Answers
Answer:
see attached
Step-by-step explanation:
You are given two solutions to a 3-step inequality and are asked to describe them.
3-Step inequalityThese inequalities have variable terms and constant terms on both sides of the comparison symbol. The expressions have been simplified.
These inequalities can be described as 3-step, because a straightforward solution can be accomplished in 3 steps. The first two steps separate the constant and variable terms, and the final step divides by the coefficient of the variable.
The process is virtually identical to that for solving a 3-step equation.
AllisonAllison's first step is to get rid of one of the unwanted variable terms by subtracting it from both sides. She chose the "3x" term, which has a smaller coefficient than the "5x" term, so the resulting difference will leave a positive coefficient on the x-term.
Then she removed the unwanted constant from the side with 2x by adding its opposite.
Since the x-term has a positive coefficient, Allison did not have to change anything about the inequality symbol when she divide both sides by that coefficient.
JohnJohn used a first step similar to Allison's but he chose to eliminate the 5x term. The result was the x-term ended up with a negative coefficient. That introduces an extra bit of procedure at the end when he divides by the -2 coefficient of x: the inequality symbol must be reversed.
The constant term on the side with the x-term was removed by adding its opposite. This is the same step Allison performed as step 2.
When John finally divides by the coefficient of x, he has to reverse the inequality symbol, since that coefficient is negative.
__
Additional comment
You can compare one line of the solution to the one above to see what is different. Identifying that difference will tell you what step was taken to get the current line from the previous one. It helps to understand the way equations and inequalities are solved, so you better know what to look for.
Related Questions
PLEASE HELP I NEED THE STEPS AND ANSWER TO THIS QUESTION
Answers
Answer:
x = 12
Step-by-step explanation:
Definition of a point between two points:
Point B is between points A and C if and only if AB + BC = AC.
Now we apply it to this problem.
AB = 3x + 5
BC = 2x + 3
AC = 68
AB + BC = AC
Substitute each segment length with the expression or length above. Then, solve the equation for x.
3x + 5 + 2x + 3 = 68
5x + 8 = 68
5x = 60
x = 12
Write an expression for which subtracting 5 from an expression would isolate the variable
Answers
An expression for which subtracting 5 from an expression would isolate the variable is -9x + 5 = x + 2
What are algebraic expressions?Algebraic expressions are described as expressions that consists of coefficients, terms, variables, factors and constants.
These expressions are also known to consist of arithmetic operators, which includes;
Floor divisionDivisionExponentiationAdditionMultiplicationSubtraction, etcFrom the information given, we have to subtract five from an expression to isolate the variable
Now, let's us the algebraic expression;
-9x + 5 = x + 2
Let's subtract 5 from both sides of the equation, we get;
-9x + 5 - 5 = x + 2 - 5
add and subtract the like terms
-9x + x = -3
-8x = -3
x = 3/8
Hence, the expression is -9x + 5 = x + 2
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Please help me solve this question The chapter its from is called graphing linear equations
Answers
Answer: 14
Step-by-step explanation: 175 divided by 12.5 is 14
on the bus 12/40 of the seats were taken what is the fraction simplest form?
Answers
Answer:
Step-by-step explanation:
3/10 you find the GCF of both
when the product of 10 and 15 is divided by the sum of 10 and 15, what is the quotient?
Answers
Answer:
The answer would be 6
Step-by-step explanation:
first multiply 10*15=150 then 10+15=25 150 divided by 150 is 6
Determine whether the equation $6d+8=14+3d$ has one solution, no solution, or infinitely many solutions.
Answers
Answer: One solution
Step-by-step explanation: We start with 6d+8=14+3d. We can move 3d to the other side of the equal sign and 8 to the other side of the equal which then we will have 6d-3d=14-8. When we simplify we get 3d=6 which is d=2. Which means it is one solution.
Answer: Only one solution
Step-by-step explanation:
6d + 8 = 14 + 3d
-3d from both sides
3d + 8 = 14
3d = 6
d = 2
What are the 5 properties of equality?
Answers
The reflexive, symmetric, transitive, additional, and multiplication characteristics are the five algebraic qualities of equality.
The reflexive property states that a = a for every real integer.
For any two real numbers, a and b, the symmetric condition is that if a = b, then b = a.
For each real number, a, b, and c, the transitive property states that if a = b and b = c, then a = c.
For every real integer a, b, and c, if a = b, then a + c = b + c. This is known as the addition property of equality.
