Answer: Muriel has 5 peaches
Step-by-step explanation:
17 = 3p+2
15 = 3p
p=5
5 peaches
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x2 – 3
y > –x2 + 2
The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is an expression that shows the non equal comparison of two or more numbers and variables
The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.
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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)
How to modify the graphsThe complete question is in the attached image (the first graph)
From the graph, we have:
f(x) = x^2 - 3 and g(x) = -x^2 + 2
To derive y ≤ x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.
To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than
How to identify the solution setThe inequalities of the graphs become
y ≤ x^2 - 3 and y > -x^2 + 2
From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)
Hence, the solution of the set of inequalities is (±1.581, -0.5)
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what is the difference between the sum of 1/2 and 1/2 and the product of 1/2 and 1/2
Answer:
0.75 or 3/4
Step-by-step explanation:
The sum of 1/2 and 1/2 is 1. (1/2 + 1/2 = 1)
The product of 1/2 and 1/2 is (1*1)/(2*2) = 1/4.
If you subtract 1/4 from 1, you get 3/4.
The difference between the sum of 1/2 and 1/2 and the product of 1/2 and 1/2 will be 3/4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The difference between the sum of 1/2 and 1/2 and the product of 1/2 and 1/2 will be given as,
⇒ (1/2 + 1/2) - [(1/2)(1/2)]
⇒ 1 - 1 / 4
⇒ (4 - 1) / 4
⇒ 3 / 4
The difference between the sum of 1/2 and 1/2 and the product of 1/2 and 1/2 will be 3/4.
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The pentagons ABCDE and JKLMN are similar.
Find the length x of JK.
The value of x in the pentagon JKLMN is 7.2.
What is Polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The pentagons ABCDE and JKLMN are similar.
when two figures have the same shape but their sizes are different, then such figures are called similar figures.
We need to find the value of x.
1/1.8=4/x
Apply cross multiplication
x=4×1.8
x=7.2
Hence, the value of x in the pentagon JKLMN is 7.2.
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An amount of Birr 500 is deposited in an account at the end of each six-month period with an interest computed at 6% compounded semi-annually. How many years does it take for the amount to reach Birr 56,398.43?
It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.
We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.
Let's substitute the given values into the formula and solve for t:
56,398.43 = 500(1 + 0.06/2)^(2t)
Divide both sides by 500:
112.79686 = (1 + 0.03)^(2t)
Take the natural logarithm of both sides to eliminate the exponent:
ln(112.79686) = ln(1.03)^(2t)
Using the property of logarithms, we can bring down the exponent:
ln(112.79686) = 2t * ln(1.03)
Now, divide both sides by 2 * ln(1.03):
t = ln(112.79686) / (2 * ln(1.03))
Using a calculator, we find t ≈ 17.12.
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The following shape has 0 pairs of parallel sides.
Answer:
67.5 UNITS 2
Step-by-step explanation:
1/2 x 3 x 5 = 7.5
35 + 25 + 7.5 = 67.5 units 2
The area of a 2D form is the amount of space within its perimeter.The area of the compound figure is 67.5 units².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units, such as cm², m², etc. To find the area of a square formula or any other quadrilateral, multiply its length by its width.
The area of the compound figure will be the sum of the different shapes and can be named as shown below.
The area of the compound figure = Area of triangle A + Area of triangle B + Area of rectangle C + Area of triangle D
\(\text{The area of the compound figure} = (0.5 \times 7 \times10) + (0.5 \times 5 \times5) + ( 5\times 3 ) +(0.5\times5\times2)\\\\\text{The area of the compound figure} = 35 + 12.5 + 15 + 5\\\\\text{The area of the compound figure} = 67.5\rm\ units^2\)
Hence, the area of the compound figure is 67.5 units².
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00:00
Estimate 25.65 + 13.23 + 6.35 by rounding each number to the nearest tenth.
