When we reflect a point across the line y = x, the x- and y-coordinates swap positions.
What do we mean by Reflection across y = x?When we reflect a point across the line y = x, the x- and y-coordinates swap places. When we reflect over the line y = -x, the x- and y-coordinates swap places and become negated (the signs are changed). The line y = x defines the point (y, x).The line y = -x is the point (-y, -x).Remember that each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. The line of reflection will be directly in the middle of the original figure and its image.Therefore, when we reflect a point across the line y = x, the x- and y-coordinates swap positions.
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Is there any value(s) of the domain of 2 2=8 that passes the vertical line test?
The value of domain that will pass the vertical line test is ±2√2.
What is a domain?The collection of inputs a function can accept is referred to as the domain of the function in mathematics. [tex]dom(f)[/tex] is a common way to refer to it, with f standing for the function.
To be more specific, the domain of f is X when the function [tex]f:X--Y[/tex] is specified. The domain of a function is not a characteristic of it, but rather an element of the definition in contemporary mathematical terminology.
The function f can be represented as a graph in the Cartesian coordinate system in the particular case where X and Y are both subsets of. A projection of the function's graph onto the graph's x-axis in this instance serves as the domain's representation.
Explanation:
Finding the domain,
[tex]x^2+ y^2[/tex] = 8
[tex]\sqrt{x^2} + \sqrt{y^2}[/tex] = √8
x + y = ±2√2
So, the domain is ±2√2.
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the length of a rectangle is twice as long as he width. the perimetter of the rectangle is 72 in. what tare thte length and width of this rectangle
For the given rectangle, having perimeter = 72, the length of the rectangle will be 12 cm and breadth will be 24 cm
What is the perimeter of rectangle?The overall length of the outline determines a shape's perimeter in two dimensions. We sum the lengths of all four corners of a rectangle to determine its perimeter.
Since the opposing sides of a rectangle are always equal, we must determine the length and breadth of the rectangle in order to determine its perimeter. The rectangle's perimeter may be expressed as the product of its length and breadth times two. As a linear measurement, the perimeter can be expressed in meters, centimeters, inches, feet, etc.
Given,
perimeter = 72
let us assume length = x
The breadth will thus be = 2x.
Now that these numbers have been plugged in, we may solve the equation for x.
perimeter of rectangle = 2 (L + B)
72 = 2 (x + 2x)
72 = 2 (3x)
72 = 6x
x = 72/6
x = 12
2x = 24
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If a(x) = 3x + 1 and b(x) = √x-4, what is the domain of (bºa)(x)?
SOlution : Domain of (bºa)(x) = [4, ∞]
The term domain is most commonly used to describe the set of values D for which a function (map, transformation, etc.) is defined. For example, a function f(x) that is defined for real values x in R has domain R, and is sometimes said to be "a function over the reals." The set of values to which D is sent by the function is then called the range.
The domain (in its usual established mathematical sense) of a probability density function (and therefore also its distribution function) is available with the undocumented Wolfram Language command DistributionDomain[dist].
The meaning of "domain" in topology is a connected open set.
Another meaning of "domain" is what is more properly known as an integral domain, i.e., a ring that is commutative under multiplication, has an identity element, and no divisors of 0.
In the algebra of the function that is (f ± g)(x), (fg)(x) and (f/g)(x) the domain of the function will be an intersection of the domain of the functions f and g
Here the domain of the product of the function is asked thus the required domain will be an intersection of the domain of the function a and b.
Given a(x) = 3x + 1 ⇒ Domain, D1 = R
b(x) = √(x - 4) ⇒ Domain, D2 = [4, ∞]
Now, Domain of (b*a)(x) = Domain b(x) ⋂ Domain a(x)
= D2 ⋂ D1
= [4, ∞] ⋂ R
= [4, ∞]
Domain of (bºa)(x) = [4, ∞]
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Bruce spent $30 on lunch. If he had $55 in his wallet, what percent of his money did he spend on lunch?
Answer:
your answer is 54%
I need help with this
Answer:
7×7=7×(5+2)
=(5×7)+(7×2)
=35+14
=49
Answer:
Step-by-step explanation:
7x7=7(5+2)
=
What is the missing product?
4 times 6 equals an empty box, shown horizontally.
Responses
10
12
24
46
Answer:
The answer is 24
Step-by-step explanation:
6×4 =24
We can also further simplify it by everything down.
we could use
(3×4) + (3×4)
12 + 12
=24
and we can do the same for
(6×2) + (6×2)
12 + 12
= 24
Hope this helps!
