The solution to a system of equations is (2,-4).one equation in the system is 2x+y=0.explain how you can find a second equation for the system.then find a second equation.solve by system of equations to justify your answer
The second equation is 3x + y = 2.
Let the other equation be of the form ax + by = c, where a, b and c are constants.
Given equation is 2x + y = 0
We have, a₁ = 2 and a₂ = 1
And b₁ = a and b₂ = b
Since, both equations have a unique solution,
∴ a₁ ÷ b₁ ≠ a₂ ÷ b₂
2 ÷ a ≠ 1 ÷ b
2b ≠ a … (1)
Also, (2, -4) is the solution of the equations, so it will satisfy the equations
2a - 4b = c
b = (2a - c)/4
Let c=2
b = (2a - 2) ÷ 4
b = 1
Now we can take any value for a and b which satisfy eq.(1)
Let a=3
b = (2(3) - 2) ÷ 4
b = 1
Thus, a = 3 and b=1 satisfy eq.(1)
Hence the second equation is 3x + y = 2
The equations are justified by keeping the values -
2x+y=0 ... (2)
3x+y=2 ... (3)
From eq.(2),
y=-2x
Putting value of y in eq. (3), we get,
3x+(-2x)=2
3x-2x=2
x=2
Now, putting x=2 in eq.(2)
2(2)+y=0
y=-4
Hence, the solution is justified.
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I bought 2 books. One cost twice as much as the other. Together they cost £3.45.
How much did the dearer book cost?
We can express this as:
x + 2x = £3.45
We can solve for x with no additional work.
x + 2x = £3.45
3x = £3.45
3x/3 = £3.45/3
x = £1.15
Im guessing you're British by the use of the £ symbol, and I don't understand what "dearer" means as in America we don't use that term. I'll just give you both values.
x = £1.15 (this is the first book)
2x = £2.30 (this is the second book, which costs twice as much as the first.)
(100) points and branlyist PLS HELP
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 18 gallons of water. Ryan used 9.7 gallons to water his garden in June and 3 and one eighth gallons in July. How much water is left in the barrel?
24.575 gallons
5.175 gallons
3.168 gallons
3.125 gallons
Answer: 5.175
Step-by-step explanation: 18 - 9.7 - 3 1/8 = 5.175
Please help solve this equation. -3(5w-3y-2)
Answer:
-15w+9y+6
Step-by-step explanation:
I think that you are asking to simplify the expression. An equation has an equal sign and I do not see one.
We need to distribute the -3 to everything inside of the parentheses.
A negative times a negative is a positive.
A negative times a positive is a negative.
-3(5w-3y-2)
-3(5w) -3(-3y) -3(-2)
-15w + 9y + 6
Hi!
To simplify this, use the Distributive Property:
[tex]\tt{a(b+c)=ab+ac}[/tex] | Basically, we distribute a so that it gets multiplied by b and c.Now, let's simplify the given expression:
[tex]\dashrightarrow\sf{-3(5w-2y-2)}[/tex]
Like the property said, We should distribute -3 so that it's multiplied by each term:
[tex]\bullet\dashrightarrow\sf{-15w+9y+6}[/tex]
Therefore,
[tex]\bullet\dashrightarrow\stackrel{\heartsuit}{\boxed{\boxed{\boldsymbol{-15w+9y+6}}}}}\dashleftarrow\bullet[/tex]
Good luck.- stargazing :')
rewrite the following statements less formally, without using variables. determine, as best as you can, whether the statements are true or false
All of the statements are True when the expressions are evaluated using appropriate illustrations.
What are Real numbers?Real numbers are made up of both rational and irrational numbers. Real numbers include integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as 3, (22/7), and so on.STATEMENT: 1
Real numbers have both rational and irrational values and can thus be manipulated using arithmetic operators like addition.
As a result, the statement is correct.
[tex]1+\frac{1}{2}=1 \frac{1}{2}[/tex]
STATEMENT: 2
Real numbers can be expressed or raised to the power of another number in a variety of ways, including being squared.
