Answer:
Step-by-step explanation:
Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force.
If you are standing on separate sheets of paper and start running, your body will experience a forward motion. However, the sheets of paper under your feet will initially resist the motion due to friction. The force of friction will create an equal and opposite force, causing the sheets of paper to slide backwards. As you continue to run, the friction between your feet and the paper will decrease, and the sheets of paper may eventually stop sliding and you will continue running with a constant velocity.
This is an example of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force you apply to the ground when running is the action, and the force of the ground pushing back on you is the reaction.
Which of the following best describes the expression 6(x + 10)? (1 point)
The sum of a constant factor 6 and a 2-term factor x + 10
The product of a constant factor 6 and a 2-term factor x + 10
The sum of constant factors 6 and x + 10
The product of constant factors 6 and x + 10
The best description of the expression 6(x + 10) is given as follows:
The product of a constant factor 6 and a 2-term factor x + 10.
How to describe the expression?The expression for this problem is defined as follows:
6(x + 10).
The 6 before the parenthesis means that the distributive property is applied, meaning that we have a product of two amounts, which are given as follows:
6.x + 10.Meaning that the second option is the correct option.
More can be learned about expressions at https://brainly.com/question/30347671
#SPJ1
26 : 48 : : 82 : ?
(a) 125 (c) 115
(b) 122 (d) 120
Answer:
x is (a) 125.
Step-by-step explanation:
We can solve this proportion by using the property that the ratios of two equal proportions are equal. In other words:
a : b :: c : d if and only if a/b = c/d
Using this property, we can set up the proportion:
26 : 48 :: 82 : x
where x is the unknown term we want to find.
To solve for x, we can cross-multiply the terms in the proportion:
26 * x = 48 * 82
Simplifying the right side of the equation:
26 * x = 3936
Dividing both sides of the equation by 26:
x = 3936/26
x = 152
Therefore, the value of x is 152. However, 152 is not one of the answer choices provided. To choose the closest answer choice, we can round 152 to the nearest value among the answer choices. Rounding 152 to the nearest value, we get:
125: 27 less than 152
122: 30 less than 152
115: 37 less than 152
120: 32 less than 152
The closest value to 152 is 150, which is between 122 and 125. Therefore, the answer closest to the value of x is (a) 125.
Prove the following statement by mathematical induction:
[tex]\sum_{i=1}^{n+1}{i*2^i = n * 2^{n+2} + 2}[/tex] for all integers n ≥ 0.
The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
What is mathmetical induction?Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.
The process involves two steps:
Base case: Prove the statement is true for some initial value, usually n = 1 or n = 0.Inductive step: Assume the statement is true for an arbitrary value of n, and use this assumption to prove that the statement is also true for the next value, n + 1.Here,
First, we need to prove the statement is true for the base case n=0,
When n=0, we have,
[tex]\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2[/tex]
and
[tex]n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2[/tex]
Therefore, the statement is true for n=0.
Next, we assume the statement is true for some arbitrary integer k, meaning:
[tex]\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2[/tex]
We want to show that the statement is also true for n=k+1,
[tex]\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2[/tex]
We can rewrite the left-hand side of the equation as,
[tex]=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2[/tex]
This last step used the assumption that the statement is true for n=k.
Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
Learn more about mathematical induction here:
https://brainly.com/question/29503103
#SPJ1
The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F Question 7(Multiple Choice Worth 1 points) (05.06 MC) A class trip to a ski resort has been planned for your senior trip. The mountain only allows skiing when the temperature is between −10 degrees and 35 degrees. There is room for 38 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip. −10 < x < 35 and 0 < y ≤ 38 x < 35 and y > −10 0 < x ≤ 38 and −10 < y < 35 x > −10 and y < 35 Question 8(Multiple Choice Worth 1 points) (05.06 MC) A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 15 to create a system that represents this situation? 2x + 3y < 60 3x + 2y < 60 2x + 3y > 60 3x + 2y > 60 Question 9(Multiple Choice Worth 1 points) (05.06 MC) Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. a dashed line g of x rising left to right that is shaded below and a dashed line f of x that is falling left to right that is shaded above a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above a dashed line
The point that is a solution to the system of inequalities y < −2x + 10 and y < 1/2x − 2 is point E at (4, -2). This is because point E satisfies both inequalities.
