The difficulty between theorems and proofs in geometry is subjective. Theorems are proven true statements, while proofs are the logical processes used to establish the truth of theorems. Students may find one harder than the other depending on their individual abilities and understanding.
In the study of geometry, students often ask which are harder: theorems or proofs. To address this, it's important to understand the nature of both. A theorem is a statement that has been proven to be true through a logical sequence of statements, starting from agreed-upon assumptions, known as axioms. The Pythagorean Theorem, for instance, states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem provides a consistent and reliable outcome as long as the arithmetic is carried out correctly.
On the other hand, a proof is the process by which a theorem is shown to be true. Proofs involve a series of logical deductions from accepted principles and previously proven theorems. They are essentially the 'work' or argument that establishes the truth of a theorem. In any proof, each step must logically follow from the previous ones based on established geometric postulates and existing theorems. Therefore, a proof can be viewed as a bridge that connects the basic assumptions of geometry to the theorem being proven.
Whether theorems or proofs are harder is subjective and depends on the student's strengths. Some students find memorizing theorems challenging, while others may struggle with the logical sequence and creativity required to craft proofs. Nonetheless, the study of geometry contributes valuable reasoning skills and knowledge that connects fundamental truths of mathematics to practical applications in the real world, like engineering and physics.
Are there 32 thousands in 32,601?
Answer:
yes
Step-by-step explanation:
technically though there is 32.601 thousands in 32,601 lol
The number 32,601 does indeed have 32 thousands in it. It is composed of 32 thousands and 601 ones when breaking down the number.
Explanation:Yes, there are 32 thousands in 32,601. This is because the number 32,601 can be broken down into 32 thousands (which gives us 32,000) and 601 ones. For example, if you have the number 40,000 – one of the numbers you provided – it consists of 40 thousands. Thus, the number 32,601 has 32 thousands in it when breaking down the number into thousands and ones.So, the answer is YES.
Learn more about Number breakdown here:https://brainly.com/question/35696164
#SPJ12
Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function. Y=2x+5
Answer:
pic has correct graph
domain and range in the highlighted pic are right
the relation is a function
Step-by-step explanation:
y=2x+5 has y-intercept 5 and slope 2
You have the correct pic for that.
The domain is the values of x that relation takes on, it takes on all real numbers so you have that part right.
The range is the values of y that relation takes on, it takes on all real numbers so you have that part right.
The relation is a function because it passes the vertical line test. (I can' see your is it a function part or not)
y = 2x+5 has y-intercept 5 and slope 2. The domain is the values of x that relation takes on, it takes on all real numbers so you have that part right.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The range is the values of y that relation takes on, it takes on all real numbers from ( -2.5,0) to ( 0, 5 ).
The relation is a function because it passes the vertical line test.
Therefore, y = 2x+5 has y-intercept 5 and slope 2. The domain is the values of x that relation takes on, it takes on all real numbers so you have that part right.
To know more about domain and range follow
https://brainly.com/question/26098895
#SPJ2
will give brain less
Which of the following ordered pairs could be the y-intercept of a function? (1, 2) (-3, 2) (5, 0) (0, 0)
Answer:
(0, 0)
Step-by-step explanation:
The y-intercept refers to the point where the graph of a function intersects or crosses the y-axis. The value of x is usually zero at this particular point since the y-axis has the equation;
x = 0
From the alternatives given, the ordered pair (0, 0) could be the y-intercept of a function since x has a value of 0.
Which value completes the table? A. -17 b. -3 c. 1 d. 3
Given : Function f(x) = x⁵ + (x + 3)²
The Question is to find the image of the given function at x = -1
In order to find the image of a function for a given value, We need to substitute the value in the respective function
[tex]:\implies[/tex] f(-1) = (-1)⁵ + (-1 + 3)²
[tex]:\implies[/tex] f(-1) = -1 + (2)²
[tex]:\implies[/tex] f(-1) = -1 + 4
[tex]:\implies[/tex] f(-1) = 3
d. 3 is compleates the table
How do you solve function notation?An equation involving x or y, which is also the function, could be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” or means that y is a function of x.
