Euclidean geometry is more beneficial. Analytical geometry, with its algebraic tools and coordinate system, is often more practical when dealing with complex calculations and numerical analysis.
Analytical geometry, also known as coordinate geometry, combines algebra and geometry by representing geometric figures and relationships using coordinates in a Cartesian coordinate system. This approach offers a more algebraic perspective on geometry, allowing for the use of equations and formulas to analyze geometric properties. It provides a systematic way to solve problems by applying algebraic techniques.
Euclidean geometry, on the other hand, is the traditional branch of geometry that focuses on the study of geometric figures, their properties, and relationships, without the use of coordinates or equations. Euclidean geometry is based on a set of axioms and postulates established by Euclid, emphasizing concepts like points, lines, angles, and shapes.
When it comes to extending beyond two dimensions, the analytical geometry approach is generally easier to work with. Cartesian coordinates readily extend to three dimensions and beyond, allowing for the representation and analysis of objects in higher-dimensional spaces. This is particularly useful in fields such as physics, computer graphics, and engineering, where three-dimensional and multidimensional spaces are commonly encountered.
In situations where precision and exactness are essential, Euclidean geometry is more beneficial. Euclidean principles are applicable in fields like architecture and construction, where the physical properties and measurements of shapes and structures are crucial. Euclidean geometry's emphasis on geometric proofs and deductive reasoning helps establish rigorous mathematical foundations.
Analytical geometry, with its algebraic tools and coordinate system, is often more practical when dealing with complex calculations and numerical analysis. It is frequently employed in fields such as calculus, optimization, and data analysis, where quantitative methods are needed.
Ultimately, the choice between analytical and Euclidean geometry depends on the specific problem, context, and goals at hand. Both approaches have their strengths and applications, and a comprehensive understanding of geometry often involves proficiency in both analytical and Euclidean techniques.
Learn more about Cartesian coordinates here:
https://brainly.com/question/8190956
#SPJ11
Please answer ASAP
The perimeter of a rectangle is 176 m. The length is equal to 3 times the width decreased by 4. Find the dimensions of the rectangle.
Answer:
L=65m
W=23m
Step-by-step explanation:
[tex]3W-4=L\\2L+2W=176\\\\2L+2W=176\\-2L+6W=8\\8W=184\\W=23m\\L=23*3-4=65m[/tex]
The length and width of the rectangle are 63m and 25m.
What is a rectangle?A rectangle is a quadrilateral, a 2d shape that has four sides and four vertices.
We have,
The perimeter of a rectangle = 176 m
Length of the rectangle = L = 3 x (W- 4 )
Width of the rectangle = W
The perimeter of a rectangle is given by:
176 = 2 ( L + W )
176 = 2 ( 3 ( W - 4 ) + W )
176 = 2 ( 3W - 12 + W )
176 = 2 ( 4W - 12 )
176 = 8W - 24
176 + 24 = 8W
200 = 8W
W = 200 / 8
W = 25 m
Now,
Put W = 25 in L = 3 x ( W - 4 )
L = 3 x ( 25 - 4 )
L = 3 x 21
L = 63 m
We can cross-check:
Perimeter = 2 ( 63 + 25 ) = 2 ( 88 ) = 176 m
Thus the length and width of the rectangle are 63m and 25m.
Learn more about rectangles here:
https://brainly.com/question/14207995
#SPJ2
PLEASE ANSWER!!!!!
An eagle is flying at an altitude of 280 feet. The angle of depression from the eagle to a mouse on the ground is 15º. What is the direct line distance from the eagle to the mouse? Round answer to the nearest thousandth.
[tex] \sin = \frac{opp}{hyp} [/tex]
[tex] \sin(15) = \frac{280}{hyp} [/tex]
[tex]hyp = \frac{280}{ \sin(15) } [/tex]
[tex]hyp = 1081.836925 \: feet[/tex]
The direct line distance from the eagle to the mouse is 1081.837 feet
A student claims that x=3 and 2+3i are the zeros of a quadratic function. Explain why this is incorrect
Answer:
Because it's not a quadratic function.
Step-by-step explanation:
The imaginary roots of a quadratic equation will always be in form of a ± b thus 3 and 2 + 3i will be incorrect.
What are the roots of an equation?The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.
The standard form of a quadratic equation is,
ax² + bx + c = 0
The root of it is given by,
x = [-b ± √(b²-4ac)]/2a
For being this as imaginary the term b²-4ac < 0
Let's say b²-4ac = -m then
x = (-b/2a) ± (m/2a)i so both root will be imaginary.
Given that one root is real (3) and the second is imaginary (2 + 3i) is not possible.
Hence "The imaginary roots of a quadratic equation will always be in form of a ± b thus 3 and 2 + 3i will be incorrect".
To learn more about the roots of equations,
https://brainly.com/question/12029673
#SPJ2
please help me I will mark brainiest
Answer:
x = 6
Step-by-step explanation:
To solve for x, do inverse operations on both sides of the equation:
x + 4 = 10
- 4 - 4
---------------
x = 6
x = 6
Answer:
6
Step-by-step explanation:
x + 4 = 10
6 + 4 = 10
For a school fundraiser, Tory sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 candy bars and made $160.50.