Answer:
4 · 6 = 24
➲ I hope this helps.
the number between -4/9 and -7/8
a) -5/-6
b) 5/-6
c) -5/6
d) 4/-6
Answer:
Just from looking at the distorted and wrong places to put the minus sign, the answer is option C.❌First option (A): there is no way a minus sign will be in the numerator and denominator, If so they would cancel out to be a positive number.
❌second option(B): there is no way a minus sign would stay in the denominator, it always stays in the numerator (even if it's in the denominator you take it up to the numerator).
❌ Fourth option (D): again no way a minus sign stays in the denominator so this option is wrong.
✅ Option (C): The minus sign is in the right place which is the numerator.
you see how I solved this problem without writing on paper or anything like that, sometimes you can find your answers by spotting abnormalities in the options you're given.
I believe this will definitely helpAce that testGood luck ✅WILL MARK
PLEASE HURRYYY
What is the rate of change of the function?
-3
-1/3
1/3
3
Answer:
-1/3
Step-by-step explanation:
Solve the rational equation:
7/(s + 8) = −2/(9s + 1)
Answer: s=?
Answer:
s = (-23/65)
Step-by-step explanation:
7 -2
------ = -------
(s + 8) (9s + 1)
7 (9s + 1) -2 (s + 8)
------ = -------
(s + 8) (9s + 1) (9s + 1) (s + 8)
7 (9s + 1) -2 (s + 8)
(------------------ = ---------------------) ((9s + 1) (s + 8))
(s + 8) (9s + 1) (9s + 1) (s + 8)
7 (9s + 1) = -2 (s + 8)
63s + 7 = -2s - 16
+2s +2s
65s + 7 = -16
-7 -7
65s = -23
÷65s ÷65s
s = (-23/65)
Logan is a salesperson who sells computers at an electronic store. He paid a 1.25 commission for every sale he makes and he also make a guaranteed base pay of $80 each day. Write an equation for p in terms of x representing Longan’s total pay on a day on which he sells x computer
Answer: Here is ur answer
p=1.25x + 80
p is the pay and the 1.25 depends on how much computers he sells but he gets at least 80$ for his paycheck
Step-by-step explanation: i really really hope this helps lmk if im wrong tho have a good day (:
yolanda spends 8 2⁄3 hours per month playing soccer. approximately how many hours does she play soccer in a year? (there are twelve months in a year.)
The total time she spends playing soccer in a year is 104 hours, which is calculated using the concept of fraction and arithmetic operations.
What is a fraction?
Any numerical number which does not represent the entire quantity is called a fraction. It depicts a part or portion of something. It is generally written in the form of numerator by denominator.
Calculation of the total time Yolanda spends playing soccer
Given that Yolanda plays soccer for 8 ⅔ hours in a month
Firstly, convert the hours in mixed fraction to improper fraction i.e. 8 ⅔ = (8 × 3 + 2) / 3
= 26 / 3
Now, we need to calculate the no. of hours she played in a year, which is done by multiplying the obtained improper fraction with 12
i.e. (26 / 3) × 12
= 104 hours
Hence, Yolanda spends 104 hours a year playing soccer.
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Harry buys 3 granola bars for $5. Sidney buys 9 granola bars for $15 what is the constant of proportionality
The constant of proportionality is 5/3.
What is the constant of proportionality?In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to by the terms constant ratio, constant rate, unit rate, constant variation, or even change rate.
Let the constant of proportionality is k.
Harry buys 3 granola bars for $ 5. So, we can write it as
3 × k = 5
k = 5/3
To Check:
Sidney buys 9 granola bars for $ 15, we can write it as
9 × k = 15
Put k= 5/3 in the equation
9 × 5/3 = 15
3 × 5 = 15
15 =15
The Left and right-hand sides are equal. Hence, the constant of proportionality is k=5/3.
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If a population consists of 5,400,000 people and a census is taken, how many
people are sampled?
Answer: 54,000,000
Step-by-step explanation: hope this helps
[tex](800)×(3×10 −1 )= ?[/tex]
The answer is 23200.
BODMAS is an acronym that stands for Bracket, Order, Division, Multiplication, Addition, Subtraction. In certain regions, a synonym for BODMAS is used: PEMDAS (parentheses, exponents, multiplication, division, addition, and subtraction). It describes the order of operations performed when solving an equation. According to the BODMAS rule, if an expression contains parentheses ((), {}, []), first break or simplify the parentheses, then "order" (meaning exponentiation, root, etc.), division, multiplication , addition and subtraction from the left.By using BODMAS , we will first simplify the bracket term.
