The elimination method is used for solving linear equations. Here we make use of the addition property of equality, that is when same number is added on both sides of equation, it still remains equal.
Lets look into some examples.
Example 1x + y = 10
x - y = 2
By adding both equations,
x + y + x - y = 10 + 2
+ y and - y are cancelled or y term is eliminated.
2x = 12
x = 6
Example 22x + 3y = 10
-3x + 3y = 15
Here to eliminate y, we have to add the additive inverse of second equation.
2x + 3y + 3x - 3y = 10-15
5x = -5
x = -1
Example 3x + 4y = 5
3x - y = 2
To equalize the y term we multiply the second equation by 4
12x - 4y = 8
Adding both equations,
x + 4y + 12x - 4y = 5 + 8
13x = 13
x = 1
So elimination method is used for solving linear equations.
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Help aspp please thank you show ur work if you like
Driving from North Carolina to Florida at an average speed of 70 mph takes about 7 hours and 12 minutes.
What is speed?Velocity is a term used to describe how fast an object is moving in a particular direction. It is measured as distance traveled in a period of time and is usually expressed in units of meters per second (m/s). Velocity is an important concept in physics and is used to calculate how fast an object moves in a given environment. Velocity is related to speed, which is the rate of change of distance in a particular direction. Speed is an important factor in many sports and activities such as running, cycling and driving. It is also used in different ways in our daily life. For example, it is used to determine how fast a car can go from A to B, or how long it will take to walk to a destination.
Speed = Distance/Time
55 = Distance/9
Distance = 495 miles
When speed is 70 mph:
70 = 495/Time
Time = 495/70
Time = 7 hours and 12 minutes
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A granola recipe calls for 3 cups of oats, 1 cup of almends. 1 cup of pecans, and 1 cup of dried fruit. What is the ratio of fruit to eats? Yolanda says that for every 2 cups of nuts, there are 2 cups of fruit. Explain why her answer is incorrect and give the correct ratio of nuts to fruit. Explain your answer.
The ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a granola recipe calls for 3 cups of oats, 1 cup of almonds. 1 cup of pecans, and 1 cup of dried fruit
The ratio of nuts to fruits is -
r = (3 oat cups + 1 almond cup + 1 pecan cup)/(1 dried fruit cup)
r = 5/1
5 : 1
For every 5 cups of nuts, there is 1 cup of dried fruit cup.
Therefore, the ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.
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Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21 . Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the null and the alternative hypothesis?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is calculated as follows:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]
z = (8.8 - 8.5)/(1.11/square root of 21)
z = 1.24.
What is the p-value and conclusion?The p-value is obtained using a z-distribution calculator.
We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:
0.215.
(2 multiplied by the subtraction of one and the p-value of z = 1.24).
The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.
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Is X² is a variable?
A is the variable and X is the coefficient term in the supplied X2 expression. An algebraic expression is used to solve a particular mathematical problem .
what is variable ?In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.
given
The coefficient term is denoted as X2, and the variable is A.
An algebraic expression is used to solve a particular mathematical problem by combining words and numbers.
For instance, the numerical coefficient in the equation 5x is 5, meaning that the variable x has been multiplied by 5 times.
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When x 12" to the "-x^3+3x^2+5x+1"
The value of expression -x³+3x²+5x+1 is -1235 when x is 12
What is Expression?An expression is combination of variables, numbers and operators.
Given polynomial is -x³+3x²+5x+1
We need to find the value of the polynomial when x is 12.
To find this we just need replace x with 12
-(12)³+3(12)²+5(12)+1
Minus twelve cube plus three times of twelve square plus five times of twelve plus one
-1728+3(144)+5(12)+1
-1728+432+60+1
-1728+493
-1235
Hence, the value of expression -x³+3x²+5x+1 is -1235 when x is 12
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Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers. The sum of two numbers is 71. One number is 27 more than the other. Find the numbers. D Let x be the smaller number and y be the larger number. Write an equation that represents the fact that the sum of the numbers is 71. =71 (Simplify your answer.)
Given that the sum of two numbers is 71 and one number is 27 more than the other, we can set up the following system of equations:
What is the straightforward definition of a system of equations solution?
A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
x + y = 71 (equation 1 represents the fact that the sum of the numbers is 71)
y = x + 27 (equation 2 represents the fact that one number is 27 more than the other)
To solve the system of equations, we can use the substitution method. We'll substitute equation 2 into equation 1:
x + (x + 27) = 71
Combining like terms:
2x + 27 = 71
Subtracting 27 from both sides:
2x = 44
Dividing both sides by 2:
x = 22
Now we can substitute x = 22 back into equation 2 to find the value of y:
y = x + 27
y = 22 + 27
y = 49
So the two numbers are x = 22 and y = 49, and they satisfy the given conditions that the sum of the two numbers is 71 and one number is 27 more than the other.