When we plug in the x and y values of point E into the first inequality, we get -2 < -2(4) + 10, which simplifies to -2 < 2, which is true.
When we plug in the x and y values of point E into the second inequality, we get -2 < 1/2(4) - 2, which simplifies to -2 < 0, which is also true. Therefore, point E is a solution to the system of inequalities.
For question 7, the correct answer is −10 < x < 35 and 0 < y ≤ 38. This is because the temperature must be between -10 and 35 degrees, and there must be between 0 and 38 people on the trip.
For question 8, the correct answer is 2x + 3y < 60. This is because a small rug requires 2 hours for dyeing and a medium-size rug requires 3 hours for dyeing, and the total time must be less than 60 hours.
For question 9, the correct answer is the graph with a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above.
This is because the solution to the system of inequalities is the area where both inequalities are true, which is the area where they have shading in common. In this case, it is the area above both dashed lines.
https://brainly.com/question/30228778
#SPJ1
I need help will award brainliest .
Answer:
Below
Step-by-step explanation:
Due to vertical angles:
5x+21 =9x -55 shows x = 19°
then WOZ = 9x-55 = 116 degrees
WOZ and WOY are supplemenrary (add to a 180 ° straight line)
116 + WOY = 180 so WOY = 64°
What graph represents the function? G(x)={x if x < or equal to 2 -3 if x >2
The value of x for the function x > 2 is x ≤ -1. This is represented by the following graph.
What is a graph?A graph is a format similar to a set of elements in different mathematics, more categorically graph theory, in which some pairs of objects are conceptually "connected". Elements are represented by mathematical abstractions called vertices (sometimes called nodes or points), and each pair of allied vertices is called an edge (also called a link or line). A graph is usually characterized as a collection of points or circles defining vertices and lines or curves representing edges. One of the details studied in discrete mathematics is graphs.
The given function is:
G(x)={x if x < or equal to 2 -3 if x >2
Here, the value of x for x > 2 is x ≤ -1. This is represented by the following graph.
Learn more about graph here:
brainly.com/question/17267403
#SPJ1
You are a sports agent’s assistant. You are preparing a report on contracts you have obtained for the agent’s clients. You recently negotiated the following annual contracts: $2.8 million, $18.9 million, $1.5 million, $1.2 million, $1.5 million, and $3.5 million per year. The standard deviation of the data is 6.3, and the range is 17.7.
Which measure of center is most appropriate, and what is the value of the measure of center?
A median; $1.35 million
B mode; $1.5 million
C median; $2.15 million
D mean; $4.9 million
E mean; $5.58 million
The data set is as follows, going from smallest to largest:
$1,2,000,000, $1.5,000,000, $1.5,000,000, $2.8,000,000, $3.5,000,000, and $18,9,000,000
The middle two figures are $2.8 million and $3.5 million because the data set has six items. These two values' average is:
($2.8 million plus $3.5 million) / 2= $1.35 million.
As a result, the median serves as the most accurate measure of the centre, and its value is $1.35 million. The median price is (A), or $1.35 million.
Describe Standard Deviation.Standard deviation is a statistical measure that indicates how much the values in a dataset deviate from the mean or average value of the dataset. It measures the spread or variability of the data around the mean.
The standard deviation is calculated by taking the square root of the variance of the dataset. The variance is the average of the squared differences between each data point and the mean. In other words, it measures how much the data points vary from the mean squared.
The formula for calculating the standard deviation is:
Standard deviation = sqrt( Sum [tex](x - mean)^2[/tex] / (n - 1) )
where x is each data point in the dataset, mean is the average value of the dataset, and n is the number of data points in the dataset.
A higher standard deviation indicates that the values in the dataset are more spread out or have more variability, while a lower standard deviation indicates that the values are more tightly clustered around the mean.
Standard deviation is widely used in statistics and data analysis to measure the variability of data and to compare the spread of different datasets. It is used to assess the degree of risk and uncertainty associated with a given set of data, and it plays a crucial role in various fields, such as finance, engineering, and social sciences.
Given that we have a range and a standard deviation for the annual contracts obtained for the sports agent's clients, we can use these measures to determine the most appropriate measure of center.
The range is the difference between the largest and smallest values in the data set, which in this case is 17.7. The standard deviation is a measure of the spread of the data around the mean, which in this case is 6.3.