The bracket term is [tex](3\times10-1)[/tex]
After , bracket we will operate the multiplication term which is given by
[tex]30-1[/tex]
Now , we will use the subtraction operation .
[tex]29[/tex]
On solving the bracket , we get 29 .
Now we will multiply 800 by 29 ,we get
[tex]800\times29=23200[/tex]
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The complete question is mention below :
Solve [tex]800(3\times10-1)[/tex]
Midpoint Find the midpoint of the line segment with the endpoints A and B. A(4,10); B(8,6) The midpoint of the line segment is. (Type an ordered pair.)
Answer:
Step-by-step explanation:
A(2,6); B(10,8)
whats the midpoint of the segment?
13. For a party, Bob's Pizza charges $12 for each
supreme pizza while Mike's Pizzeria charges based
on the equation y = 8x + 20. How many pizzas
must you order for the price to be the same?
The number of pizzas you must order for the price to be the same is 5
How many pizzas must you order for the price to be the same?Bob's Pizza charges = $12 for each supreme pizza
This can be represented as
y = 12x
For Mike's Pizzeria, we have
y = 8x + 20
Substitute y = 12x in y = 8x + 20
12x = 8x + 20
Evaluate the like terms
4x = 20
Divide by 4
x = 5
Hence, the number of pizzas you must order for the price to be the same is 5
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an equilateral triangle has sides of equal length. determine whether the triangle with vertices 1-1, -12, 12, 32, 1-4, 32 is equilateral.
The triangle with the given vertices (-1, -1), (2, 3), and (-4, 3) is not an equilateral triangle.
What is an equilateral triangle?An equilateral triangle can be defined as a special type of triangle that has equal side lengths and all of its three (3) interior angles are equal.
In order to determine whether the triangle with the given vertices is an equilateral triangle, we would apply the distance formula to calculate the length of each side of this triangle as follows:
Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
For the vertices (-1, -1) and (2, 3), we have;
A = √[(2 - (-1))² + (3 - (-1))²]
A = √[(2 + 1)² + (3 + 1)²]
A = √[3² + 4²]
A = √[9 + 16]
A = √25
A = 5 units.
For the vertices (2, 3) and (-4, 3), we have;
B = √[(-4 - 2)² + (3 - 3)²]
B = √[-6² + 0²]
B = √[36 + 0]
B = √36
B = 6 units.
For the vertices (-1, -1) and (-4, 3), we have;
C = √[(-4 - (-1))² + (3 - (-1))²]
C = √[(-4 + 1)² + (3 + 1)²]
C = √[-3² + 4²]
C = √[9 + 16]
C = √25
C = 5 units.
Therefore, the triangle with the given vertices is not an equilateral triangle because C = A ≠ B.
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Complete Question:
An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.
joey chestnut is trying to break his own record for eating the most whole hot dogs in 101010 minutes. he needs to eat more than 727272 hot dogs to break his record. after 111 minute, joey has eaten 11 \frac{1}{4}11 4 1 11, start fraction, 1, divided by, 4, end fraction hot dogs. let ddd represent the number of hot dogs joey eats per minute for the next 999 minutes. which inequality represents the number of hot dogs per minute joey could eat for the last 999 minutes to break his record? choose 1 answer: choose 1 answer: (choice a) a 11\frac{1}{4} 9d>7211 4 1 9d>7211, start fraction, 1, divided by, 4, end fraction, plus, 9, d, is greater than, 72 (choice b) b 11\frac{1}{4} 9d
An inequality that represents the number of hot dogs per minute joey could eat for the last 9 minutes to break his record is: 9d + [tex]11\frac{1}{4}[/tex] > 72
For given question,
Joey chestnut is trying to break his own record for eating the most whole hot dogs in 10 minutes.
He needs to eat more than 72 hot dogs to break his record.
After 1 minute, joey has eaten [tex]11\frac{1}{4}[/tex] hot dogs.
let d represent the number of hot dogs joey eats per minute for the next 9 minutes.
9d + [tex]11\frac{1}{4}[/tex] is the expression that shows how many hot dogs he will eat in total.
9d being how much he'll eat in the remaining 9 minutes, and [tex]11\frac{1}{4}[/tex] being the number of hot dogs he's already eaten in the first minute.
