Answer:
……….
Step-by-step explanation:
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.
Write from leas to greatest 4/6 7/12 5/10
Answer:The answer would be 5/10, 7/12, and then 4/6
How: What you will do is fine the common denominator between the fractions, which is 60.
5/10: Multiply numerator and denominator by 6 to get, 30/60.
7/12: Multiply numerator and denominator by 5 to get, 35/60.
4/6: Multiply numerator and denominator by 10 to get, 40/60.
HOPE THIS HELPS YOU! ^_^ ❤️
Step-by-step explanation:
Answer:The answer would be 5/10, 7/12, and then 4/6
How: What you will do is fine the common denominator between the fractions, which is 60.
5/10: Multiply numerator and denominator by 6 to get, 30/60.
7/12: Multiply numerator and denominator by 5 to get, 35/60.
4/6: Multiply numerator and denominator by 10 to get, 40/60.
HOPE THIS HELPS YOU! ^_^❤️❤️❤️
Step-by-step explanation:
PLEASE ANSWER AS SOON AS POSSIBLE
Answer:
4 to 1
Step-by-step explanation:
Tablespoon of cocoa to Tablespoon of sugar
8 : 2
\(\frac{8}{2}\) : \(\frac{2}{2}\)
4 to 1
When recipe is doubled: ( 8 x 2) to (2 x 2)
16 : 4
\(\frac{16}{4}\) : \(\frac{4}{4}\)
4 to 1
It can be observed that the ratio remains the same
find the LCM and solve, it's very very urgent.
Answers:
1. 10502. 12003. 12004. 33605. 10806. 480please see the attached picture for full solution..
Hope it helps....
Good luck on your assignment...
Help me!!!??? Now!!!!!!!!!!
Answer:
%75
Step-by-step explanation:
15+14+11+20
15+20=35
14+11=25
total is 60
15 is 25% of 60
so there is %75 chance not to get pink
Hey there!
The answer to your question is 0.75
We can find this by first adding up all of the starbursts:
14 + 15 + 11 + 20 = 60 total starbursts.
Then, we add the number of starbursts that are not pink.
14 + 11 + 20 = 45.
This means that there are 45/60 starbursts that are not pink.
Then, we can simplify the fraction into 3/4, or, in decimal form, 0.75.
Hope this helps! Good luck and have a great day!
Jeremy designed a capsule container with dimensions shown below. Please help him find the volume of the container, to the nearest hundredth of inches.
Answer:
83.00 inches
Step-by-step explanation:
4x+5(7x-3)=9(x-5)
x=???
Answer:
i think its 3 im not sure
Step-by-step explanation:
Answer:
x = -1
Step-by-step explanation:
Given equation,
→ 4x + 5(7x - 3) = 9(x - 5)
Now the value of x will be,
→ 4x + 5(7x - 3) = 9(x - 5)
→ 4x + 35x - 15 = 9x - 45
→ 39x - 15 = 9x - 45
→ 39x - 9x = -45 + 15
→ 30x = -30
→ x = -30/30
→ [ x = -1 ]
Hence, the value of x is -1.
Circle Project 1. Draw a point at (1, -2) 2. Draw an 8-unit long radius 3. Using a compass, Draw a circle with your point from step one as your center and the point from step two as the side. 4. Using a protractor, draw a 70 degree arc 5. Draw a central angle which intercepts your arc 6. Draw an inscribed angle which intercepts a 40 degree arc 7. Draw a tangent line 8. Draw a secant line 9. Write the equation of your circle.
Answer:
I can explain how to complete each of the steps you have provided.
1. Draw a point at (1, -2)
This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).
2.
Draw an 8-unit long radius
Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.
3. Using a compass
Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.
4. Using a protractor draw a 70 degree arc
Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.
5. Draw a central angle which intercepts your arc
Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.
6. Draw an inscribed angle which intercepts a 40 degree arc
Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.
7. Draw a tangent line
Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.
8. Draw a secant line
Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.
9. Equation of your circle
The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.
S= hp + 2B.
h = height
p = perimeter of base
b = area of base
Solve for h and b
The equation solved for the variable are;
h = S- 2B/p
b = S - hp/2
How to determine the equationsTo determine the equation, we need to know that the subject of formula for an equation is described as the variable that is made to stand on one end of the equality sign.
It is the variable that is being worked out.
From the information given, we have that;
S= hp + 2B.
To make the height with the variable 'h' the subject, we have;
collect the terms
hp = S - 2B
Divide by the coefficient
h = S- 2B/p
For b, we have;
S - hp = 2b
divide by the coefficient
b = S - hp/2
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7. f(x) = x + 8 ; g(x) = 8x - 12
Find f(g(x)). (1 point)
O f(g(x)) = 2 2x+1
O f(g(x)) = 8 x+8 - 12
O f(g(x)) = 2 2x-1
O f(g(x)) = 8 2x+1
Which property is illustrated by the statement 6x4=4x6
Answer:
commutative property of multiplication
Answer:
commutative property of multiplication
Step-by-step explanation:
How many variables are in 10 - 3x + 4y - z?
Answer: 10
Step-by-step explanation:
PLEASE HELP (0.1)^5 simplified
Answer:
0.1^5=0.00001
Step-by-step explanation:
\(0.1^5\\0.1^5=0.00001\)
Which of the following is equivalent to 5/20 ? *
Mark only one oval.
2/10
10/30
5/10
1/4
Cost of car = $3,800
Years driven = 6
Trade-in value = $1,250
Average yearly depreciation?