The equality's multiplication property states that if any real integer, a, b, and c, are equal, then a * c is equal to b * c.
These features serve as the basis for algebraic manipulation and are employed in the decomposition of expressions and the solution of equations.
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Why is the addition method of solving a system with two variables also called the elimination method?
Answers
Using the Addition Method to Solve Two-Variable Equation Systems The addition approach, often known as the elimination method, is a third strategy for resolving linear equation systems.
What is meant by the elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by adding or subtracting, as well as multiplying or dividing the variable coefficients.
What is the process of elimination's formula?
Utilizing the addition property of equality, the elimination approach is used to solve systems of linear equations. Both sides of an equation can be increased by the same amount.
The first equation can be solved by adding x + y to the left side and 8 to the right side if your system is x - 6 = 6 and x + y = 8.
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Which statement could describe the returns from a bond?
Answers
Answer:
A bond is a debt security, meaning that it represents a loan made by an investor to a borrower (typically a corporation or government). The bond issuer promises to pay interest to the bondholder, usually at regular intervals, and to repay the principal when the bond matures.
So, a statement that could describe the returns from a bond is:
"Bonds typically provide a steady stream of income in the form of interest payments, but the return on investment is generally lower than that of stocks."
Another statement that could describe the returns from a bond is:
"Bonds are considered to be a relatively safe investment option, but they are not as profitable as stocks in terms of returns."
In general, bonds are considered to be less risky than stocks, but they also typically offer lower returns.
Answer: B
Step-by-step explanation:
How do you write an equation in intercept form from vertex form?
Answers
Answer:
y = a · (x -(h +√(-k/a))) · (x -(h -√(-k/a))) . . . . . . from y = a(x -h)² +k
Step-by-step explanation:
You want to know how to write an equation in intercept form from vertex form.
Solve for x"Intercept form" of the equation of a parabola is the factored form. The x-intercepts are the values of x that make the factors zero. This form can be found from vertex for by solving for the x-intercepts—the values of x where y=0.
X-interceptsThe vertex form equation is ...
y = a(x -h)² +k . . . . . . . vertex (h, k)
Solving for x when y=0, we have ...
0 = a(x -h)² +k
-k/a = (x -h)² . . . . . . . subtract k and divide by 'a'
±√(-k/a) = x -h . . . . . take the square root
x = h ±√(-k/a) . . . . . add h
These are the x-intercepts.
Intercept formTo write the equation in intercept form, we use these values to form factors of the quadratic. Each x-intercept (p) corresponds to a factor (x-p). The factors are multiplied by 'a' to keep the same vertical scaling of the graph that the original function had.
y = a · (x -(h +√(-k/a))) · (x -(h -√(-k/a))) . . . . . . intercept form
WILL GIVE BRAINLIST!!
Answers
In the figure, mGE = 97 and mHF = 43. Since GPEQ is a parallelogram, opposite angles are congruent. Therefore, m<GPE = m<EQG = mGE = 97.
m<GPEQ = 97
How do you tell if a system of equations has no solution or infinitely many formula?
Answers
When the graphs are parallel, a system of linear equations cannot have a solution. endless options. When the graphs are on the exact same line, a system of linear equations has an infinite number of solutions.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.
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Please help! percentage rates
12. The fire department hopes to raise $30,000 to repair a fire house. So far the department has raised $1,750.00. What percent is this of their goal?
14. A TV is advertised on sale. It is 35% off and has a new price of $195. What was the pre-sale price?
16. Store A and Store B both sell bikes, and both buy bikes from the same supplier at the same prices. Store A has a 40% mark-up for their prices, while store B has a 90% mark-up. Store B has a permanent sale and will always sell at 60% off those prices. Which store offers the better deal?
Answers
the percent of cash the Fire branch raised is 5.833 and the pre-sale rate of the TV is $300.
What is percentage?A price or ratio that can be said as a fragment of one hundred is called a percent in mathematics. If we want to compute a percent of a number, we need to divide it with the aid of using its complete after which multiply it with the aid of using one hundred. The percentage consequently refers to an issue in keeping with a hundred. Per one hundred is what the time period percentage signifies. The letter "%" stands for it.
Given, The fire department hopes to raise $30,000 to repair a firehouse. So far the department has raised $1,750.00
From the general formula of Percentage, we have to divide the value by the total value and then multiply the resultant by 100.
Percentage = (1750/30,000) * 100 = 5.833%
Also given, A TV is advertised for sale. It is 35% off and has a new price of $195.
