20m and the height 5m. It is full to the top with 1300kg of waste. Find the density of the waste.
Step-by-step explanation:
density is mass/volume.
usually it is expressed as grams/cm³.
the question does not give us the information about the dimensions for density. so, I am going with my assumption.
the volume of a cylinder is
ground area × height
the ground area is a circle, so this is
pi×r²×height
r is the radius and therefore half of the diameter.
so, we have in our case as volume :
pi×(20/2)²×5 = pi×100×5 = 500pi = 1,570.796326... m³
1 m = 100 cm
1 m³ = 100×100×100 = 1,000,000 cm³
so, the volume of our cylinder is then also
1,570,796,326.7948966192... cm³
1 kg = 1000 g ("kilo" means 1000)
1300 kg = 1,300,000 g
so the standard density is
1,300,000/1,570,796,326.7948966192... g/cm³ =
= 0.000827606... g/cm3
The density of the waste is approximately 0.827 kg/m³.
What is density?A physical property is known as density gauges a substance's mass per unit volume. It is referred to as the mass-to-volume ratio.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height.
Since the diameter of the silo is 20m, the radius is 10m. Therefore, the volume of the silo is:
V = π(10m)²(5m) = 500π m³
Since the silo is full to the top with 1300kg of waste, the density of the waste is:
density = mass/volume
density = 1300kg/(500π m³)
density ≈ 0.827 kg/m³
Therefore, the density of the waste is approximately 0.827 kg/m³.
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