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I’d love you he help for all of it but i’ll take what I can get
Answer:
Parallelogram formula- 1/2 x base xheight
Step-by-step explanation:
What is the difference of polynomial and equation with example?
A polynomial is an expression involving variables and coefficients, which is formed by adding, subtracting, multiplying, and taking non-negative integer exponents of the variables. A mathematical statement that two expressions are equal is known as an equation.
A mathematical statement that two expressions are equal is known as an equation.
Example of a polynomial:
2x^2 + 3x + 5
Example of an equation:
2x^2 + 3x + 5 = 0
Let's say we are solving the equation 2x^2 + 3x + 5 = 0
Step 1: Subtract 5 from both sides.
2x^2 + 3x = -5
Step 2: Divide both sides by 2.
x^2 + 3/2 x = -5/2
Step 3: Use the quadratic formula to solve for x.
x = (-3 ± √17) / 4
Step 4: Simplify the answer.
x = (-3 ± 4.12) / 4
Step 5: Solve for the two values of x.
x = -0.78 or x = 3.28
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I need help on that soooo
Answer:
3⅛ ÷ 1⅔ = 1.9083969465648855.
Step-by-step explanation:
To arrive at this answer, we can first convert 3⅛ and 1⅔ to fraction form.
3⅛ can be written as 3 + 1/8, which is equal to 3 + 1/8 = 25/8.
Similarly, 1⅔ can be written as 1 + 2/3, which is equal to 1 + 2/3 = 5/3.
Therefore, 3⅛ ÷ 1⅔ is equal to (25/8) ÷ (5/3) = (25/8) * (3/5) = (325)/(85) = 75/40 = 1 + 35/40 = 1 + 35/40 = 1.875.
This is the exact result, but if you want to round to the nearest hundredth, the result would be 1.91.
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)
Step-by-step explanation:
CDEF is a square so all sides of CDEF are 6cm.
This tells us the area of CDEF which is 36cm squared
This tells us the radius of AE which is the side FE which we know is 6cm.
Area of a half circle= pi x r squared/2
Area of AE= pi x 36/2= 18pi
Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)
Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.
So the area of ABCF is 36-4.5pi.
CD would also have an area of 4.5pi as it is the exact same half circle.
Area of AE=18pi cm squared
Area of CDEF= 36cm squared
Area of ABCF= 36-4.5pi
Area of CD= 4.5pi
18pi+36+(36-4.5pi)+4.5pi
simplified to:
22.5pi + 36 + (36-4.5pi)
What is the equation for the linear relationship in slope intercept form?
Answer:
y=-2/3x+4
Step-by-step explanation:
slope intercept form = y=mx+b
y=-2/3x+4
A rectangle and a _________ are quadrilaterals with four right angles.
Answer:
A rectangle and a square are quadrilaterals with four right angles.
Step-by-step explanation:
Hope it helps! =D
A $280 suit is marked down by 30%. Find the sale price.
Answer: The Sale price is $196
Step-by-step explanation:
We can start by converting 30% to a decimal 0.3, then we will multiply the $280 by the decimal (280*0.3 = $84) This means it is marked down by $84, so to get the sale price we subtract the mark down by the original price, ($280-$84 = $196).
Answer:
The suit's sale price is $196.
Step-by-step explanation:
⭐What is "mark down"?
the percentage the price of an item is reduced byTo find the sale price, we need to form an equation representing the given situation.
MARK DOWN:
original price - (mark down percentage)(original price) = sale price
Substitute the known values.
280 - (0.3)(280) = sale price
Compute.
280 - 84 = sale price
∴ $196 = sale price
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Each grid square is 1 square unit. Find the area, in square units, of the shape without counting every square. Be prepared to explain your reasoning.
The total area of the two rectangles is given by the equation A = 33 units²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the total area of the 2 rectangles be A
Now , each grid square represents = 1 square unit
Now , let the first rectangle be represented as P
The length of P = 4 grid squares
The width of P = 3 grid squares
Let the second rectangle be represented as Q
The length of Q = 7 grid squares
The width of Q = 3 grid squares
So , Area of Rectangle = Length x Width
The area of rectangle P = 4 x 3
The area of rectangle P = 12 units²
The area of rectangle Q = 7 x 3
The area of rectangle Q = 21 units²
So , the total area of figure A = area of P + area of Q
On simplifying the equation , we get
Total area of figure A = 12 units² + 21 units²
Total area of figure A = 33 units²
Therefore , the value of A is 33 units²
Hence , the area is 33 units²
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Which statements are correct when translating this phrase into a variable expression?
