PLEASE HELP!!Discussion TopicEarlier in this course, you explored Euclidean geometry, which is the study of flat space. Thisapproach follows the teachings of Euclid, in which he describes the relationships betweenpoints, lines, and planes without any numerical measurement. You saw evidence of Euclideangeometry inside several proofs and geometric constructions.In contrast, the focus of this unit is understanding geometry using positions of points in aCartesian coordinate system. The study of the relationship between algebra and geometry waspioneered by the French mathematician and philosopher Ren Descartes. In fact, theCartesian coordinate system is named after him. The study of geometry that uses coordinatesin this manner is called analytical geometry.It's clear that this course teaches a combination of analytical and Euclidean geometry. Basedon your experiences so far, which approach to geometry do you prefer? Why? Whichapproach is easier to extend beyond two dimensions? What are some situations in which oneapproach to geometry would prove more beneficial Han the other? Describe the situationand why you think analytical or Euclidean geometry is more applicable.

PLEASE HELP!!

Discussion Topic
Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This
approach follows the teachings of Euclid, in which he describes the relationships between
points, lines, and planes without any numerical measurement. You saw evidence of Euclidean
geometry inside several proofs and geometric constructions.
In contrast, the focus of this unit is understanding geometry using positions of points in a
Cartesian coordinate system. The study of the relationship between algebra and geometry was
pioneered by the French mathematician and philosopher René Descartes. In fact, the
Cartesian coordinate system is named after him. The study of geometry that uses coordinates
in this manner is called analytical geometry.
It's clear that this course teaches a combination of analytical and Euclidean geometry. Based
on your experiences so far, which approach to geometry do you prefer? Why? Which
approach is easier to extend beyond two dimensions? What are some situations in which one
approach to geometry would prove more beneficial Han the other? Describe the situation
and why you think analytical or Euclidean geometry is more applicable.

Answers

Answer 1

Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.

Which approach is easier to extend beyond two dimensions?

The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.

Take for instance a triangle; it is easy to go from a two-dimensional equilateral triangle to a square pyramid.

What are some situations in which one approach to geometry would prove more beneficial than the other?

Analytical geometry is a superior technique for discovering objects (points, curves, and planes) based on their qualities in some situations than Euclidean geometry is in others (for example, when employing topography or building charts).

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Related Questions

There is a mound of g pounds of gravel in a quarry. Throughout the day, 200 pounds of gravel is added to the mound. Two orders of 700 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.

Answers

Answer:

[tex]\fbox {2,400 pounds}[/tex]

Step-by-step explanation:

Information we have :

200 pounds is added2 orders of 700 pounds is removed1,200 pounds remain

What we need to find :

Original amount

Solving :

g + 200 - 2(700) = 1200g + 200 = 1200 + 1400g + 200 = 2600g = 2,400 pounds of gravel

A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles 3:4; but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday

Answers

The weight of each pile yesterday will be 6 and 8 pounds.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

It is Given that Yesterday the ratio of seeds in these piles was 3:4.

Let 3x and 4x represent the seeds.

If the 2 pounds of seeds are added in the bigger pile, then

4x + 2

He also ate 1/4 pound from the smaller pile,

3x - 1/4

The quantities of seeds in those piles is in the ratio of 5:16.

So, 4x + 2 = 5x

3x - 1/4 = 16x

Solve;

So, 4x + 2 = 5x

2 = 5x - 4x

x = 2

The weight of each pie will be

3x = 6 pound

4x = 8 pound

Hence, The weight of each pile yesterday would be 6 and 8 pounds.

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ABCD is a parallelogram. Find the measure of angle C.
A
B
C (3x+6)
D (2x+9)
Find out the measure for angle C

Answers

Answer:

C = 105°

Step-by-step explanation:

added in the picture

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

Answers

By solving a system of equations, we will see that the parking lot is 210ft by 200ft.

How to get the dimensions of the parking lot?

For a rectangle of length L and width W, the perimeter is:

P = 2*(L + W)

And the area is:

A = L*W

Here we know that the perimeter is 820 ft and the area is 42,000 ft²

Then we can write the two equations (ignoring units).

820 = 2*(L + W)

42,000 = L*W

We can isolate L in the first equation to get:

820/2 = L + W

410 - W = L

Now we can replace that in the other equation:

42,000 = (410 - W)*W = 410*W - W^2

Now we want to solve the quadratic equation:

-W^2 + 410*W - 42,000 = 0

The solutions are given by:

[tex]W = \frac{-410 \pm \sqrt{410^2 - 4*(-1)*(-42000)} }{-2} \\\\W = \frac{-410 \pm 10 }{-2}[/tex]

Then the solutions are:

W = (-410 + 10)/(-2) = 200

W = (-410 - 10)/2 = 210

If we take W = 200, then:

L = 410 - W = 410 - 200 = 210

So we can conclude that the parking lot is 200ft by 210ft.