Given,
Function f(x) = x⁵ + (x + 3)²
The problem is to find the image of the given function at x = -1
In order to find the image of the function for a given value, We need to substitute the value in the respective function
f(-1) = (-1)⁵ + (-1 + 3)²
f(-1) = -1 + (2)²
f(-1) = -1 + 4
f(-1) = 3Learn more about function here https://brainly.com/question/12431044
#SPJ2
what is the value of the rational expression 2x+1 : x*2 when x=5?
Answer:
The correct answer option is [tex] \frac { 1 1 } { 2 5 } [/tex].
Step-by-step explanation:
We are given the following rational expression and we are to evaluate and find its value when x is equal to 5 ([tex] x = 5 [/tex]:
[tex] \frac { 2 x + 1 } { x ^ 2 } [/tex]
So substituting the given value of [tex] x [/tex] to find the value of the given rational expression:
[tex] \frac { 2 (5) + 1 } { 5 ^ 2 } [/tex] = [tex] \frac { 1 1 } { 2 5 } [/tex]
Answer:
The correct answer is third option
11/25
Step-by-step explanation:
It is given an expression (2x + 1)/x²
To find the value of x
We have (2x + 1)/x²
When x = 5, substitute the value of x in expression we get,
(2x + 1)/x² = (2 * 5 + 1)/5²
= (10 + 1)/25
= 11/25
The correct answer is third option
11/25
Amber is learning how to jump rope. She made 21 jumps the first day, 33
jumps the second day, and 45 jumps on the third day. If this pattern
continues, how many jumps will she be making on the eighteenth day?
OA) 225
OB) 209
OC) 69
OD) 57
Answer: 209 i think. hope it helped
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
Each day she increased by 12 jumps. 12 x 17= 204 (you would multiply 12 by 17 instead of 18 since you wouldn't count the first day) 204+21=225
A system of equations is shown below:
3x − y = 2
x + y = 6
The x−coordinate of the solution to this system of equations is
[tex]
3x-y=2 \\
x+y=6 \\ \\
4x=8\Longrightarrow x=\boxed{2}
[/tex]
The x coordinate is equal to 2.
Here we used elimination to eliminate y by adding both equations.
Hope this helps.
r3t40
The probability that the person is male or married is?
[tex]|\Omega|=257\\|A|=129+136-68=197\\\\P(A)=\dfrac{197}{257}\approx76.7\%[/tex]
What’s the answerrrrrr
Answer:
∠3 = 62°
Step-by-step explanation:
The diagonals of a kite are at right angles to each other, hence
Triangle containing ∠ 3 is a right triangle
The sum of the 3 angles in a triangle = 180°, thus
90 + 28 +∠3 = 180
118 + ∠3 = 180 ( subtract 118 from both sides )
∠3 = 62°
What is the range of the data below?
22
28
41
42
Final answer:
The range of the data set (22, 28, 41, 42) is calculated by subtracting the smallest number from the largest, resulting in a range of 20.
Explanation:
The question asks for the range of a given data set. The range of a set of numbers is the difference between the largest and smallest numbers. In the provided list of numbers: 22, 28, 41, 42, the smallest value is 22 and the largest is 42.
To calculate the range, you subtract the smallest number from the largest number:
Range = Largest number - Smallest number
Range = 42 - 22
Range = 20
Therefore, the range of the data is 20.
Are the graphs of the lines in the pair parallel? Explain. y = 6x + 9 27x – 3y = –81 No, since the y-intercepts are different. Yes, since the slopes are the same and the y-intercepts are different. No, since the slopes are different. Yes, since the slopes are the same and the y-intercepts are the same.
Answer:
No, since the slopes are different
Step-by-step explanation:
Parallel lines by definition have the same slope but different y-intercepts. The slope of the line y = 6x + 9 is 6, the coefficient of x since the equation is given in slope-intercept form. Its y-intercept is 9.
For the second equation, 27x – 3y = –81 , we have to solve for y or re-write the equation in slope-intercept form;
-3y = -27x - 81
y = 9x + 27
The slope of this line is thus 9, the coefficient of x since the equation is in slope-intercept form. Its y-intercept is 27.
