In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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How would I be able to get the step by step prosses of this and the answer of y?
(-7) = (-4y) + 5
Answer:
y = 3
Step-by-step explanation:
-7 = -4y + 5
Subtract 5 from both sides to isolate variable y:
-7 - 5 = -4y + 5 - 5
-12 = -4y + 0
-12 = -4y
Divide both sides by -4 to isolate variable y:
-12 ÷ -4 = -4y ÷ -4
(Negative ÷ Negative = Positive)
3 = 1y
3 = y
Check your work:
-7 = -4(3) + 5
Use PEMDAS:
-7 = -12 + 5
-7 = -7
Correct!
A cabinet door is 19 inches tall and 5 inches wide.
What is its area?
Answer:
95
Step-by-step explanation:
19 x 5 = 95
Some epidemiologists are planning a second study to evaluate the PSA screening test. The only difference is that this time, the men from Reno who they randomly sample will be 44-59 years of age. Age is a strong risk factor for prostate cancer. The prevalence of prostate cancer in men 44-59 years of age will be much lower than the prevalence of prostate cancer in men 60-75 years of age. How do you expect the results of the second study will compare with the results from the study conducted among 60-75 year old men
Answer:
The second test result will be lower and more sensitive to changes than the first test result and it will better test the efficacy of the PSA screening test
Step-by-step explanation:
The evaluation the epidemiologist are planning = Prostrate Specific Antigen, PSA, screening test
The given difference between the first and second study = The age range of the study group
The age range of the first study = 60 to 75 years
The age range of the second study = 44 to 59
The prevalence of prostrate cancer in men 44 to 59 years of age < The prevalence of prostrate cancer in men 60 to 75 years of age
Therefore, due to the low prevalence, the result of the second test will be more sensitive than the result of the first test.
Charles and Paul each have a computer repair business.
Charles charges a diagnostic fee of around 60$ plus 12$ per hour spent on computer repairs.
Y= 12x+60
Paul charges a diagnostic fee of 40$ plus 16$ per hour spent on computer repairs.
The situation is graphed in the picture
Y= 16x+40
*Which statement BEST describes the system of equations?
A. For repairs requiring 2 hours of work, the total amount charged by Charles will be 72$ and the total amount charged by Paul will be 84$
B. For repairs requiring 8 hours of work, the total amount charged by Charles will be 168$ and the total amount charged by Paul will be 156$
C. For repairs requiring 5 hours of work, the total amount charged by both Charles and Paul will be 100$
D. For repairs requiring 5 hours of work, the total amount charged by both Charles and Paul will be 120$
(This is just too much to look at for me so If anyone can figure it out I greatly appreciate it)
For repairs that take five hours to complete, Charles and Paul will each charge a total of $120.
What is the graph's equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
What are the three techniques for graphing equations?For charting linear functions, there are three fundamental techniques. The first method involves tracing a line through a set of points that have been plotted. The second method makes use of the slope and y-intercept. Applying transformations to the identity function f(x)=x f(x) = x is the third step.
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Homework please help
Answer:
b. one solution
Step-by-step explanation:
hope this helps :)
Answer:
B. One solution
Step-by-step explanation:
Hope this helps!!
Simplify: [tex]\frac{10m}{5m}[/tex]
Answer:
2
When you cancel out the m (cause its the common factor) the only thing left is to simplify 10/5 which is 2.
From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]
Back with the braids.
Solve the given differential equation. 3x^2y'' + 6xy' + y = 0
The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)
This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.
The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.
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A different computer is advertised as 30% off of the original price. After the discount, the tax is $78.75
• Determine the original price of this computer.
Show your work or explain your answer.
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
How to calculate original price of computer?The original price of the computer is 112.5 .The amount saved is 33.75The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Here,
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Coupon = 30% off
Coupon = 30% off= 78.75
This means that the cost of the computer is only 70% since 30% is off.
70% = 78.75
We know that the original price is 100%.
So,
70% = 78.75
Multiply 100/70 on both sides.
100/70 x 70% = 100/70 x78.75
100% =112.5
The original price of the computer is 112.5
The amount saved is:
112.5-78.75=33.75
Thus,
The original price of the computer is 112.5
The amount saved is 33.75
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Answer this pls I really need it
Answer:
x = - 6
y = - 2
Step-by-step explanation:
Given,
y = - 2
To find : x = ?