If the range is relatively small compared to the standard deviation, then the mean is the most appropriate measure of the center, since it takes into account the value of every data point. However, if the range is relatively large compared to the standard deviation, then the median is a more appropriate measure of center since it is less affected by extreme values in the data set.
In this case, the range of 17.7 is relatively large compared to the standard deviation of 6.3, which suggests that the median is the most appropriate measure of the center. We can find the median by arranging the data set in order from smallest to largest and finding the middle value. If there are an even number of values, we take the average of the two middle values.
The answer (B) mode; $1.5 million is incorrect because there are two modes ($1.5 million appears twice). The answers (D) mean; of $4.9 million and (E) mean; of $5.58 million are incorrect because the range is relatively large compared to the standard deviation, which indicates that the mean may be influenced by the extreme values in the data set.
To know more about the median visit:
brainly.com/question/3515636
#SPJ1
Solve: |x−5|>−2. Write your solution in interval notation.
(If there is no solution, enter your answer as ∅.)
Answer:
x ∈ R or (-∞,∞)
Step-by-step explanation:
The equation |x - 5| > -2 results in true for all x-values. No matter which x-values you substitute in the absolute value; positive, negative real numbers or zero, you'll always end up with the positive value which is greater than negative
Therefore, |x - 5| > -2 is true for all real x-values.
Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as a nondefective bettery is obtained.a. Give five possible outcomes for this chance experiment.b. What can be said about the number of outcomes in the sample space?c. What outcomes are in the event E, that the number of battery examined is an number?
Answer:
a. Possible outcomes for this chance experiment are:
NDNDDNDDDNDDDDN(Here, D means a defective battery, and N means a nondefective battery.)
b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.
c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.
A market research company was interested in comparing three communities A, B and C to determine whether there are any differences in their use of water filters in homes. Each of 100 homeowners sampled from each community was asked whether or not they have installed water-filtering system in their homes. Their responses (Yes or No) are summarized in the following contingency table.
Use Filters
Community | Yes | No
A 62 38
B 58 42
C 73 27
a) Clearly state the null and alternative hypotheses in this problem.
b) Calculate the expected count for the bottom right cell (i.e., Community ‘C’ and ’No’), and explain what the number means.
c) The Chi-square statistic has been calculated to be 13.22. What can we conclude from this finding?
a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.
b) To calculate the expected count for the bottom right cell, we can use the formula:
Expected count = (row total x column total) / grand total
The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:
Expected count = (100 x 100) / 300 = 33.33
The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.
c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.
Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). 6y'' + y' − y = 0; y1 = ex/3
So, in response to the above question, we can state that The differential equation has a second solution, which is this.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical.
When we differentiate y2(x) with regard to x, we obtain:
[tex]y2'(x) = v'(x)y1(x) plus v(x)y1' (x)\\v"(x)y1(x) + 2v'(x)y1'(x) + v(x)y1" = y2"(x) (x)\\y2'(x) - y2(x) = 6y2"(x)\\[v"(x)y1(x), 2v'(x)y1'(x), and v(x)y1'(x)] [v(x)y1'(x) + v'(x)y1(x)] - v(x)y1(x) = 0\\3 + 2ex/3)v'(x) + 6v"(x) = 0\\[/tex]
A first-order linear differential equation in v' is shown below (x).
[tex]e(x/2 + (2/9)e(x/3)) = u(x)\\3 + 2ex/3 + 6u(x)v"(x)\\u(x)v'(x) = 0\\6u(x)v'(x) = C1[/tex]
where C1 is an integration constant. Calculating v'(x), we obtain:
[tex]v'(x) = C1/(6u(x))[/tex]
the expression [tex]v(x) = C1e(-x/2 - (2/9)e(-x/3)) dx/6[/tex]
[tex]y2(x) = y1(x)e(-P(x) dx)e(-P(x) dx)y1(x)e(-2) dx[/tex]
where P(x) = (3 + 2ex/3)/6 is the differential equation's coefficient for y'(x). When we replace y1(x) = ex/3 and P(x), we obtain:
y2(x) = (ex/3)
∫e^(-∫(3+2ex/3)/6 dx)
[tex](e^{(-2x/3)/9)} ex/3 e(x/2 - (2/9)e(x/3)) dx y2(x) =[/tex]
[tex]y2(x) = C1y1(x) (x)[/tex]
[tex]"e" (-x/2 - (2/9)e" (-x/3)") dx/6[/tex]
where C1 is an integration constant. The differential equation has a second solution, which is this.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
We encounter three persons, P1, P2, and P3. We know that each one belongs to a different type. They give us the following statements: ➢ P1: I belong to type A. ➢ P2: P1 does not belong to type B. ➢ P3: P2 does not belong to type B. Find the type each person belongs to, given the above information
The types for each person are:
P1 belongs to type A
P2 belongs to type C
P3 belongs to type C
What is Statements?