26 +13 + 6 = 45
25.7 + 13.3 + 6.4 = 45.4
25.6 + 13.2 + 6.3 = 45.1
25.7 + 13.2 + 6.4 = 45.3
Answer:
\(25.7 + 13.2 + 6.4 = 45.3\)
Step-by-step explanation:
Given
\(Expression: 25.65 + 13.23 + 6.35\)
Required
Approximate to nearest tenth and solve
Approximating each term to the nearest tenth, we have
\(25.65 = 25.7\)
\(13.23 = 13.2\)
\(6.35 = 6.4\)
Bring the approximated term together:
\(Expression: 25.65 + 13.23 + 6.35\) becomes
\(Expression: 25.7 + 13.2 + 6.4\)
\(25.7 + 13.2 + 6.4 = 45.3\)
Hence:
Option D answers the question
A store is having a sale to promote a new product. Every item in the store is 1/6 off the regular price. If an item is on sale for $74, what was the regular price? Show your work.
1/6 off means the regular price for that item should be: $88.8
Work:
The sale = $74 ÷ 5 × 1 = $14.8
=> The regular price = $14.8 x 6 = $88.8
a closed rectangular tank measures 12 meters by 6 meters by 10 metersfind the surface area of the shape
Answer:
Just Took The Test
C!!
Step-by-step explanation:
Trust
PLS HELPPP!!!!!
its due soon, and mainly its asking for verbal
1. Write a polynomial of degree 3 with zeros
x = 3,x= -4, and x = 5.
The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.
To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.
The factor corresponding to x = 3 is (x - 3).
The factor corresponding to x = -4 is (x + 4).
The factor corresponding to x = 5 is (x - 5).
To obtain the polynomial, we multiply these factors together:
P(x) = (x - 3)(x + 4)(x - 5)
Expanding this expression gives us:
\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)
\(= (x^2 + x - 12)(x - 5)\)
\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)
\(= x^3 - 4x^2 - 17x + 60\).
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QUESTION 3 Read the extract below and answer the questions that follow. Cape Town- a thirteen-year-old-boy was arrested and released on warning after he was caught on video assaulting an assistant teacher on the body and on head using his closed fists. Published: Dec 7, 2021 By: Siphokazi Vuso The grade 12 pupil from Harmony Primary in Steenberg can be seen on the video assaulting an assistant teacher after she had confiscated a ball from another pupil. Spokesperson Captain Frederick Van Wyk said witnesses tried to keep the learner away from the teacher when he broke loose and assaulted her. He said the boy was arrested on December 3 and was released in the care of his parents on a warning to appear in the Wynberg Magistrate's Court on Wednesday. [Adapted from: https://www.iol.co.za Accessed on 02 January 2023] /15/ 3.1 Define the term 'conflict resolution' and explain how the above situation is an example of bad conflict resolution. (1+2)(3) 3.2 Suggest TWO strategies that learners and teachers could put in place to decrease the culture of violent within their schools.
These two situations are examples of poor conflict resolution because they do not offer a space for dialogue between the individuals involved, but rather there is only judgment by law without any mediation.
What is conflict resolution?Conflict resolution is a term that refers to the ability of individuals to resolve conflicts or differences with others in a peaceful manner agreed upon by all parties involved. In this case, these two examples are not examples of good conflict resolution because there is no space for dialogue between students and teachers, but rather there is only aggression and prosecution before the entities in charge of justice in each country.
Due to the above, we believe that some strategies to end the culture of violence in schools is to spread messages of dialogue and conflict resolution in a peaceful manner. Also, offer workshops for parents so that from home conflict resolution is reinforced through dialogue.
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Given: The length of AB, whose endpoints are A (-3,3), and B (x,-3) is 3 square root of 5. Determine the value of x coordinate.
The value of x-Coordinate is -6
To find the value of the x-coordinate, we can use the distance formula, which gives us the distance between two points in the coordinate plane.
The distance between points A (-3,3) and B (x,-3) is given as 3√5. Using the distance formula, we get:
d = √[(x-(-3))^2 + (-3-3)^2]
d = √[(x+3)^2 + 36]
We know that d = 3√5, so we can substitute this into the equation:
3√5 = √[(x+3)^2 + 36]
Squaring both sides, we get:
45 = (x+3)^2 + 36
9 = (x+3)^2
x+3 = ±3
x = -6 or 0
Therefore, the possible values of x are -6 and 0. However, we need to check which value satisfies the condition that the distance between A and B is 3√5
If x = -6, then
d = √[(-6+3)^2 + (-3-3)^2] = √[9 + 36] = 3√5, which is true.