The two equations have different slopes and thus they are not parallel
Evaluate 2x2 - 1 when x = 3.
Hello!
2.x^2 - 1 = 2.3^2 - 1 = 2.9 - 1 = 18-1 = 17
Good luck!
Answer:11
Step-by-step explanation:2(3)x2-1=11
Help me out here please and thank u
Answer: C, -1.9
Step-by-step explanation:
Its obviously a negative, so it can't be D.
And it's a greater negative then A, so its not B.
And then A is just toooo far away.
So the answer is C
Hope this helps ;)
Lelia says that 75% of a number will always be greater than 50% of a number. Complete the inequality to support Lelia's claim and one to show that she is incorrect.
Answer:
Let 'x' and 'y' be two different numbers.
Leila says that 75% of a number will always be greater than 50% of a number. The inequality that represents this statement is the following:
0.75x > 0.5y
Let x = 100 and y=200. We have that:
0.75(100) > 0.5(200)
75 > 100 ❌ INCORRECT ❌
Given that we found a case in which 75% of a number is not greater than 50% of a number, we can conclude that Leila's claim is incorrect.
Two questions for 30 points.
Answer:
The first question is c
Answer:
The first question is c
Step-by-step explanation:
yes its correct
This the question complete the table below to show how to find the variance. After finding the variance, calculate the standard deviation
Answer:
Step-by-step explanation:ik
Final answer:
To find the variance, calculate the average of the squared differences between each data point and the mean. The standard deviation is found by taking the square root of the variance.
Explanation:
To calculate the variance, follow these steps:
Find the mean of the data set.
For each data point, subtract the mean and square the result.
Find the average of the squared differences.
To calculate the standard deviation, take the square root of the variance.
For example, if the data set is {2, 4, 6, 8, 10}, the mean is 6. The squared differences are {(2-6)^2, (4-6)^2, (6-6)^2, (8-6)^2, (10-6)^2}, which equals {16, 4, 0, 4, 16}. The average of the squared differences is (16+4+0+4+16)/5 = 40/5 = 8. Therefore the variance is 8. The standard deviation is the square root of the variance, so in this case, the standard deviation is √8 = 2.83.
15/33=22/46
true or false?
Answer:
FALSE
Step-by-step explanation:
Let's use the denominator 33(46), or 1518.
Then 15/33 = 22/46 becomes:
690 726
--------- = ---------
1518 1518
Clearly, these two ratios are NOT equal, and so the statement is FALSE.
Answer:
false
Let's use the denominator 33(46), or 1518.
Then 15/33 = 22/46 becomes:
690 726
--------- = ---------
1518 1518
Clearly, these two ratios are not equal, and so the statement is false.
9/14 - 9/20 is the <,>,or =
[tex]\dfrac{9}{14}-\dfrac{9}{20}[/tex]
The denominator of both fractions is different however the numerator is the same therefore we can conclude that the fraction with bigger denominator will be smaller than the one with smaller denominator.
Therefore [tex]\dfrac{9}{14}>\dfrac{9}{20}[/tex]
Hope this helps.
r3t40
The scatter plot below shows the profit earned each month by a new company over the first year of operation. The owner writes a line of best fit equation, shown below, to model the relationship between profit earned and month. y = 2,500x - 2,500 Explain how you know that the line of best fit equation is appropriate, mentioning both the slope and y-intercept in your response.
Answer:
The regression line fits the data well. Problem can be when there is a trend, like exponential growth, but someone still wants to use linear regression. Although in this case it seems to be okay. In other words, the data points can be found under or over the line randomly. In a problematic case is when for example, there are 5 data points next to each other under the line. Usually companies don't make profit when they're first starting.
First I focused on 3 or more points that were collinear to each other. Collinear means that when you connect these points, you get a straight line. These points are at months 1, 2, 3, and 9. Then of these points, I chose 2 points to find the slope between them.
Point 1 = (1, 0)
Point 2 = (2, 2.5) or (2, 2500) because profit is measured in thousands
These are the first two points.