Write a system of equations which represents this situation.
A. 28p + 17p and 40c + 20c = 160.50
B. 28p + 20c = 282 and 17p + 40c = 160.50
C. 28p + 40c = 282 and 17 + 20c = 160.50
D. 28p + 40c + 17p + 20c = 282 + 160.50
Pleaseeee help I need a answer fast
Answer:
300
Step-by-step explanation:
im smart
Solve for xxx.
Your answer must be simplified.
15 < -5 x
Answer:
x < - 3
Step-by-step explanation:
Given
15 < - 5x
Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity
- 3 > x , that is
x < - 3
The simplified expression is x < -3.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.
For the given situation,
The expression is 15 < -5x
⇒ [tex]15 < -5 x[/tex]
Divide both sides by -5,
⇒ [tex]\frac{15}{-5} < \frac{-5}{-5} x[/tex]
When we divide an inequality with negative number, we need to change the sign,
⇒ [tex]-3 > x[/tex]
⇒ [tex]x < -3[/tex]
Hence we can conclude that the simplified expression is x < -3.
Learn more about inequalities here
https://brainly.com/question/22406619
#SPJ2
1/6(x + 6) = 11 What is x
Answer:
x = 60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
[tex]\frac{1}{6}[/tex](x+6)=11
[tex]\frac{1}{6}[/tex]x + 1 = 11
[tex]\frac{1}{6}[/tex]x +1 -1 = 11 -1
[tex]\frac{1}{6}[/tex]x * 6 = 10 *6
x = 60
To double check
[tex]\frac{1}{6}[/tex](60+6)=11
10+1 = 11
11 = 11
Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now attempt two free throws. The probability that Helen makes the second free throw given that she made the first is 0.85. What is the probability that she makes both free throws?
Answer: 0.6375
Step-by-step explanation:
Let's assume that the event that she'll make the first shot is given as P(A) while making the second shot is P(B). Therefore, P(A/B) = 0.85
Therefore, the probability that she makes both free throws will be denoted as:
= 0.75 × 0.85
= 0.6375
Write the equation 9 = -5x + 4 in the form ax + b = c, where c = 9.
What are the values of a and b?
Answer:
a = - 5x and b= 4
Step-by-step explanation:
So it becomes - 5x +4=9
Hope this helps pls tell if any mistakes
Answer:
dil bende ingilizce göründüğü için anlamıyoruuumm
Answer the photo below thanks
I really don't understand this
Answer:
First Game: She wins
Second game: She loses
Third game: She loses
Step-by-step explanation:
If the graph go down she loses, if it goes up she win.
for example on the first try she won so she gets 1 point there is a dot at 1, for the second try she loses so she gets 0 points, the mean score which is (1+0)/2 is .5
on the third try she lost again so she gets another 0 point so (1+0+0)/3 = .33
and so on
el área de un mosaico es de 900cm2 ¿cuánto mide por lado cada mosaico
Answer:
El lado de cada mosaico tiene una longitud de 30 cm.
Step-by-step explanation:
El area de un mosaico cuadrado es:
[tex]A=l^{2}[/tex]
Donde l es el lado del mosaico.
Entonces, si sabes que el area es 900 cm², el lado valdra:
[tex]900=l^{2}[/tex]
[tex]l=\sqrt{900}[/tex]
[tex]l=30\: cm[/tex]
Por lo tanto el lado de cada mosaico tiene una longitud de 30 cm.
Espero te haya servido!
Write the equation of the line that passes through the points (8, 14) and (-2,-16) in slope-intercept form.
Answer:
y = 3x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (- 2, - 16)
m = [tex]\frac{-16-14}{-2-8}[/tex] = [tex]\frac{-30}{-10}[/tex] = 3 , then
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 14 ) , then
14 = 24 + c ⇒ c = 14 - 24 = - 10
y = 3x - 10 ← equation of line
Identify the cross section that results from slicing the three-dimensional figure with a plane that is parallel to its base
A)Pyramid
B)Rectangle
C)Square
D)Triangle
Answer:
D) triangle
Step-by-step answer:
A pyramid is a three-dimensional figure with a plane that is parallel to its base.
PyramidA three dimensional figure is a figure with a length, width and height. 3D shapes have faces, edges, and vertices.
Rectangle, square and triangle are two dimensional shapes while pyramid is a three dimensional shape.
A pyramid is a three-dimensional figure with a plane that is parallel to its base.
Find out more on Pyramid at: https://brainly.com/question/218706
anyone think they could help me with this question???
Answer:
61
Step-by-step explanation:
As we can see the triangles are congruent so
< F = < C ( being corresponding angles of congruent triangle)
< C = 29
Now
<A +<B + <C = 180° { being sum of angles of triangle }
5x + 1 + 90 + 29 = 180°
5x = 180° - 120°
5x = 60°
x = 12°
<A = 5 * 12° + 1 = 61°
Hope it will help :)
1 + 7x
The sum of two numbersis 23. The greater number
is b. Select the expression that represents the lesser
number.