Facts regarding a mixed company are key statements to add in the objective summary.
Let's assume that there are three possible types: A, B, and C. Then, we can use a process of elimination to determine the type of each person based on the given statements.
First, we know that P1 claims to belong to type A. Therefore, we can eliminate type A as a possibility for P2 and P3.
Next, P2 claims that P1 does not belong to type B. Since P1 has already claimed to be type A, we can eliminate type B as a possibility for P1. Therefore, we know that P1 belongs to type A and P2 does not belong to type B.
Finally, P3 claims that P2 does not belong to type B. Since we have already determined that P2 does not belong to type B, we can eliminate type B as a possibility for P3. Therefore, we know that P3 belongs to type C.
So the types for each person are:
P1 belongs to type A
P2 belongs to type C
P3 belongs to type C
To know more about statements visit,
https://brainly.com/question/25046487
#SPJ1
Difference Quotient Problem
The difference quotient expression for the given function is
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
Difference Quotient Formula:The expression in single-variable calculus is usually referred to as the difference quotient.
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.
The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.
Consider the difference quotient formula,
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
Evaluate the function at x = x + h
replace the variable x with (x + h) in the given expression
[tex]f(x+h)=\sqrt{(x+h)^2-1}[/tex]
simplify the result ,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
find the components of the definition,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
[tex]f(x)=\sqrt{(x+1)(x-1)}[/tex]
plug in the components,
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
Learn more about difference quotient , visit:
https://brainly.com/question/29054033
#SPJ1
a rectangle below has an area 84 cm saquered, what is half of the rectangle area?
What is the x axis and the y axis
Write an equation in
point-slope form for the line
shown on the graph.
Use the right-hand point.
= 2
S
5
4
3
2
+
654321
+4
-2
-3
&
-5
€
123456
Submit
X Cive up
< Previous
> Skip
Overview
Save Can
The required point slope of the line shown in the graph is y + 4 = 2(x - 3).
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
From the graph, we have two points on the line (3, -4) and (6, 2)
The slope of the line, with the help of the two-point, is given as,
m = (y₂ - y₁) / (x₂ - x₁)
m = 2 + 4 / 6 - 3
m = 6/3
m = 2
Now,
The equation of the line having a slope of m = 2 and passing through (3, -4) is given as
y - y₁ = m (x - x₁)
y + 4 = 2(x - 3)
y = 2x - 6 - 4
y = 2x - 10
Thus, the required point slope of the line shown in the graph is y + 4 = 2(x - 3).
Learn more about slopes here:
https://brainly.com/question/3605446
#SPJ1
100 POINTS WILL MARK BRAINLIEST PLEASE HELPPPP
Answer: B. 3300
Step-by-step explanation: Answers in the 5000 range would be Expenses, and 2000 would be Liabilities, which are both opposite of capital. "S.E." in accounting typically stands for "Shareholder Equity" or "Stockholder's Equity" and would be one type of capital.
A rectangle is 1/2 feet long and 3/4 feet wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form
Answer: 3/8
Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.
Numerators first- 1x3Denominators second 2x40,0 2,0 2,2 3,4 is it a function
Yes, it is a function.
The reason is that the values on each row all align in a manner that shows the graph is moving in a clear direction. This is consistent with the behavior expected from the standard function, with all of the values on each row being the same distance from the origin.
simplify:
• 4 cos² θ + 4 sin² θ
• tan² θ cos² - sin² θ
• 1 + tan² θ
Answer:
1. 4
2. [tex]cos^2(sin^2(0))tan^2(0)[/tex]
3. sec^2 theta
Hope it helped!
p(x)=-14+30x+26x^4 How many roots does this have
P(x) = -14 + 30x + 26x⁴ has four roots. The solution has been obtained by using properties of polynomials.
What is a polynomial?
The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
We are given a polynomial as P(x) = -14 + 30x + 26x⁴.