The product of 8 and y decreased by 10
A 8y + 10
B Product means to multiply
C 8y-10
D product means to multiply
E y/x - 10
Therefore , the solution of the given problem of algebra comes out to be
Product means to multiply and decreased means to subtract so option C only seems valid
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
Product means to multiply and decreased means to subtract so option C only seems valid
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Stefanie has 18 grams of 20% sugar syrup and john 30 of 25% what is the concentration in the new mixture
The concentration in the new mixture will be 11.1 grams.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Stefanie has 18 grams of 20% sugar syrup.
And, john has 30 grams of 25%.
Here,
Stefanie has 18 grams of 20% sugar syrup.
Hence, The amount of sugar = 18 × 0.2
= 3.6 grams
And, john has 30 grams of 25%.
Hence, The amount of sugar = 30 × 0.25
= 7.5 grams
Thus, The concentration in the new mixture = 3.6 + 7.5 grams
= 11.1 grams
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Working as a team, 8 mathletes solve 20 problems in 10 minutes. At this rate, how many mathletes solve 30 problems in 5 minutes
Step-by-step explanation:
the given ratio is
8 / 20/10 = 8 / 2 = 4
for x mathletes we need to keep the same ratio :
x / 30/5 = 4
x / 6 = 4
x = 4×6 = 24
24 mathletes.
If you take a number of times by four then subtract one you get the same is it you took the number standby shift then organise what is the number
The unknown number deduced by solving the equation 4x - 1 = 6x +9 is -5.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let the unknown number be x.
First multiply the number by 4 = 4x
Then subtract 1 from it = 4x -1
This results in the same number as when the number is multiplied by 6 and 9 is added to it = 6x + 9.
So the equation will be -
4x - 1 = 6x +9
4x - 6x = 9 + 1
-2x = 10
-x = 10/2
x = -5
Therefore, the number obtained is -5.
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If you take a number, times by 4 then subtract 1. You get the same as if you took the number, times by 6 then add 9. What is the number?
What is the value of the polynomial 5x − 4x^2 3 at x =- 1?
The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.
The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,
Now solve the polynomial by putting the value of x equal to -1:
5(-1) - 4(-1)^2 + 3 , x = - 1
-5 - 4 ( 1 ) + 3 , squaring -1 gives + 1
minus 5 minus 4 plus 3
( - 9 + 3)
( - 6 )
Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.
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h=?ft
what is the correct answer
Answer:
h = 4 ft
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 8 and h = 3 , then
A = 8 × 3 = 24 ft²
Now consider the other base b = 6 with perpendicular height h , then
6h = 24 ( divide both sides by 6 )
h = 4
Which tables of (x, y) values given below could represent functional relationships? Explain your thinking.
Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.
what is function ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
y = x+5
2.When x = 10,y = x+5 = 10+5 = 15
3.When x =15,y = x+5 = 15+5 = 20
4.When x = 20,y = x+5 = 20+5 = 25
Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.
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Hi everyone, I need some help please. The question is asking -
Which set of ordered pairs does not represent a function?
A: (0, -4) , (8,5) , ( -5,6) , (6,5)
B: (0, -1) , ( -4,0) , ( -2, -1) , (7, -7)
C: (0,3) , ( -3,6) , ( -7,3) , (9, -5)
D: (8, -2) , ( -2, -3) , (6,6) , ( -2, -6)
B: (0, -1) , ( -4,0) , ( -2, -1) , (7, -7)
What exactly is an ordered pair?Image result for ordered pair definition
An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair’s numeric values can be integers or fractions.
The origin is the place where both axes cross. Every point on the coordinate plane is represented by an ordered pair (x, y), with the first element x referred to as the x-coordinate and the second element y referred to as the y-coordinate.
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Question 6 of 10
Which is the best estimate of the circumference of this circle?
3
OA. 18 units
OB. 42 units
OC. 3 units
O D. 6 units
The best estimate for the circumference of a circle with 3 units radius is equal to 18 units. The correct option is A.
Given the radius of the circle is equal to 3 units.
The formula for the circumference of the circle is equal to
[tex]C=2*\pi *r[/tex].
By substituting the value of the radius and pi we will get:
[tex]C=2*3.14*3\\C=18.86[/tex].
Therefore the best estimate will be 18 units.
Complete question:
Which is the best estimate of the circumference of this circle?
radius = 3 units.
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What is the opposite inverse of 4?
4 is the additive inverse of -4.
OR
The opposite of 4 is -4, or negative four.
Now, According to the question:
Opposite numbers:-
Every number has an opposite. In fact, every number has two opposites: the additive inverse and the reciprocal—or multiplicative inverse. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.
If a number is added to its additive inverse, the sum of both the numbers becomes zero.
For any given number, the additive inverse is a number or a value which when added to the original number results in zero.