2² = 4; (1/3)² = 1/9STATEMENT: 3
All positive integers have a squared value that is greater than or equal to the value.
n = 2; n² = 2² = 44 > 2STATEMENT: 4
A sum's absolute value is always less than or equal to the sum of two numbers' absolute values.
a = 3 ; b = - 4|a + b | = |3-4| ≤ |-3|+|4||-1| ≤ 3 + 4-1 ≤ 7Therefore, all of the statements are True when the expressions are evaluated using appropriate illustrations.
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The complete question is given below:
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false.
a. There are real numbers u and v with the property that u+v b. There is a real number x such that x2 c. For all positive integers n,n2≥n.
d. For all real numbers a and b,|a+b|≤|a|+|b|
how is everyone?
10+2x3=??
Answer:16
Step-by-step explanation:
2x3+10
Answer:
The answer is 60
Step-by-step explanation:
10+2= 20
20x3=60
Point L is on line segment KM. Given KL
length KM.
=
15 and LM = 3, determine the
Step-by-step explanation:
ano po ? pwede e bou nyo yong Tanong
Factor completely:
4x2−144
A
4(x2−36)
B
4(x+6)(x−6)
C
(2x−12)(2x+12)
D
(x+12)(4x−12)
Answer:
C
Step-by-step explanation:
(2x - 12)(2x + 12)
4x² + 24x - 24x - 144
4x² - 144
Which function would you use to locate the index of the first character of the first occurence of a substring within another string?
You would use the CHARINDEX string function to locate the index of the first character of the first occurrence of a substring within another string.
What is the CHARINDEX function?The CHARINDEX() function is defined as returning the substring's location within the given string. Like the SUBSTRING function, it operates in reverse.
⇒ Syntax of CHARINDEX() function is CHARINDEX (substring, input_string)
Substring: Here, we specify the substring within the input string that we wish to look for. A maximum of 8000 characters may be used in this argument.
Input_string: The input string is defined in this argument.
Therefore, You would use the CHARINDEX string function to locate the index of the first character of the first occurrence of a substring within another string.
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Miranda bought a square frame that has an area of 30 square inches.What is the approximate side length of the frame to the nearest tenth?
Answer:
6in lenght
Step-by-step explanation:
cause 30in square = 5 multiplied by 6 = 30
*PLS HELP*
Suppose a and b give the populations of two states where a > b. Compare the expressions and tell
which of the given pair is greater or if the expressions are equal.
a-b
5
(select)
b
5
What property is (3+2) x 4 = 4 x (3+2)
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
Hello!
(3+2) and 4 are factors of the multiplication equation. Flipping them around would still give the same answer.
This is the Commutative Property, specifically the Commutative Property of Multiplication.
Error Analysis ( PLS I NEED THIS ANSWERD TODAY! :(
Mr.Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some bracelets that cost $4.50 each, including tax. Write an equation to determine x, the maximum number of bracelets Mr.Gonzales could buy. Solve the equation to determine the number of bracelets Mr.Gonzales could buy.
Show your work.
42.50 - 29= 13.5
13.5÷4.50=3
Answer: 3
Solve the problem correctly.
Explain, in complete sentences, the error(s) made. In your explanation, make sure to include how you can fix there error(s), how you could have checked that the answer was incorrect, and diagram/drawing yo explain your thinking.
The maximum number of bracelets Mr.Gonzales could buy is 3
How to write an equation to determine x, the maximum number of bracelets Mr.Gonzales could buyThe given parameters are:
Budget = $42.50
Shirt = $29
Bracelet = $4.50 each
Represent the number of bracelets with x
So, we have
Shirt + Bracelet * x = Budget
This gives
29 + 4.50x = 42.50
Evaluate the like terms
4.50x = 13.5
Divide both sides b 4.50
x = 3
Hence, the maximum number of bracelets Mr.Gonzales could buy is 3
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Помогите пожалуйста!!
Задумали чесло умножили его на 5 из результата вычли 12 и получили 38. Какое число задумали?
Решить с помощью уровнения
Помогите пожалуйста!!