It is a polynomial of degree 4 as the highest power is 4.
We know that the number of roots is equal to the degree of the polynomial.
Here, since the degree is 4, so it has 4 roots.
Hence, P(x) = -14 + 30x + 26x⁴ has four roots.
Learn more about polynomial from the given link
https://brainly.com/question/4142886
#SPJ1
Someone help me ASAP. What is the period and frequency.
The period of the sine function is given as follows:
2π.
Hence the frequency is given as follows:
0.5/π Hz.
How to define the sine function?The standard definition of a sine function is given as follows:
y = Asin(Bx + C) + D.
The parameters are given as follows:
A: amplitude.
B: the period is 2π/B.
C: phase shift.
D: vertical shift.
From the function defined in this problem, the parameter B is given as follows:
B = 1.
Hence the period of the function is given as follows:
P = 2π/1 = 2π.
The frequency is the inverse of the period, hence it is given as follows:
f = 1/p
F = 1/(2π)
F = 0.5/π Hz.
More can be learned about trigonometric functions at brainly.com/question/21558626
#SPJ1
HELP URGENT! LIMITED TIME TEST!!!
An ice cream truck tracks its sales for a year. They create a scatter plot using the data with the average monthly temperature temperature on the x-
axis and the sales along the y- axis.
The data in the graph (the photo added) suggest a linear association. Which of the functions best represents the equation of the line of best fit?
[Pay attention to the scale of the x and y axis]
Choose one,
y= 0.01x + 152
y= 0.5x + 100
y= x + 100
y = 30x - 159
A linear relationship between two quantities can be modeled using a mathematical function.
What is function?Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.
The form of the function is generally expressed as y = mx + b, where y is the dependent variable, m is the slope of the line, x is the independent variable, and b is the y-intercept. The slope of the line, m, can be calculated from two points on the line using the formula m = (y2-y1)/(x2-x1). The y-intercept, b, can be calculated by substituting any point into the equation y = mx + b and solving for b.
Once the slope and y-intercept are known, the equation can be used to predict the value of the dependent variable given a certain value of the independent variable. For example, if the equation is y = 3x + 4, then for any given value of x, the corresponding value of y can be calculated. For x = 5, the corresponding value of y is 19 (5 x 3 + 4 = 19). This equation can also be used to graph the linear relationship between the two variables; by plotting the equation, a straight line is produced.
By using a function to model a linear relationship between two quantities, it is possible to calculate the relationship between them and predict values for either one given the other. This can be a useful tool for understanding the data and for making predictions about the data.
To know more about function click-
https://brainly.com/question/25638609
#SPJ1
Select the correct answer. Victor solved this inequality as shown: Step 1: 3x - 5 > x + 5 Step 2: 2x - 5 > 5 Step 3: 2x > 10 Step.4: x>5 What property justifies the work between step 3 and step 4? O A. division property of inequality O в. inverse property of multiplication O c. subtraction property of inequality O D. transitive property of inequality
Therefore , the solution of the given problem of inequality comes out to be the correct answer is (A) division property of inequality.
What does inequality actually mean?A mathematical inequality is a relationship or group of values without the equal sign. Equity usually comes after equilibrium. When two parameters are not equal, inequality results. Between equality and inequality, there are differences. Because the numbers are not equal or variable it was chosen to use the most common symbol (). Any difference, no matter how little or significant, can be utilised to compare values.
Here,
The correct answer is (A) division property of inequality.
Step 3 shows that
=> 2x > 10, and to solve for x,
we need to isolate x on one side of the inequality.
We can do this by dividing both sides by 2,
which gives x > 5. This is step 4.
The division property of inequality states that if a > b and c is a positive number, then a/c > b/c. In this case,
we have
=> 2x > 10, and
we can divide both sides by 2 (which is a positive number) to get
=> x > 5.
Therefore, the work between step 3 and step 4 is justified by the division property of inequality.
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
the ratio of fiction and non-fiction books in a library is 5 : 2. total books are 1421, how many more fiction books than non fiction books are in library, please explain in simple terms complicated answers are hard to understand
Answer:
Step-by-step explanation:
The ratio of fiction books to non-fiction books is 5:2, which means that for every 5 fiction books in the library, there are 2 non-fiction books.
We know that the total number of books in the library is 1421. To figure out how many of those books are fiction, we need to divide the total by the sum of the parts in the ratio (5 + 2 = 7), and then multiply the result by the number of parts that represent fiction books (5).