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Answer: C, 210 ft

Step-by-step explanation: edge :)

Write an expression to represent:
The sum of 5 and the quotient of a
number x and 2
O 2x + 5
O 2/x - 5
O x/2 + 5

Answers

Answer:

Step-by-step explanation:

2/x-5

HURRY Given f(x) = - 3/4x + 2, find ƒ(16). The solution is

Answers

Answer: Read attachment.

Step-by-step explanation: Attached is my work. Hope it helps!

If my answer was helpful, please mark as brainliest. Or not, it's fine.

Answer:

[tex]\fbox {f(16) = -10}[/tex]

Step-by-step explanation:

Given :

f(x) = -3/4x + 2

Substitute x = 16 :

f(16) = -3/4(16) + 2

f(16) = -12 + 2

f(16) = -10

What is the explicit formula for this sequence?
60, 30, 15, 7.5, ...
A. an = 60.
(9)
OB. an= = (1.60
OC. an = 60.
• (+)-
OD. an=3.2(n-1)
60(n-1)
(n-1)

Answers

i beilive this is unknown

If it is now 1:15, what time will it be in 1 1/2 hours' time?

Answers

Answer:

2:45

Step-by-step explanation:

1 1/2 hour is 1 hour and 30 minutes.

If we add 30 minutes to 1:15, we get 1:45

if we add 1 hour to 1:45, we get 2:45, which is our answer.

need help with this question please

Answers

∠ A = 132°

Step-by-step explanation:

∠ A + ∠C = 180° (Angle sum of cyclic quadrilateral)

∠ A = 180° - ∠ C = 180° - 48°

∠ A = 132°

Eve has two more marbles than Solene. Solene has twice as many marbles as Steve. Steve has 7 less marbles than eve. How many marbles do they have in all?

A. 27 B. 20 C. 34 D. 13

Answers

Using a system of equations, the total number of marbles that they have is given by:

A. 27.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Variable x: Eve's marbles.Variable y: Solene's marbles.Variable z: Steve's marbles.

Eve has two more marbles than Solene, hence:

x = y + 2.

Solene has twice as many marbles as Steve, hence:

y = 2z -> z = y/2.x = 2z + 2.

Steve has 7 less marbles than eve, hence:

z = x - 7.

Hence:

[tex]\frac{y}{2} = x - 7[/tex]

y = 2(x - 7)

y = 2(y + 2 - 7)

y = 2y - 10

y = 10.

Then:

x = y + 2 = 10 + 2 = 12.z = x - 7 = 12 - 7 = 5.

Hence the total is given by:

T = 12 + 10 + 5 = 27.

Which means that option A is correct.

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What's the solution to –9x + 4 < 40? Question 4 options: A) No solutions B) All real numbers C) x > –4 D) x < –6

Answers

Hey there!

-9x + 4 < 40

SUBTRACT 4 to BOTH SIDES

-9x + 4 - 4 < 40 - 4
SIMPLIFY IT!

-9x < 40 - 4

-9x < 36

DIVIDE -9 to BOTH SIDES

-9x/-9 < 36/-9

SIMPLIFY IT!

x < 36/-9

x < -4

Therefore, the answer should be:

x < -4

(The graph is down below)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Please help me!!! I will give brainliest to the correct answer.

Answers

2(10+2)=3(y+3)2(12)=3y+924=3y+93y=15y=5

[tex]\mathsf {2(10 + 2) = 3(y + 3)}[/tex]

[tex]\mathsf {24 = 3y + 9}[/tex]

[tex]\mathsf {3y = 15}[/tex]

[tex]\textsf {y = 5}[/tex]

[tex]\textsf {The value of y will be 5. }[/tex]

Prove: m/EIF = m/GIH
Step
m/EIF+m/FIG = 180
m/FIG+m/GIH
= 180
m/EIF+mZFIG= m/FIG+mZGIH
m/EIF = m/GIH
Reason
Distributive Property Transitive Property of Equality Definition of Supplementary Angles
Subtraction Property of Equality Multiplication Property of Equality Simplify
Division Property of Equality Reflexive Property of Equality Addition Property of Equality
Substitution Property of Equality Definition of Complementary Angles
An
13
Se
Tea
16
Finis

Answers

The question is incomplete. Below you will find the missing content in the figure.

Prove: m/EIF = m/GIH

Step Reason

m∠EIF+m∠FIG = 180°

m∠FIG+m∠GIH= 180°

m∠EIF+m∠FIG= m∠FIG+m∠GIH

m∠EIF = m∠GIH

The figure is shown below.

The correct answer is m∠EIF = m∠GIH

Here lines FH and GE intersect each other at the point I.

we have to prove the angle

m∠EIF = m∠GIH

so,

m∠EIF+m∠FIG = 180° as angels ∠EIF and ∠FIG forming a linear pair summing up to 180°. angels ∠EIF and ∠FIG form straight angels on a line EG.

m∠FIG+m∠GIH= 180° as angels ∠FIG and ∠GIH forming a linear pair summing up to 180°. angels ∠FIG and ∠GIH form straight angels on a line FH.

m∠EIF+m∠FIG= m∠FIG+m∠GIH because of the substitution property of equality. we replace 180° by m∠FIG+m∠GIH.

m∠EIF = m∠GIH because of the subtraction property of equality. We can subtract the same elements from both sides by the subtraction property of equality.