Slope = (2500 - 0) / (2 - 1)
Slope = 2500 / 1
Slope = 2500
Then I plug in the slope and values of point 1 into the slope-intercept form of the line.
y = mx + b
0 = 2500(1) + b
Now we have to Solve for b.
0 = 2500 + b
-2500 = b
Plug in this value of b into the slope intercept form of the equation to get the best fit line.
y = 2500x - 2500
Answer:
i agree with the guy above
Step-by-step explanation:
What is the area of the mombus shown below?
Answer:
A
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = half the product of the diagonals
here AC = 13 and BD = 15 ← diagonals, hence
A = 0.5 × 13 × 15 = 97.5 units² → A
Answer:
Its A. 97.5
Step-by-step explanation:
just took the test
There are six __ triangles in a regular hexagon
A. Obtuse
B. Acute
C. Equilateral
D. Isosceles
Step-by-step explanation:
the correct answer is C equilateral hope this helps have a great day
There are six (C). Equilateral triangles in a regular hexagon
Equilateral triangles
An equilateral triangle exists in a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, exist equal in measure.
In a regular hexagon, there are six equal sides and the number of triangles inscribed stands at six.Each side of the triangle constructed will be equal in measure. Thus, the triangle formed will be equilateral and every angle will measure. The solution will be, that there are six Equilateral triangles in a regular hexagon.Option(C). Equilateral exists the correct option.
To learn more about Equilateral triangles refer to:
https://brainly.com/question/16251591
#SPJ2
What number is the same as 3 tens + 24 ones?
Answer:
54
Step-by-step explanation:
3 tens = 3*10 = 30
24 ones = 24*1 = 24
30+24 = 54
Final answer:
The number that represents 3 tens + 24 ones is 54. This is found by adding 30 (representing the 3 tens) to 24 (representing the 24 ones).
Explanation:
The number that is the same as 3 tens + 24 ones is calculated by first understanding what each term represents.
Three tens is equivalent to 30 because one ten equals 10 and 10 multiplied by 3 equals 30.
Twenty-four ones simply means 24 because one multiplied by 24 is 24.
Therefore, to find the number that represents 3 tens + 24 ones, we add 30 and 24 together.
30 (3 tens) + 24 (24 ones) = 54
So, the number that is the same as 3 tens + 24 ones is 54.
what is the initial value of the equation shown? y=-4x+3
Konichiwa~! My name is Zalgo and I am here to be of assistance for you on this confusing day. In order to find it's "Initial Value", we need to do y=mx+b. The M would equal -4 and B would equal 3. B is the Initial Value you are looking for, meaning that the answer is 3.
I hope that this helps! :)
"Stay Brainly and stay proud!" - Zalgo
(By the way, do you mind marking me as Brainliest? I'd greatly appreciate it! Arigato~! X3)
Answer:
can you give him brainliest his answer is correct and he showed good work
Step-by-step explanation:
If the greatest value of n is 8, which inequality best shows all the possible values of n? n < 8 n > 8 n ≤ 8 n ≥ 8
The greatest value is 8, which means n can be either 8 or any number less than 8.
The inequality would be n is less than or equal to 8, which is written as:
n ≤ 8
Answer:
this is from two years ago so can i just-
Step-by-step explanation:
plz answer Find the coordinates of the vertices of the figure after the given transformation.
translation: (x, y)→(x + 1, y - 1)
A) N'(0, -2), F'(4, 2), Q'(4, -2)
B) N'(-1, 1), F'(3, -3), Q'(3, 1)
C) N'(0, -1), F'(4, 3), Q'(4, -1)
D) N'(0, -5), F'(4, -1), Q'(4, -5)
Answer:
A is the correct answer.
Step-by-step explanation:
See if the translation is to be one more in x value and one less in y value then mark each dot exactly to the right by one point and down by one point. Originally the n position is at -1,-1 if the x gets one more and the y gets one less it's new point would be 0,-2.