So, the number of fiction books in the library is:
5/7 x 1421 = 1015
To find out how many non-fiction books there are, we can subtract the number of fiction books from the total:
1421 - 1015 = 406
Finally, to figure out how many more fiction books there are than non-fiction books, we can subtract the number of non-fiction books from the number of fiction books:
1015 - 406 = 609
Therefore, there are 609 more fiction books than non-fiction books in the library.
What is the value of x?
Enter your answer in the box.
Answer:
x = 54
Step-by-step explanation:
See picture below :)
Aslam purchased 1000 squad. meter land for 3 Crore to build a factory at the end of the year market value the land 2.70 Crore is this a correct treatment
Answer:
deprication a/c Dr. 30,00,000
To land a/c 30,00,000
Step-by-step explanation:
deprication is an expense so, according to modern rules of accounts Dr. debit all assets & expenses and cr. credit all income, capital, all liability
(assets ) land value is deprecating so, deprication is an expense so, we Dr. deprication a/c expense is an increase (name the expense) and the value of land (assets) is diminishing Or depricating so, cr. land a/c
In the given figure, three circles with centres P, Q and R are drawn, such that the circles with centres Q and R
touch each other externally and they touch the circle with centre P, internally. If PQ = 10 cm, PR = 8 cm and
QR = 12 cm, then the diameter of the largest circle is:
Answer:
the diameter of the largest circle is 2r = 56/3 cm.
Step-by-step explanation:
Let the largest circle have center O and radius r. Join P, Q, R and O as shown in the figure below.
Since the circle with center Q and the circle with center R touch each other externally, the distance between their centers is the sum of their radii. Therefore,
QR = QM + MR
where M is the point of contact of the two circles. Similarly, since the circle with center P touches the circle with center Q externally, the distance between their centers is the sum of their radii. Therefore,
PQ = PM + MQ
Adding these two equations, we get
PQ + QR = PM + MQ + QM + MR
Substituting the given values, we get
10 + 12 = PM + MQ + 12 + 8
or PM + MQ = 2
Now consider the right-angled triangle PQO. Since PQ is the tangent to the circle with center P at point A, OA is perpendicular to PQ. Similarly, OQ is perpendicular to QR and OR is perpendicular to RP. Therefore, angles PAO, QBO and ROC are all right angles.
Let the perpendicular from O to PQ meet PQ at X. Then PX = OQ - PQ/2 = r - 5. Similarly, let the perpendicular from O to QR meet QR at Y. Then QY = OR - QR/2 = r - 6. Let the perpendicular from O to RP meet RP at Z. Then RZ = OP - PR/2 = r - 4.
Now consider the right-angled triangle OXY. Using the Pythagorean theorem, we get
OX^2 = OY^2 + XY^2
Substituting the values of OY and XY, we get
(r - 6)^2 = (r - 5)^2 + (r - 4)^2
Expanding and simplifying, we get
3r^2 - 56r + 191 = 0
Solving this quadratic equation, we get two solutions: r = 7 and r = 28/3. Since the radius of the largest circle cannot be less than the radius of the circle with center Q, which is 6, the only possible solution is r = 28/3.
Therefore, the diameter of the largest circle is 2r = 56/3 cm.
Need help with part C, pls, thx! :)
*Please show how u got it*
The percentage of amount paid toward principal is, 70.4%
And, the percentage of amount paid towards interest is,
⇒ 20.6%
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;
An individual borrowed $95,000 at an APR of 5%.
Hence,
The percentage of amount paid toward principal can be calculated as;
Percent amount = 95,000/(450 × 25 × 12) × 100
= 95,000 / 135,000 × 100
= 70.4%
Hence, And the percentage of amount paid towards interest will be:
⇒ 100% - 70.4%
⇒ 20.6%
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ1
The conjugate of 145+ 145/3
Answer:
193 1/3
Step-by-step explanation:
First, we need to convert [tex]\frac{145}{3}[/tex] into a mixed number.
[tex]\frac{145}{3}[/tex] = [tex]48[/tex] [tex]\frac{1}{3}[/tex]Now, we can add them together:
[tex]145 +48\frac{1}{3} = 193 \frac{1}{3}[/tex]Therefore, the answer is [tex]193\frac{1}{3}[/tex].