1x - 5y = 4
x - 5 ( - 2 ) = 4
x + 10 = 4
x = 4 - 10
x = - 6
2 points
Calculate the surface area of this kleenex box. Length = 22 cm, Width = 7
cm, Height = 10 cm
Answer:
210 cm2
Step-by-step explanation:
What is associative property in math?
Answer:
This law simply states that with addition and multiplication of numbers, you can change the grouping of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT associative.
Step-by-step explanation:
Homework Progress
28/37 Marks
a) Complete the prime factor trees for 16 and 40:
16
b)
2
2
∞
2
4
2
2
40
2
What is the lowest Common Multiple of 16 and 40?
2
1
5
The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and and the common multiple of 16 and 40 could be 2 .
What is prime factor ?
prime factor can be defined as the number which is divisible by that number and the number should be prime.
The prime factor tree for 16 as follows
16 = 2*8 = 2* 2 * 4 = 2*2*2*2
16
2 8
2 4
2 2
The prime factor tree for 40 as follows
40 = 2*20 = 2*2*10 = 2*2*2*5
40
2 20
2 10
2 5
Hence, The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and the common multiple of 16 and 40 could be 2 .
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sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read
The number of books that Sofia read is 32 books and the brother read 8 books.
How to calculate the number of books read?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
From the information, Sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read
Let the number of books read by the brother = x
Number of books read by Sofia = 4x
Therefore, x + 4x = 40
5x = 40.
Divide
x = 40 / 5
x = 8
The brother read 8 books
Sofia read = 4x
= 4 × 8
= 32 books.
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Find the volume of the composite figure below round your answer to the nearest whole number
Answer:
1017in^3
Step-by-step explanation:
There are 6 times as many females as males on the maths course at university. What fraction
of the course are female?
Give your answer in its simplest form.
Answer:
i hope it helps
thank you
45 POINTS -Find the perpendicular line. Don’t explain
By analytical geometry, the line y = - 2 · x - 1 represents a line perpendicular to the line shown in the picture. (Correct choice: C)
How to find the equation of a line perpendicular to another line
According to analytical geometry, lines are described by polynomials of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the equation of the perpendicular line pass through a point of original line and is related to the slope of the line by following relationship:
m · m' = - 1
Where:
m - Slope of original line.m' - Slope of perpendicular line.First, determine the slope and intercept of the original line:
(x, y) = (0, 1)
1 = m · 0 + b
b = 1
(x, y) = (2, 0)
0 = m · 2 + b
2 · m + b = 0
m = - b / 2
m = - 1 / 2
Second, calculate the slope of the perpendicular line:
m' = 1 / (- 1 / 2)
m' = - 2
Third, we conclude by discarding options that the equation of the perpendicular line is y = - 2 · x - 1.
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Help, I don’t get the first part but understand the second
Answer:
fr ee points cuz there was nothing attached
Step-by-step explanation:
Step-by-step explanation:
Help, I don’t get the first part but understand the second
I am always there to help you
ask your question
hope it is helpful to you
It takes 126 cubes that have edge lengths of 1/3 ft to completely fill a plastic bin. What is the area of the base of the bin?
The area of the base of the bin is 9 ft^2.
The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.
Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.
We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.
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Daria chooses a paint color from 5 shades of blue, 2 shades of yellow, and 2 shades of purple to paint her room. She can choose either carpet or wood flooring. If each choice is equally likely, how much greater is the probability of her choosing a shade of blue and carpet than the probability of choosing a shade of yellow and wood flooring?
The probability of choosing a shade of blue and carpet is 1/6 greater than that of choosing a shade of yellow and wood flooring.
The total number of possible paint colors Daria can choose is 5 shades of blue + 2 shades of yellow + 2 shades of purple = 9 shades
The total number of flooring options Daria can choose from is carpet or wood = 2 options
The probability of choosing a shade of blue is 5/9 and the probability of choosing carpet is 1/2. So, the probability of choosing a shade of blue and carpet is (5/9) * (1/2) = 5/18.