Price of TV before Sale = (195 / 65) * 100
Price of TV before Sale = 300$
Therefore, the percentage of money the Fire department raised is 5.833 and the pre-sale price of the TV is $300.
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What are the characteristics of an absolute function?
Answers
The characteristics of an absolute function are listed below:
An absolute function gives the distance of a number on the number line from 0 irrespective it is on the left or right. An absolute function always gives the positive of a number.Example: | -2 | = 2
The domain of an absolute function is the set of all real numbers. The range of an absolute function is the set of all real numbers greater than or equal to zero.An absolute function is an even function.An absolute function is graphically symmetric about the y-axis.The graph of an absolute function is in the form of a V. The vertex of the absolute function graph is also the maximum or minimum point of the function.To know more absolute value:
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f the simple interest on $4000 for 5 years is $1000, then what is the interest rate?
Answers
The interest rate is 5%.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
The formula for simple interest is,
SI = PRT/100.
Where P is the principal, R is the rate and T is the time.
We have,
P = $4000
T = 5
SI = $1000
Now,
SI = PRT/100
Substitute the values.
1000 = (4000 x R x 5)/100
1000 = 200R
Divide 200 into both sides.
R = 1000/200
R = 5%
Thus,
The rate of 5%.
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Is this parabola a function?
Answers
Yes, a parabola is always a function, specifically a quadratic function.
To determine if a parabola is a function, you will need to check if it passes the vertical line test.
To do this, draw a vertical line through any point on the parabola and see if it intersects the parabola more than once. If it does, then the parabola is not a function. If it only intersects the parabola once, then the parabola is a function. To graph a parabola, you will need to find five points that make up the curve in order to get a better approximation of the general shape. This can be done by using the equation of the parabola in the form y = ax2 + bx + c . First, calculate the x-intercepts by setting y = 0 and solving for x. Then, calculate the y-intercept by setting x = 0 and solving for y. Finally, calculate two more points by solving for x when y is equal to a positive and negative value. Once the five points have been identified, plot them on a graph and draw a smooth curve through them.Learn more about parabola function:
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Solve for x.
4(2x − 13) = 4 + x
X = [?]
Answers
Hey there!
Answer:
After solving for x, our final solution is [tex]x=8[/tex].
__________________________________
Further Explanation:1. Expand [tex]4(2x-13)[/tex].
[tex]8x-52[/tex]
[tex]8x-52=4+x[/tex]
2. Move 52 to the right side.
[tex]8x=x+56[/tex]
3. Move x to the left side.
[tex]7x=56[/tex]
4. Divide both sides by 7.
[tex]\frac{7x}{7} =\frac{56}{7}[/tex]
5. Simplify.
[tex]x=8[/tex]
________________________________________
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What is meant by rules of substitution in mathematics?
Answers
A principle in logic specifying what expressions may be substituted for one another.
What is a mathematical expression?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division.
Term is defined as a constant, a single variable, or a combination of a variable and a constant combined with multiplication or division. Algebra Expression Example: 3x + 9, 5x + 10
What are an equation and an expression?
In mathematics, an expression is a word or phrase that combines variables, operators, and numbers to represent the value of something. Two expressions are assigned equal to one another in a mathematical statement known as an equation.
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Katie rolled a fair number cube, with faces numbered 1 to 6, 200 times. She rolled the number 5, five times. What is the experimental probability of landing on landing on 5? How does it compare to the theoretical probability of landing on 5?
Answers
The experimental probability of 2.5% is less than the theoretical probability of 16.67%.
What is the experimental probability?
The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.
The experimental probability of landing on 5 is the number of times that 5 was rolled divided by the total number of rolls. So, for Katie, the experimental probability of landing on 5 is:
(number of times 5 was rolled) / (total number of rolls) = 5/200 = 0.025 or 2.5%
This experimental probability, 2.5%, is the probability that Katie obtained from rolling the number cube 200 times.
The theoretical probability of landing on 5, assuming the cube is fair, is the number of ways to land on 5 divided by the total number of possible outcomes. Since a fair number cube has 6 faces numbered 1 to 6, the theoretical probability of landing on 5 is 1/6 or about 16.67%.
Hence, the experimental probability of 2.5% is less than the theoretical probability of 16.67%. This might be due to the fact that 200 rolls is not a large number to get accurate results. With more rolls, the experimental probability should get closer to the theoretical probability.
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HELP ASAP PLEASE!!!
A linear relationship is given in the table.