If x = 0, then
d = √[(0+3)^2 + (-3-3)^2] = √[36 + 36] = 6√2, which is not equal to 3√5.
Therefore, the value of x-coordinate is -6.
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James and Alex recorded the hours they worked and the amount of money they earned in the tables below. Which statement is true?
Group of answer choices
No answer text provided.
James earned $13 per hour, and Alex earned $12 per hour.
They both earned the same amount of money per hour.
James earned $12 per hour, and Alex earned $13 per hour.
James earned a $13 per hour rate and Alex earned a $12 per hour rate thus option (A) is correct.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change concerning time.
For example the speed 3meter/second.
As per the given number of hours and money earned table.
For James,
Rate of change or earned per hour = 26/2 = $13
For Alex,
Rate of change or earned per hour = 36/3 = $12
Hence "James earned a $13 per hour rate and Alex earned a $12 per hour rate".
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Brainlyest to first correct. Report to incorrect
Add.
(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)
Express the answer in standard form.
Enter your answer in the box.
Answer:
6x^5-5x^4+6x^3-x^2+12x-31
Step-by-step explanation:
(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)
To add, combine like terms
6x^5-5x^4+6x^3-x^2+12x-43+12
6x^5-5x^4+6x^3-x^2+12x-31
Standard form means from the highest power of x to the lowest power of x
One year ago, you allocated the funds in your portfolio among four securities in the proportions
listed below. The rate of return on each security for the year is given in the third column of the table.
Security
Canadian
Equity
Provincial
Bonds
Asian Equity
Ethical Funds
Proportion Rate of return for the
invested (%)
year (%)
25
10
35
30
12
7
22
-12
Calculate the rate of return for the entire portfolio.
The rate of return for the entire portfolio, given the amount allocated to each of the four securities is
How to find the rate of return ?The rate of return would be the expected return of the proportion of the amounts invested into the various investment vehicles and their rates of return.
The rate of return for the portfolio is therefore :
= ∑ ( proportion invested x rate of return )
= ( 25 % x 12 % ) + ( 10 % x 7 % ) + ( 35 % x 22 % ) + ( 30 % x - 12 % )
= 7. 8 %
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Help! How to solve the x on logX=(log27)/(log5)
Thank you!
The solution to the given logarithmic expression is: x = 111.63
How to solve Logarithmic problems?The logarithmic form of expression is written as \(log_{a} c = b\). This is simply a rearrangement of the specific exponential form, aᵇ = c. Thus, we can say that exponential equation could be written as a logarithm.
We want to solve the logarithmic expression given as:
log x = \(\frac{log 27}{log 5}\)
log x = \(\frac{log 3^3}{log 5}\)
log x = \(\frac{3 log 3}{log 5}\)
log x = 2.0478
x = \(10^{2.0478}\)
x = 111.63
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Adrian wants to purchase an electric keyboard. The price of the keyboard at Macelli’s, with tax, is $2,400. He can save $150 per month. How long will it take him to save for the keyboard? (round to a full month).
It will take Adrian 16 full months to save enough money for the electric keyboard.
- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.
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As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
Which of the following sets of ordered pairs is a function? Pls look at picture and help me out
Answer: C
Step-by-step explanation:
A function cannot have repeated x value in a set, and c is the only one without repeated x value
Select the correct answer from each drop-down menu.
The area of the shaded square is
square inches. The length of the unshaded rectangle is
inches.
The estimated value of the length of the shaded square is
inches. The estimated value of the area of the unshaded rectangle is
square inches.
The completed statement with regards to the area of the square and the rectangle are;
The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.
What is the area of a square?The area of a square is the product of the side lengths which are congruent, therefore;
Area of a square = Side length, s × Side length, s = s²
The possible figure in the question includes;
A shaded square that is 125 square inches
An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches
Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.