Since it has to beat his former record of 72, it has to be greater than 72. The inequality would be
9d + [tex]11\frac{1}{4}[/tex] > 72
Therefore, an inequality that represents the number of hot dogs per minute joey could eat for the last 9 minutes to break his record is:
9d + [tex]11\frac{1}{4}[/tex] > 72
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in a study, the data you collect is number of walk buttons that work in new york city. what type of data is this? qualitative (categorical) quantitative - discrete quantitative - continuous
In a study, the data you collect is number of walk buttons that work in New York city, which is discrete type of data.
We know that,
The data which is in numeric form is called Quantitative data.
Example: Weight, Marks, etc.
The data which we can't count is known as Qualitative data.
Example: Smoking, Non- Smoking, etc.
Quantitative data can be divided into two parts:
- Continuous
- Discrete
The data which we can count is known as the Discrete data . It includes the natural numbers only.
Example: Number of apples, Number of senior citizens in a particular area, etc.
The data which we can't count is known as Continuous data . Example: Height, Weight, etc.
In this question, the data you collect is number of walk buttons that work in New York city. This is discrete type of date.
Therefore, in a study, the data you collect is number of walk buttons that work in New York city, which is discrete type of data.
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What is the value of the expression below when y=7 y^2 +4y+3
Answer:
I believe that the value of the exprexpression is 80.
Step-by-step explanation:
Substitute 7 for every y variable.
y^2 + 4y + 3=
7^2 + 4(7) + 3=
49 + 28 + 3=
80
Find the 66th term of the arithmetic sequence -10, 7, 24, ...
========================================
Explanation:
[tex]a_1[/tex] = -10 is the first term
d = 17 is the common difference. We add this amount to each term to get the next one. Eg: -10+17 = 7
We want to find the 66th term, so we'll use n = 66
Plug these values into the nth term arithmetic sequence formula below.
[tex]a_n = a_1 + d(n-1)\\\\a_{66} = -10 + 17(66-1)\\\\a_{66} = 1095\\\\[/tex]
The 66th term is 1095
Answer:
The answer is 1095.
66th term = 1095
Step-by-step explanation:
an = a1 + (n − 1)d
= -10 + (66 - 1) (17)
I did it on calculator.
It equals to = 1095
now examine |a + bi| and complete the definition below. the absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex pl
According to the given statement the absolute value of just about any complex number Ia + biI seems to be the distance between (a, b) and (0, 0) in the complex plane is √(a² + b²).
What specifically is modulus?After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division. A modulo n seems to be the remainder of something like the Euclidean division on a by n, where an is the dividend and n is the divisor, given two positive numbers a and n.
What is the purpose of modulus?The modulus operator can be used in a variety of situations. It is frequently used to decrease a randomly generated number to a randomly generated number in a smaller range, and it may also rapidly tell you if one integer is a factor of another.
According to the given information:The modulus of any complex number is its absolute value, regarding which there is a modulus formula. √(a² + b²).
where a and b are integers
Please see the attached file for the complex plane of the provided points (a,b) (0,0).
The separation of two points (x1 ,y1) and (x2 ,y2) will be:
√((x1 - y1)² + (x2 - y2)²)
We need to calculate the distance between (a,b) because (0,0)
We will obtain by replacing the numbers in the distance formula.
√((0 - a)² + (0 - b)²).
The given statement the absolute value of just about any complex number a + bi seems to be the distance between (a, b) and (0, 0) in the complex plane is √(a² + b²).
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I understand that the question you are looking for is:
now examine |a + bi| and complete the definition below. the absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex plane.
Answer: distance , positive real on edge
Step-by-step explanation:
3. Based on the graph of the function y = g(x) shown below, answer the following questions.
y
(a) Evaluate g (-2), g(0), g (3) and g (7).
hogy
Joo 1 023
(b) What values of x solve the equation g(x)=0
(c) Graph the horizontal line y = 2 on the grid
above and label.
wirb
X
(d) How many values of x solve the equation
g(x)=2?