X-2 -1 0 1 2
y -13 -9 -5 -1 3
What is the slope of the relationship?
1/4
-1/4
4
-4
Answers
4 is the slope of the linear relationship.
What is slope?An indication as to how sharp a line is its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two places to the run in elevation between those same two points is referred to as the slope.
Slope-related equations The "change in y" over the "change in x" of a line is referred to as the slope. By dividing (y₂ - y₁) over (x₂ - x₁) and choosing two locations on the line (x₁, y₁) and (x₂, y₂), you can get the slope.
A linear relationship is given in the table.
According to the data of the table,
x: -2 -1 0 1 2
y: -13 -9 -5 -1 3
now, slope = (y₂ - y₁) / (x₂ - x₁)
slope = {-9 -(-13)} / {-1 -(-2)}
slope = 4
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What is the value of Z in the diagram below?
Answers
Answer:
Step-by-step explanation:180+59 then half the anwser
Cory is reading a graph of equivalent ratios. If 1 of the ratios is represented as 3,5 which could be another ratio
I don’t know if that made sense aaa
Answers
The other ratio equivalent to (3, 5) will be (9, 15).
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given that, Cory is reading a graph of equivalent ratios. If 1 of the ratios is represented as 3,5 which could be another ratio
In the given options,
a) (6, 8) = 3, 4
b) (8, 6) = 4, 3
c) (9, 15) = 3, 5
Since, (9, 15) = 3, 5
Hence, the equivalent ratio will be (9, 15).
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How do you find the range of K in a quadratic equation?
Answers
The range of K in a quadratic equation is the set of all possible values that K can take on in order for the equation to remain valid.
What is quadratic equation?A quadratic equation is an algebraic equation that contains a second-degree polynomial with one or more unknown variables. It can be written in the form of ax2 + bx + c = 0, where a, b, and c are just numbers, and x is the unknown variable. The solutions to the equation can be found using the quadratic formula. Quadratic equations are used to model a variety of different problems in mathematics, physics, and engineering.
To find the range of K, we must first understand the quadratic equation. A quadratic equation is an equation in which a variable (K) is raised to the second power and is equal to some other constant. The most common form of a quadratic equation is:
K2 = C
Where K is a variable, and C is a constant. The range of K in a quadratic equation can be found by forming two equations – one equation with K2 = C, and the other equation with K2 = -C.
The first equation (K2 = C) will tell us the maximum value that K can take on. To find this value, we take the square root of C and assign that value to K. The maximum value of K is the square root of C.
The second equation (K2 = -C) will tell us the minimum value that K can take on. To find this value, we take the square root of -C and assign that value to K. The minimum value of K is the negative square root of C.
Therefore, the range of K in a quadratic equation can be found by calculating the square root of C and the negative square root of C. The range of K is the set of all possible values that K can take on in order for the equation to remain valid, which is between the maximum and minimum values found.
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Deondra is going to invest $90,000 and leave it in an account for 15 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $201,000?
Answers
Interest is compounded is 4.63%
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.Compound interest is calculated by multiplying the initial loan amount, or principal, by the one plus the annual interest rate raised to the number of compound periods minus one. This will leave you with the total sum of the loan including compound interest"12% interest" means that the interest rate is 12% per year, compounded annually. "12% interest compounded monthly" means that the interest rate is 12% per year (not 12% per month), compounded monthly. Thus, the interest rate is 1% (12% / 12) per month. "1% interest per month compounded monthly" is unambiguousTo learn more about compound interest refers to:
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a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.0 minutes. find the probability that a given class period runs between and minutes.
Answers
The probability that a given class period runs between 50.5 and 51 minutes is 0.05
Understanding that a uniform probability distribution is essentially a rectangle with a surface area of one will help you to find the simplest solution to this problem.
Find a section of this rectangle's area now.
Her classes are uniformly distributed between 48.0 and 58.0 minutes so,
We have to find the probability that a given class period runs between 50.5 and 51 minutes
51−50.5-/58-48
=0.5/10
=0.05
1 X0.05=0.05
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The full question:
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.0 minutes. Find the probability that a given class period runs between 50.5 and 51 minutes.
Noah went into a movie theater and bought 9 drinks and 4 candies‹ costing a total of $6o. Nachelle went into the same movie theater and bought 10 drinks and a candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answers
Each drink costs $5.48, and each candy costs $2.67.
What are Systems of equations?
simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given, Noah went into a movie theater and bought 9 drinks and 4 candies‹ costing a total of $6o.