Which expression is equivalent to
algebra II engenuity
Answer:
the correct answer is B
Answer:
second option
Step-by-step explanation:
Given expression is:
[tex]\sqrt[3]{64a^6b^7c^9}[/tex]
Converting the expression in the exponents of multiples of three
[tex]\sqrt[3]{4^3*a^6*b^6*b*c^9}[/tex]
Solving the radical
[tex]={4^{(3*\frac{1}{3})} *a^{(6*\frac{1}{3})}*b^{(6*\frac{1}{3})}*b^{(\frac{1}{3})}*c^{(9*\frac{1}{3})}}\\=4a^2b^2c^3\sqrt[3]{b}[/tex]
Hence,
2nd option is correct ..
Archie can buy 5 buckets of popcorn and 2 drinks for $16.25. Terry can buy 3 buckets of popcorn and 1 drinks for $9.50. Assume that all buckets of popcorn are the same price and all drinks are the same price.
Answer:
The cost of one bucket of popcorn is $2.75
The cost of one drink is $1.25
Step-by-step explanation:
Let
x ----> the cost of one bucket of popcorn
y ----> the cost of one drink
we know that
5x+2y=16.25 -----> equation A
3x+y=9.50
y=9.50-3x ----> equation B
Solve the system of equations by substitution
Substitute equation B in equation A and solve for x
5x+2(9.50-3x)=16.25
5x+19-6x=16.25
6x-5x=19-16.25
x=$2.75
Find the value of y
y=9.50-3x
y=9.50-3(2.75)=$1.25
therefore
The cost of one bucket of popcorn is $2.75
The cost of one drink is $1.25
Given the parent function f(x) = 2^x, which graph shows f(x)+1?
Step-by-step explanation:
f(x) + n - move the graph n units up
f(x) - n - move the graph n units down
f(x + n) - move the graph n units to the left
f(x - n) - move the graph n units to the right
====================================================
We have f(x) = 2ˣ.
g(x) = f(x) + 1 - move the graph of f(x) one unit up.
(look at the picture)
The system shown is _____.
consistent
equivalent
inconsistent
Answer:
I believe it's C.
Step-by-step explanation:
Hope my answer has helped you!
Answer:
consistent.
Step-by-step explanation:
Consistent solution: When two lines cut at one point. The solution of system of equation is unique.Then, the solution is consistent.
Equivalent solution: When two lines are coincide then, system of equation is equivalent.
In other words, the solution set of two equation are same then, the equation is called equivalent system.
Inconsistent solution: The system of equation is called inconsistent when there is no solution or lines do not cross .
In given figure, two lines cross at point (3,2).
Therefore, there is one solution of system of equation.
Hence, the system of equation is consistent.
A. 127 cm^2
B. 144.5 cm^2
C. 172 cm^2
D. 50 cm^2
Answer:
144.5cm^2
Step-by-step explanation:
First find area of the rectangle
Area of a rectangle = L*B
= 9*13 = 117cm^2
Now find area of the triangle
Area of triangle. = 1/2 base * height
Height = 13 - 8 =5cm
Area of the triangle = 1/2 *11 *5 = 27.4
Now area of the who figure is area of rectangle + area of triangle
= 117 + 27.5
= 144.5cm^2
For this case we have that the area of the figure is given by the area of a rectangle plus the area of a triangle.
The area of a rectangle is given by:
[tex]A = a * b[/tex]
Where a and b are the sides of the rectangle.
According to the figure we have:
[tex]a = 13 \ cm\\b = 9 \ cm[/tex]
So, the area of the rectangle is:
[tex]A = 13 * 9\\A = 117 \ cm ^ 2[/tex]
On the other hand, the area of a triangle is given by:
[tex]A = \frac {1} {2} b * h[/tex]
Where b is the base of the triangle and h the height. According to the figure we have:
[tex]b = 13-8 = 5 \ cm\\h = 11 \ cm[/tex]
Substituting:
[tex]A = \frac {1} {2} 5 * 11\\A = 27.5 \ cm ^ 2[/tex]
Adding up we have the total area is:
[tex]A_ {t} = 117 \ cm ^ 2 + 27.5 \ cm ^ 2\\A_ {t} = 144.5 \ cm ^ 2[/tex]
Answer:
Option B