Mathematically: a + (-a) = 0
So here, 'a' and '-a' are the additive inverses of each other.
Therefore, for 4, the additive inverse is 4 = -4
Thus, 4 is the additive inverse of -4.
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Examine this set of ordered pairs. (7,9), (4,18), (−3,11), (16,18), (4,−11) Is the set of ordered pairs a function? Choose the answer that is entirely correct.
The set of ordered pairs represents the function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
The set of ordered pairs:
(7,9), (4,18), (−3,11), (16,18), (4,−11)
Pairs written as input and output of the relation.
In the attached table,
To prove function:
A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function.
And here each input is connected to precisely one output.
Therefore, this is a function.
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to
5.2.2 Guided Instruction: Solutions to the
Products and Quotients of Polynomials on a
Graph
Graphs can be used to determine the products and
quotients of polynomials similarly to using graphs when
adding and subtracting polynomials.
The functions a(x) and b(x), and their product, a(x) b(x),
represented by c(x), are shown on the coordinate plane.
35A
(10, 34)
-10
-30
-25-(-0,24)
MATH
20
(0.805, 105)
10
(1.5, 6)
0
(0-3)
b(x10
-15
(8,13)
C(x)
(6.5, 10)
5
(0-8)
(10, 17)
(8.695-10)
3. Find the value of c(10).
2. What is the product of a(10) · b(10)?
10, 2
15
(8,0)
-20
1. Describe how to use the graph to determine the value
of a (10) b(10).
20
25
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
Definition of the cubic function .f(x)=ax3+bx2+cx+d, where 0 and the coefficients a, b, c, and d are complex numbers, and where the variable x has real values. In other words, it is both a three-degree polynomial function and a real function.
Here,
Our role in this situation is:
y = ∛(x - 5) (x - 5)
so the cubic root is given.
In this case, we see that when x = 0, we have:
The y-intercept is y = -5.
And if x = 5, we get:
Because of the sign change, the x-intercept and inflection point are both equal to y = ∛0 = 0
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
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If a business discovered that changing the price of its muffins created an absolute value of .35 < 1, what did its price change mean
If a company found that raising the price of its muffins resulted in an absolute value of.35 < 1, then the demand for muffins is inelastic.
What is meant by mean?The mean is the set of two or more numbers' mathematical average. It is possible to calculate two different sorts of means: the arithmetic mean and the geometric mean. Add the numbers in a set together and divide by the total number of numbers in the set to find the arithmetic mean. To determine the mean, only numerical variables whether continuous or discrete can be employed.It is calculated by merely dividing the total number of values in a data collection by the sum of all the values in the data set. The mean, or average of the supplied numbers, is computed by dividing the total number of numbers by the sum of the given numbers.To learn more about mean, refer to:
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How do you find the missing angle of a triangle with all sides?
The missing angle of a triangle where only the measure of all sides are given can be calculated by using the Cosine Law .
What is Law Of Cosine ?
The law of cosine is also known as Cosine Rule. This law is useful in finding the missing information of any triangle.
For example, if you know the lengths of three sides of a triangle , this rule helps to find the angle between the two sides of the triangle.
Let a , b and c be the sides of the triangle and let A , B and C be the angle corresponding to the respective sides .
Then by the Cosine Law the angles are represented as : [tex]CosA = \frac{b^{2} +c^{2} -a^{2} }{2bc}[/tex] ;
[tex]CosB = \frac{c^{2} +a^{2} -b^{2} }{2ac}[/tex] ; [tex]CosC = \frac{a^{2} +b^{2} -c^{2} }{2ab}[/tex] .
Therefore , The Law Of Cosines is used to find the missing angle .
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In a '15% off sale, Freya bought a DVD player for £179. 99. What was the original price of this
DVD player?
The original cost of the DVD player is $ 211.75.
Calulating Original price:
To calculate the original price of an item in case of giving a discount we can use the following formula
Original Price = Selling Price / (1 - Percentage Discount/100)
(Or)
We can calculate the original price by taking a variable as the cost of the item as given below
Here we have
In a '15% off sale, Freya bought a DVD player for £179. 99
Let 'x' be the cost of the DVD player
Then the cost of the DVD player after giving a 15% discount
= x - 15% of x
= x - (15/100) x
= x - 0.15x
= 0.85x
Given that
Freya bought a DVD player for £179. 99
=> 0.85x = 179. 99
=> x = 211.75
Therefore,
The original cost of the DVD player is $ 211.75.
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Calculate the area of a rectangle with the base of 12 feet and height of 3 feet.
(I need the answer as fast as possible so if anybody could help that would be greatly appreciated)
A: 9 square feet
B: 15 square feet
C: 30 square feet
D: 36 square feet