The probability of choosing a shade of yellow is 2/9 and the probability of choosing wood flooring is 1/2. So, the probability of choosing a shade of yellow and wood flooring is (2/9) * (1/2) = 2/18
The probability of choosing a shade of blue and carpet is 5/18, and the probability of choosing a shade of yellow and wood flooring is 2/18. So, the probability of choosing a shade of blue and carpet is (5/18) - (2/18) = 3/18 or 1/6 greater than the probability of choosing a shade of yellow and wood flooring.
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What does log2 mean on a calculator?
The log base 2 calculator quickly computes the value of the logarithm function with base two, i.e., log₂(x) for arbitrary (positive) x
What do we mean by an expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules.
To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.
To find which expression is equivalent to log₅32:
Law of logarithms:
The law of logarithms states that: log(a) b = log(10)b/log(10)a
Given the log function, which is written as log₅32
a = 5
b = 32
Substitute as: log₅32 = log32/log5
Therefore, the given expression log₅32 is equivalent to the expression log32/log5.
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One pound of nuts costs $2.80. Aaron bought 2 pounds of nuts. He gave the clerk a $10.00 bill. How much change did he get?
Problem Solving Quick Check
A recipe for macaroni and cheese takes 3 tablespoons of milk and 2 tablespoons of butter Simon is going to make 5 batches of the macaroni and cheese for a family dinner how many cups of milk are
required? tpoint)
os
o
0.94 cups of milk is required for 5 batches of the macaroni and cheese.
Given that the recipe for macaroni and cheese takes:
3 tablespoons of milk
and 2 tablespoons of butter
To find: the number of cups of milk required
Let m be the number of cups of milk is required to make 5 batches of the macaroni and cheese.
a batch of the macaroni and cheese require 3 tablespoons of milk .
So by unitary method for 5 batches of the macaroni and cheese,
(5 × 3) = 15 tablespoons of milk is required.
We know that 1 US Cup = 16 US tablespoons
So by unitary method,
m = 15/16 cups of milk
m = 0.94 cups of milk
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Which expression can be used to represent the
volume of this prism?
6 × 11 units³
78°F
Sunny
O 48 x 3 units³
O 14 x 3 units³
O 8x9 units³
H
а
1
i
8 units
1
1
2
3
3 units
6 units
4
5
Volume of prism is given by V= base area × height cubic unit. The expression 48 × 3 unit³ can be used to represent the volume of the prism.
What is prism?Prism is a three-dimensional geometrical figure having identical two ends. A prism has flat faces, similar bases and equal cross sections. A prism is normally bounded by plane faces.
What is volume of prism?
Volume of prism is calculated by the product of base area and height of the prism. At first, we need to calculate the base area and then height is multiplied with it.
Prisms are different types such as triangular prism, rectangular prism, pentagonal prism and hexagonal prism so depending on the figure area for the base is different. As a result, different shaped prism has different formula for volume calculation.
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What is the domain of exponential function f/x )= BX?
The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).
What is interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .
Given exponential function is f(x) = B^x.
A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.
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PLZ HELP ASAP!!
I got the quadrant part I just need help with 0ther parts
Answer:
Step-by-step explanation:
The X intercept is 1 and the y-intercept is 1 aswell.
Answer:
x intercept: 1
y intercept: 1
Step-by-step explanation:
also, where u wrote quad: IIII, four in roman numerals in IV not IIII
(i) change 234mm into m
(ii) change 876m^2 into square cm
Answer: (i) 0.234m
(ii) 8760000cm^2
Step-by-step explanation:
234÷1000=0.2234m
876x10^4=8760000cm^
PLEASE HELP IF YOU KNOW ALGEBRA AND SPANISH
I don't know Spanish but I'm reasonably sure I know what the questions are asking. Please correct me if I'm wrong.
a. f(2) = -2^2+4(2)-10 = -4+8-10 = -6.
b. g(6) = 5(6)+1 = 30+1 = 31.
c. f(-1) = -(-1)^2+4(-1)-10 = -1-4-10 = -15.
d. This is saying to solve g(x)=16:
5x+1=16Subtract 1 from each side: 5x=15Divide both sides by 5: x=3.The answer is x=3.
Points if listen to kpop and watch anime:
My favorite are Captain levi and stray kids.
Step-by-step explanation:
i dont watch anime for shi and fav group Blackpink ;)
Answer: What is you’re favorite anime show?
Step-by-step explanation:
hello! pls help if you can, it will very much be appreciated T-T
Answer:
download algemator then you can find the answer