Therefore;
The side length of the square = √(125) inches = 5·√5 inches
The estimated value of the side length of the square is; 5·√5 inches
The area of a rectangle = Length × Width
The length of the rectangle = 7·√5 inches
The width of the rectangle = 5·√5 inches
Therefore;
The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175
The estimated area of the unshaded rectangle is 175 square inches
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Which type of data would be BEST displayed in a dot plot?
Answer:
Fourth Option
Step-by-step explanation:
State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. The repair bills of a car and its fuel consumption.
Answer:
I believe they are correlated: positive correlation.
Step-by-step explanation:
The higher the repair bills of a car, it means maybe having bad fuel injectors, will cause bad mileage allowing the car to consume more fuel. It is like say the inexorable decline of a car in areas including minor wears and incorrect adjustment etc impairs fuel economy. Thus, the higher the repair bills, the higher the fuel consumption. This is an example of a positive correlation. This means the value of y increases as there is an increase in the value of x.
Make a sketch of a fourth degree polynomial function with two complex roots and two real roots
I cannot really graph it but I will try my best to explain.
When you have a coordinate plane draw from right to left, up to down.
Now starting from righthand top corner, draw a smooth curve just like how you will draw a quadratic equation, through the x axis then curve back making the graph touch the axis at 2 points. That's the 2 real roots
Now make another curve down but this time not touching the x axis and then curving back up to the top left corner, this meant the 2 complex roots.
This is not the only way to do it, as long as one complete curve is not touching the x axis and another complete curve, weather as a whole or combined is touching the x axis at 2 points, it has 2 real and complex roots.
helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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florida wants to estimate the mean mercury level in the fish from a particular lake. they take a random sample of 56 fish from the lake and record the mercury level of each fish. Fill in the following in the context of this problem: Sample: A sample of 56 fish from a randomly selected Florida lake Variable: Mean mercury level in 56 fish from a randomly selected Florida lake Type of variable: qualitative quantitative continuous quantitative-discrete Mean mercury level in fish of all Florida lakes Parameter of interest: Random sample of 56 fish from the lake Statistic that will be used:
Sample: A sample of 56 fish from a randomly selected Florida lake.
Variable: Mean mercury level in 56 fish from a randomly selected Florida lake
Type of variable: quantitative-discrete
Mean mercury level in fish of all Florida lakes: Parameter of interest
Statistic that will be used: Mean (arithmetic average) of the mercury levels in the sample of 56 fish from the lake.
The Statistic of Florida sampleThe sample of 56 fish from a randomly selected Florida lake represents a portion of the population of fish in all Florida lakes. The mean mercury level in these 56 fish represents a statistic, which is an estimate of the population parameter, the mean mercury level in fish of all Florida lakes.
The mean (arithmetic average) is used as the statistic because it summarizes the data by finding the central tendency of the mercury levels in the sample of 56 fish. It is a suitable measure to describe the typical mercury level in the fish from the lake because it takes into account all the observations in the sample.
Since mercury levels are measured in numerical values, the variable "mean mercury level" is quantitative. Since it is a continuous measurement, it is also a continuous quantitative variable.
In summary, the sample and the mean mercury level in the sample of 56 fish are used to make inferences about the population and its parameter, the mean mercury level in fish of all Florida lakes. The mean is used as the statistic to summarize the data and describe the central tendency of the mercury levels in the sample.
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Carl wants to give away 1/3 of his baseball card collection. He is going to divide it among his 3 friends. What fraction of the original collection will each of Carl's friends receive?
Answer:
1/9!
Step-by-step explanation:
answer: is 1/9
from sara
what’s the answer????
Answer:Domar range x
Step-by-step explanation:
k(-1)=
I attached the graph. Please help, thank you in advance.
Which expression represents the product of a number, x, and the difference of 5 and 1?
5x- 1
5x+1
x (5 - 1)
x (5+1)
Answer:
.
Step-by-step explanation:
A small television cost $120, the sales tax is 6.5%. What is the total cost of 50 the television? * Your answer
Answer:
$127.80
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)