Let "d" be the price of a drink, and "c" be the price of a candy.
So,
9d + 4c = 60
Also given, Nachelle went into the same movie theater and bought 10 drinks and one candy, costing a total of $57.50
So,
10d + c = 57.50
c = 57.50 - 10d
From equation 1
9d + 4(57.50 -10d) = 60
9d + 230 -40d = 60
31d = 170
d = 170/31
d= 5.48
After substituting this value in equation 2
c = 57.50 - 54.83
c = 2.67
Therefore, The price of each drink is 5.48$, and candy cost $2.67.
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The radius of a quarter circle is 4 feet. What is the quarter circle's perimeter?
r=4 ft. help
Answers
The perimeter of the quarter circle is 6.28ft
What is the perimeter of a circle ?The perimeter of a circle is called as the circumference of the circle. The circumference is the external body of a circle.
The perimeter of a circle = 2πr
where r is the radius of the circle.
The perimeter of a quarter circle will be 1/4 ×2πr
= 1/2πr
the radius of a quarter circle is still thesame as the radius of a complete circle.
Therefore the perimeter of the quarter circle = 1/2πr
= 1/2 ×3.14 × 4
= 6.28ft
Therefore the radius of the perimeter of the quarter circle is 6.28ft
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Find the missing sides in the triangle below. Show or explain your work
Help i’ve been trying for so long
Answers
The missing sides in the triangle is 2
How to determine a right triangle's sides?If leg an is the missing side, change the equation such that an is on one side and compute the square root of that number: a = √(c² - b²)
Leg b is equal to (c2 - a2) if leg b is unknown.
The formula for a missing hypotenuse is c = (a2 + b2).
When given the length of one side, multiply it by 2 to determine the length of the hypotenuse. You can get the side lengths of a triangle with sides of 45°, 45°, and 90° by simply dividing the hypotenuse by 2.
c = (a2 + b2) = 8
here
[tex]2a^{2}[/tex] =8
[tex]a^{2}[/tex] = 8/2 =4
a = [tex]\sqrt{4} = 2[/tex]
The missing sides in the triangle is 2
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Identify the initial value and rate of change for the graph shown.
A coordinate plane graph is shown. A line is graphed that passes through the y-intercept at 4 and through the point 4 comma 1.
a
Initial value: 5.5, rate of change: negative 3 over 4.
b
Initial value: 4, rate of change: negative 3 over 4.
c
Initial value: negative 3 over 4., rate of change: 4
d
Initial value: negative 3 over 4., rate of change: 5.5
Thanks :')
Answers
The solution is Option B.
The equation of line is given by y = ( -3/4 )x + 4 , where the rate of change is the slope m = ( -3/4 ) and the initial value is 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
A line is graphed that passes through the y-intercept at 4 and through the point P ( 4 , 1 )
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
y = mx + 4 be equation (1)
when y = 1 , x = 4
1 = 4m + 4
Subtracting 4 on both sides of the equation , we get
4m = -3
Divide by 4 on both sides of the equation , we get
m = -3/4
So , the slope of the line is m = -3/4
Therefore , the equation of line is y = ( -3/4 )x + 4
Now , the initial value of the equation is when x = 0
So ,
y = ( -3/4 ) ( 0 ) + 4
y = 4
So , the initial value of f ( 0 ) = y = 4
Hence , the equation of line is y = ( -3/4 )x + 4
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One solution graph what does situation mean
Answers
From the slope of the graphs we can say that Robert and Elizabeth will reach the top at the same time , Mei will reach 10 mins after them and Jordan will reach the top in the least time.
What is Graph ?A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Write the equation in the form y = mx + b to determine the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept (0, b). Plot the y-intercept next. 3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.
The slope of the graphs will give the speed at which the stairs are climbed.
For Elizabeth :
slope (s) = (y2 - y1)/(x2 - x1) = (400 - 0)/(10-0) = 400/ 10 = 40 stairs/ min
For Jayden :
Slope (s) = (y2 - y1)/(x2 - x1) = (400 - 0)/(10-5) = 80 stairs/ min
Both for Robert and Mei will have the same slope but Mei started her journey 10 minutes late
Slope (s) = (y2 - y1)/(x2 - x1) = (400 - 0)/(10-0) = 400/ 10 = 40 stairs/ min
From the slope of the graphs we can say that Robert and Elizabeth will reach the top at the same time , Mei will reach 10 mins after them and Jordan will reach the top in the least time.
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https://brainly.com/question/29118955
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