Answer:
Step-by-step explanation:
a+b = 23
a<b
a = 23-b
A
walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the equation that represents the new path.
Answer:
We are given the path, y=-3x-6
The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.
Thus, the slope of the given line is -3.
As, we have that the incipient path is perpendicular to the given path.
And, we ken that, 'Product of slopes of perpendicular lines is -1'.
Since, the incipient path passes through the point (-3,3). Superseding the values in the general form, we get,
b= 3+1
b= 4.
Step-by-step explanation:
factor out the gcf 12y³+10y²
Answer:
Find the prime factors of each term in order to find the greatest common factor (GCF).
2y^2
Factoring out the greatest common factor (GCF)To factor the GCF out of a polynomial, we do the following: Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.
Step-by-step explanation:
Hope it is helpful.....
the cost of contructing a 63mcube wall is rs 84000. find the volume of each brick if the cost of a bric is rs 13
Answer:
0.00975 m^3 each
Step-by-step explanation:
rs 84000 / rs 13 = 6461.539 bricks
63 m^3 / 6461.539 = 0.00975 m^3 each
What is the exact length of each side?
Answer:
[tex]6a^{2} \sqrt{ab}[/tex]
Step-by-step explanation:
area of square = side x side
thus, each side = square root of area
[tex]\sqrt{36a^5b}[/tex] = 6[tex]\sqrt{a^{4} ab}[/tex] = 6[tex]a^{2}[/tex][tex]\sqrt{ab}[/tex]
Drop the answer love:)
Or.. i'll drop ur ip<3
mwa
First okay and second umm my what?! Lol
The answer is : - 112
We add 14 to both side
-16x - 14 = -126
+ 14 +14
-16x = - 112. <- that’s the answer
Then we divide both sides by 16
X = 7
Ta -Da!!
Also I’ll leave this.....
Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answer
Describe how you would estimate the square root of a number that is not a perfect square without using a calculator
Answer:
The square root must be between the square roots of the perfect squares just above and just below your number.
For example the square root of 89 must be between 9 and 10.
Step-by-step explanation:
is 8 x 2/8 less than 8 or greater than 8
Answer: yes if is
Step-by-step explanation:
Condense to a single logarithm : log 12 18+3 log 12 2
Answer:
2 or [tex] \log_{12} 144 [/tex]
Step-by-step explanation:
I assume 12 is the base.
[tex] \log_{12} 18 + 3 \log_{12} 2 = [/tex]
[tex] = \log_{12} 18 + \log_{12} 2^3 [/tex]
[tex] = \log_{12} (18 \times 8) [/tex]
[tex] = \log_{12} 144 [/tex]
[tex] = \log_{12} 12^2 [/tex]
[tex] = 2\log_{12} 12 [/tex]
[tex] = 2 [/tex]
The entire expression simplifies to 2, but if you need the simplest log expression, then you can use
[tex] \log_{12} 144 [/tex]
The product of two numbers is 24. One of the numbers is 10 units less than the other. The numbers are:
A. 0 and 12
B. 12 and -2
C. 10 and 14
D. -12 and 2
E. -12 and -2
Which is true?
Please I need your help fast
Answer:
E. -12 and -2
Step-by-step explanation:
-12 x -2 = 24
brainliest please
Answer:
Obviously -12 and -2 is true.
Your parents are building a pool that is 7 ft wide and 12 ft long. They want to put a walkway around the pool that is x ft wide on all sides. Write a polynomial that represents the combined area of the pool and walkway. Answer needs to be in standard form and use x as your variable.
Answer:
Combined area = 4[tex]x^{2}[/tex] + 38x + 84
Step-by-step explanation:
The rectangle formed by the pool and walkway is 12 + 2x long and 7 + 2x wide.
Area of the rectangle = lw = (2x + 12)(2x + 7) = 4[tex]x^{2}[/tex] + 38x + 84
Help please! Thank youuuuuy
Step-by-step explanation:
can an.y gi.rl message me. i have no power to inbox
The number of possible high fives, H, within a group of n people is given by the formula h = 1/2(n^2-n). After the Angels won the world series, there were 66 high fives at Jon’s house. How many people were at Jon’s house?
Answer:
maybe uh 34567
Step-by-step explanation:
find the value of a and b of a+root5 is (root5+root3)(root5-root3)
Given:
Consider the value of [tex]a+b\sqrt{5}[/tex] is [tex](\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex].
To find:
The values of a and b.
Solution:
According to the given information,
[tex]a+b\sqrt{5}=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex]
[tex]a+b\sqrt{5}=(\sqrt{5})^2-(\sqrt{3})^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]a+b\sqrt{5}=5-3[/tex]
[tex]a+b\sqrt{5}=2[/tex]
It can be written as
[tex]a+b\sqrt{5}=2+0\sqrt{5}[/tex]
On comparing both sides, we get
[tex]a=2,b=0[/tex]
Therefore, the value of a is 2 and the value of b is equal to 0.