The values of x that solve the equation g(x) = 0 are x = -3, 1, 5 and 7 and there are four values of x that solve the equation g(x) = 2
How to answer the questions based on the graph of the function y = g(x) shown?The graph represents the given parameter
(a) Evaluate g (-2), g(0), g (3) and g (7)
To do this, we take the function value at the given value of x
The function g(-2) means
x = -2
So, we have
When x = -2, g(x) = -3
This means that g(-2) = -3
The function g(0) means
x = 0
So, we have
When x = 0, g(x) = -3
This means that g(0) = -3
The function g(3) means
x = 3
So, we have
When x = 3, g(x) = 4
This means that g(3) = 3
The function g(7) means
x = 7
So, we have
When x = 7, g(x) = 0
This means that g(7) = 0
(b) What values of x solve the equation g(x) = 0On the graph, we have the following values of x at g(x) = 0
x = -3, 1, 5 and 7
Hence, the values of x that solve the equation g(x) = 0 are x = -3, 1, 5 and 7
(c) Graph the horizontal line y = 2 on the grid above and label.See attachment
(d) How many values of x solve the equation g(x)=2Using the line in (c), the line crosses the curve four times at y = 2
Hence, there are four values of x that solve the equation g(x) = 2
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A fundamental distinction between trend projection and linear regression is that:____.
A fundamental distinction between trend projection and linear regression is that: in trend projection the independent variable is time; in linear regression, the independent variable need not be time.
We need to find the fundamental distinction between trend projection and linear regression.
What is trend projection?The trend projection method is based on the assumption that the factors liable for the past trends in the variables to be projected shall continue to play their role in the future in the same manner and to the same extent as they did in the past while determining the magnitude and direction of the variable.
Linear regression: Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.
A fundamental distinction between trend projection and linear regression is that in trend projection the independent variable is time; in linear regression, the independent variable need not be time but can be any variable with explanatory power.
Therefore, a fundamental distinction between trend projection and linear regression is that: in trend projection the independent variable is time; in linear regression, the independent variable need not be time.
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A rectangular garden has a length of 7 feet and a width of 6 feet what is the area of the garden
Answer:
42
Step-by-step explanation:
L*W= Area
7*6=42
Hope this helps! :)
Please help?!?!?! Determine the length of BD, given by x in the figure. Give your answer to two decimal places.
Answer:
3.71
Step-by-step explanation:
AC² + BC² = AB²
3² + 6² = AB²
9 + 36 = AB²
AB = √45
AB = 3√5
AB = AD + BD
3√5 = 3 + BD
BD = 3√5 - 3
BD = 3.71
Initial Knowledge Check
Suppose Deon places $3000 in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
$
(b) Find the amount in the account at the end of 2 years.
(a) The amount in the account at the end of 1 year is $3330
(b) The amount in the account at the end of 2 year is $3696.3
Compound interest is interest calculated on the principal and the interest accrued in previous periods. General formula for the number of annual interest on the principal. If the interest is compounded annually, the amounts is given by [tex]A=P(1+\frac{R}{100} )^t[/tex] where "A" represents the new principal sum or the total amount of money after compounding period , "P" represents the original amount or initial amount , "r" is the annual interest rate , "t" represents the number of years .It is given that Deon deposit $3000 that pays 11% interest compounded each year .
(a) Putting P = $3000, R = 11% , T = 1 year in equation (1) , we get
[tex]A=3000(1+\frac{11}{100} )^1\\\\A=3000(1+0.11)\\A=3000(1.11)\\A=3330[/tex]
(b) Putting P = $3000, R = 11% , T = 2 year in equation (1) , we get
[tex]A=3000(1+\frac{11}{100} )^2\\\\A=3000(1+0.11)^2\\A=3000(1.11)^2\\A=3000\times1.23\\A=3696.3[/tex]
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When you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.
b. What is m∠2? Classify this angle as acute, right, or obtuse.
The measure of angle 2 from the given figure is an acute angle.
Given that, when you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.
What is refraction?Refraction is the "bending" of light (or any electromagnetic wave) when entering a different medium.
In the given figure, the three angles, are angle 1, angle 2 and angle 3.
Angle 1 and 2 are formed with the surface of the water. Angle 1 in the medium air and angle 2 is in the medium water.
From the figure, given below we can see that angle 2 is less than 90° and greater than 0°.
Therefore, the measure of angle 2 from the given figure is an acute angle.
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how do u work out 1/2(2y+4)=-6
Answer:
The answer is y = -8
Step-by-step explanation:
You distribute,
1/2 x 2y = y
1/2 x 4 = 2
y+ 2 = -6
(then you subtract 2)
y=-8
If you would like to check, just put -8 into the equation in place of y
So it would look like this: 1/2(2 x -8 + 4) = -6
If it equals -6 then it means your answer is correct
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
whats the answer for
−2x9 = y −3x2y = 16
Answer: x = -[tex]\sqrt[3]{2}[/tex]
Step-by-step explanation: sorry if i am wrong