Answer:
good question it is very hard question
five less than twice a number is 7 algebraic expression
Which scales of data measurement are associated with quantitative data? interval and ratio ratio and nominal ordinal and interval nominal and ordinal
Interval and ratio scales of data measurement are associated with quantitative data.
Data measurement:- Data measurement is the way in which data can be subcategorized to analyze the data properly. Data can be classified into two types-
Quantitative data:- The data, which can be measured with numbers is called as quantitative data. Ex: duration, speed etc. This kind of data can be again subcategorized into two types-Discrete:- The data, which is of whole number, that can't be broken. Ex: a number of items.Continuous:- The data, which can be broken. Ex: height, weight etc. This type of data can be measured using interval and ratio measurement scales.Qualitative data:- The data, which is non-numerical value and categorical is called as qualitative data. Ex: yes, no responses or eye color etc. This type of data can be measured using nominal and ordinal measurement scales.Thus we can conclude that, Interval and ratio scales of data measurement are associated with quantitative data.
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________ is a statistical measure of how much scores in a sample vary around the mean. multiple choice normal distribution standard deviation frequency accuracy
Standard deviation is a statistical measure of how much scores in a sample vary around the mean. The correct option is B.
What is the 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.
Therefore, the standard deviation is a statistical measure of how much scores in a sample vary around the mean. The correct option is B.
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please help me with this problem
Answer:
The equivalent fraction of 6/9 is 4/6
Marcus is throwing a party, he is expecting 150 guests at the party. the cost per person for food is $30 dollars. how much money does marcus need to pay for food?
Answer: 4500
Step-by-step explanation:
Please help due in less than an hour
Answer: 1: (0,-5) 2: (0.5,1) 3: (1.5, -4.5) 4: (-2.5,-0.5)
Step-by-step explanation:
Helpppp...
[tex]{e}^{x} = {2e}^{ - x} [/tex]
Pls gv explaination to the solution
Write an expression that computes the difference of the variables ending_time and starting_time .
ending_time - starting_time is expression that computes the difference of the variables ending_time and starting_time.
What does a variable schedule mean?
There is an alternative to the standard 8-hour workday, five days a week work schedule: a variable work hours program. It is a program that provides staff members more freedom and control over their time, both at work and at home.What is an example of variable schedule?
A variable-ratio schedule is a partial reinforcement schedule used in operant conditioning when a response is reinforced after a variable number of responses. Using this plan, a constant, high rate of reaction is produced. Games of chance and lotteries are two excellent examples of rewards with variable-ratio schedules.An expression that computes the difference of the variables ending_time and starting_time = ending_time - starting_time
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5X to the second power times 2X to the fifth power
Answer:
10xto the power of 7
Step-by-step explanation:
Multiply x2x2 by x5x5 by adding the exponents.Tap for fewer steps...Move x5x5.5⋅2(x5x2)5⋅2(x5x2)Use the power rule aman=am+naman=am+n to combine exponents.5⋅2x5+25⋅2x5+2Add 55 and 22.5⋅2x75⋅2x7Multiply 55 by 22.10x710x7
If A, B, C, and D are collinear, then
they lie in the same plane. A, B, C,
and D lie in the same plane.
If BD bisects ABC, then D lies in
the interior of ABC. D lies in the
interior of ABC.
The hypothesis of both statements are false.
How to Interpret Collinear Points?1) Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear,
Thus, if A, B, C, and D are collinear, then they cannot lie in the same plane.
Thus, the hypothesis is not true.
2) When we bisect an angle, it is possible that one of the endpoints of the line may be outside the interior of the bisected angle. Thus, the hypothesis is Not true.
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a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5×102nm thick, how many square meters will the oil slick cover?
The square meters of the area the oil slick will cover is 9.6 × 10⁶ m².
What is meant by volume?Volume is defined as the amount of three-dimensional space enclosed by a closed surface.