Answer:
the answer is monkey epaulets monkey
Step-by-step explanation:
123
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
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What are the coordinates of the image of ΔABC after a dilation with center (0, 0) and a scale factor of 3? Drag numbers to complete the coordinates. Numbers may be used once, more than once, or not at all.
Answer: 6,6. 12,18. 18,6
Step-by-step explanation:
cause I got it right..
The coordinates of the image of ΔABC after a dilation with center (0, 0) and a scale factor of 3 are A'(6,6), B'(12, 18) and C'(18, 6)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given graph has a triangle ABC.
The coordinates of A, B and C are A(2, 2), B(4, 6) and C(6, 2)
We have to find the coordinates of triangle ABC after a dilation with scale factor 3.
Dilation is the scaling of an object, where it gets bigger or smaller
Now the coordinates after dilation are A'(6,6)
B'(12, 18)
C'(18, 6)
Hence, the coordinates of the image of ΔABC after a dilation with center (0, 0) and a scale factor of 3 are A'(6,6), B'(12, 18) and C'(18, 6)
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What is 28.6 rounded to the nearest tenth ?
Answer: 28.6
Step-by-step explanation:
To round 28.6 to the nearest tenth consider the hundredths’ value of 28.6, which is 0 and equal or more than 5. Therefore, the tenths value of 28.6 increases by 1 to 7.28.6 rounded to the nearest tenth = 28.6 hope that helps
what is the answer of 42 x 598 estimate
Please hurry!!!! The quotient of 56 and n is multiplied by 3.
Create an equivalent expression using n to represent the unknown number.
Answer: n8→ I used n as the unknown number. Explanation: The quotient is the result of division between two numbers. The quotient of a number (I used n ) and 8 would be n8.
Step-by-step explanation:
I think it's 56/n=3n.
What is the median of these figure skating ratings?
6.0 6.0 7.0 7.0 7.0 8.0 9.0
Answer:
The median would be 7.0.
Step-by-step explanation:
The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.
k+12=23
plsssss help
20% of what numbner is 100
Answer:
The number is 500.
Step-by-step explanation:
Let n be the number
Convert percent to decimal
20% = 0.20
0.20n = 100
Divide both sides of the equation by 0.20
0.20n/0.20 = 100/0.20
n = 500
According to the graph, what is the value of the constant in the equation below
Step-by-step explanation:
There is no graph .so there is no way it can be answered.
please don't be offended
Is 0.6294 terminating or repeating
Answer:
This is terminating. As a fraction it would be: \(\frac{6294}{10000}\) not simplified
Step-by-step explanation:
If it was repeating you would see a repeat bar over part of the number. Or 3 .... showing that the number goes on.
Students at a certain school were surveyed, and it was estimated that 10% of college students abstain from drinking alcohol. To estimate this proportion in your school, how large a random sample would you need to estimate it to within 0.02 with probability 0.95, if before conducting the study (a) you are unwilling to predict the proportion value at your school and (b) you use the results from the surveyed school as a guideline.
Answer:
a)
you are unwilling to predict the proportion value at your school = 0.90
b)
The large sample size 'n' = 864
Step-by-step explanation:
Given estimated proportion 'p' = 10% = 0.10
Given Margin of error M.E = 0.02
Level of significance α = 0.05
a)
you are unwilling to predict the proportion value at your school
q = 1- p = 1- 0.10 =0.90
b)
The Margin of error is determined by
\(M.E = \frac{Z_{\frac{\alpha }{2} } \sqrt{p(1-p)} }{\sqrt{n} }\)
\(0.02 = \frac{1.96 X \sqrt{0.10 (0.90)} }{\sqrt{n} }\)
Cross multiplication , we get
\(\sqrt{n} = \frac{1.96 X \sqrt{0.10 (0.90)} }{0.02 }\)
√n = 29.4
Squaring on both sides , we get
n = 864.36
Conclusion:-
The large sample size 'n' = 864
What is the value of this expression when d = 4 7/8 and f = 3 1/2
6 (d - f) + f
7+(10−4)2:4⋅231=7+62:4⋅81=7+36:4⋅81=7+9⋅81=7+89=7+181=881
For functions f(x)=x−5 and g(x)=x2−2x+3, find a. (f⋅g)(x) b. (f⋅g)(2).
In conclusion solution for this question is (f⋅g)(2) = −9.
How to solve and what is algebra?
a. To find the product of two functions f and g, we need to multiply them together as (f⋅g)(x) = f(x)g(x). Thus:
(f⋅g)(x) = f(x)g(x)
= (x−5)(x2−2x+3)
= x3−2x2+3x−5x2+10x−15
= x3−7x2+13x−15
Therefore, (f⋅g)(x) = x3−7x2+13x−15.
b. To find (f⋅g)(2), we substitute x=2 into the expression we found in part (a):
(f⋅g)(2) = (2)3−7(2)2+13(2)−15
= 8−28+26−15
= −9
Therefore, (f⋅g)(2) = −9.
Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating these symbols. It involves solving equations and inequalities, finding unknown variables, and analyzing and graphing mathematical functions.
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Each person at a
baseball game receives 3 raffle tickets
and a $2 certificate for the team store.
A group of people receives 39 raffle
tickets. How much money in certificates
does the group receive?
In a case whereby baseball game receives 3 raffle tickets and a $2 certificate for the team store. A group of people receives 39 raffle tickets the amount of money in certificates the group receive is $26.
How can this be calculated?If one baseball game receives 3 raffle tickets and a $2 certificate for the team store, then we can say that each raffle ticket is worth 2/3 dollars ($2 divided by 3 tickets).
So, for 39 raffle tickets, the group would receive (39 x 2/3) = $26
Therefore, the amount of money in certificates the group receive is $26
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