The liter (L) is the metric system's base volume unit, with several extended volume units also available. There are also many metric volume units based on the a cubic length dimension, including such cubic meters or cubic centimeters. Gallons and ounces are examples of imperial volume units.Now, as per the given question;
First, we determine the entire volume of oil in gallons by multiplying the volume per barrel even by total number of barrels:
15×42 gal = 630 gal
This volume must be converted to square meters:
V = 630 gal × (0.00379 m³/ gal
V = 2.4 m³
The thickness (height) of a oil film in meters is required:
h = 250 nm × (m/10⁻⁹nm)
h = 2.5 × 10⁻⁷m
The surface area of a oil film is calculated by dividing the oil volume by height of the oil film.
A = V/h
A = 2.4 m³/2.5 × 10⁻⁷m
A = 9.6 × 10⁶ m²
Therefore, the area of the oil slick cover is found to be 9.6 × 10⁶ m².
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Use what you know about addition and subtraction of polynomials to find the missing term represented by the question mark in each equation. (â€""4x2 6x 3) (8x 5 ?) = 2x2 14x 8 ? = (â€""b3 3b2 8) â€"" (? â€"" 5b2 â€"" 9) = 5b3 8b2 17 ? =
According to the given statement the value for:
A. = 6x²
B. = 6x³
What do you mean by Polynomials?An expression that only uses the same operations of addition, subtraction, multiplication, and non-negative integer exponentiation of factors is said to be a polynomial. It consists of indeterminates and coefficients. x²+4x + 7 is an illustration of a polynomial of one uncertain x.
According to the given data:Polynomials are added by combining like terms.
We can see that adding 6 and 8 together yields 14, and adding 3 and 5 together yields 8.
We also understand that adding something to -4x² yields 2x². We deduct to obtain the value that is missing:
2x²-(-4x²) = 2x²+4x² = 6x².
Similarly for the second equation on solving we get:
Polynomials are added by combining like terms.
We also understand that adding something to -b³ yields 5b³. We deduct to obtain the value that is missing:
5b³-(-b³) = 5b³+ b³ = 6x³.
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I understand that the question you are looking for is:
Use what you know about addition and subtraction of polynomials to find the missing term represented
by the question mark in each equation.
(-4x² + 6x + 3) + (8x + 5 + ?) = 2x² + 14x + 8
? =
(-b³ + 3b2 + 8) – (? - 562 - 9) = 5b³ + 8b2 + 17
? =
You want to make 20 plates and have 30 bags of shredded cheese. How can you determine how much cheese to put on each plate so that each plate has the same amount of shredded cheese?
The amount of cheese in each plate = 1.5x
There are 30 bags of shredded cheese.
Let 'x' be the quantity of cheese in each bag. Then,
The total quantity of cheese in 30 bags = 30x
Number of plates = 20 plates
We need to determine the quantity of cheese put on each plate so that each plate has the same amount of shredded cheese.
For this we just need to divide the total amount of shredded cheese by the number of plates.
The equal amount of cheese in each of 20 plates = 30x/20
= 3x/2
= 1.5x
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14
Starting with the number 0 and counting left
to right,
0
35
5
40
10
45
Date:
15 20 25 30
50
55
60
65
write the first number
write the fourth number
write the ninth number
Answer:
first number: 0
fourth number: 15
ninth number: 40
nina goes to the neighborhood store to buy 14 rolls of paper towels. if she pays $20.02 in all for the purchase, how much does one roll of paper towels cost?
Answer:
$1.43
Step-by-step explanation:
To find how much one roll of paper towels cost, we have to divide the total purchase ($20.02) by the number of paper towel rolls (14).
20.02 ÷ 14
= $1.43
One paper towel roll costs $1.43
Have a lovely rest of your day! :)
When the same number is added to the numerator and denominator of 5/7, the result is 17/23. what is that number?
The number added to the numerator and the denominator is 2/3.
It is given in the question that when the same number is added to the numerator and denominator of fraction 5/7, the result is 17/23.
We have to find the number added to the numerator and the denominator.
Let the number be x.
Hence, according to the data given in the question, we get,
(5 + x)/(7 + x) = 17/23
By cross - multiplication, we get
23(5 + x) = 17 (7 + x)
Opening the bracket according to the distributive property of addition and multiplication, we get,
115 + 23x = 119 + 17x
23x - 17x = 119 - 115
6x = 4
x = 4/6
x = 2/3
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