Therefore m∠EIF = m∠GIH.

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a woman at a point a on the shore of a circular lake with radius 1.2 mi wants to arrive at the point B diametrically opposite A on the other side of the lake in the shortest possible time (see the figure). she can walk at the rate of 5 mi/h from C to B and row a boat at 3.5 mi/h from A to C . setting T (x) function to the time by interlaced AC, x is interlacted AC. how to move for shortest.

Answers

The angle θ to the diameter that she should row is; θ = 56.44°

How to find the angle of an arc?

It should be noted that;

a = 90° - θ. Thus;

b = 2θ

For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .

The time required to walk this distance is given by;

t_w = 4θ/5 = 0.8θ

The distance rowed is given by: cos θ = d_r/2.4

d_r = 2.4cos θ while the time needed for it is;

t_r = 2.4cos θ/3.5

t_r = 0.6857θ

Thus, total time is;

T(θ) = t_r + t_w

T(θ) = 0.6857θ + 0.8θ

T(θ) = 1.4857θ

Now we need the critical numbers:

T'(θ) = 1 - 1.2 sin θ

At T'(θ) = 0, we have;

1 - 1.2 sin θ = 0

1/1.2 = sin θ

θ = sin⁻¹(1/1.2)

θ = 56.44°

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In the year 2015, New Jersey had 1,218 people per square mile. The land area of New Jersey is 7,354 square miles. What was the approximate population of New Jersey in 2015? In the year 2015 , New Jersey had 1,218 people per square mile . The land area of New Jersey is 7,354 square miles . What was the approximate population of New Jersey in 2015 ?

Answers

Answer:

8,957,172 people

Explanation:

Population = 1,218 people per square mile

Land area of New Jersey = 7,354 square miles

Total population:

people living in per square mile × total land area

1,218 × 7,354

8,957,172

There are 5 white balls. 8 red balls, 7 yellow balls, and 4 green balls in a container. A ball is chosen randomly. Find the probability of the following events.

1.What is the probability of choosing

green?
Answers:________ work space:______

2. What is the probability of choosing

red?
Answers:________ work space:______

3. What is the probability of choosing

neither white nor green?
Answers:________ work space:_______

4. . What is the probability of choosing

other than yellow?
Answers:________ work space:_______

5. What is the probability of choosing

purple?
Answer:_________ work space:_______

Answers

Given :

White balls = 5 Red balls = 8 Yellow balls = 7Green balls = 4

Answer 1 :-

We know that,

P (E) = No. of favourable outcomes / Total number of outcomes.

>> Total no. of outcomes = 5 + 8 + 7 + 4

>> Total no. of outcomes = 24

As there are 4 green balls. Therefore,

P (E) = 4 / 24P (E) = 2 / 12 P (E) = 1 / 6

Answer 2 :-

We know that,

P (E) = No. of favourable outcomes / Total number of outcomes.

>> Total no. of outcomes = 5 + 8 + 7 + 4

>> Total no. of outcomes = 24

As there are 8 red balls. Therefore,

P (E) = 8 / 24 P (E) = 4 / 12 P (E) = 2 / 6 P (E) = 1 / 3

Answer 3 :-

We know that,

P (E) = No. of favourable outcomes / Total number of outcomes.

>> Total no. of outcomes = 5 + 8 + 7 + 4

>> Total no. of outcomes = 24

As there are 15 balls that are neither green nor white. (Red balls+ yellow balls)

P (E) = 15 / 24 P (E) = 5 / 8

A rectangular floor of area 21.6 m2 is going to be tiled. Each tile is rectangular, and has an area of 288 cm2. An exact number of tiles can be put into the space. How many tiles will be needed?

Answers

Answer:

Area of Floor = 21.6.m²

Area of tile = 288 cm² = 0.0288 m²

No. of tiles = Area of floor/ area of tile

= 21.6/0.0288

= 750

750 tiles can be put into the space

Write the equation of the line with a slope of 3/4 and a y'-intercept of -7 in Slope-Intercept and Poin Slope Form.

Answers

Slope intercept form: y = 3/4 x - 7
Point slope form: y + 7 = 3/4 (x+0)

What is the distance in units between the points (-1, 5) and (-1,
-3)?

Answers

Answer:

8 [units].

Step-by-step explanation:

if to see the given coordinates, then it is clear the x-coordinates are equal. It means, the required distance can be calculated:

d=5+3=8 [units].

What are the zeros of the quadratic function f(x) equals 6X squared +12 X -7

Answers

The zeroes of the function will be [tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]

What is a Quadratic Function ?

A quadratic function is given by ax² +bx+c = f(x)

The given quadratic function is

f(x) = 6x² +12x - 7

The zeroes of the function will be given by

f(0) = 0

6x² +12x - 7 = 0

The zeroes are given by

[tex]\rm \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

here

a = 6

b = 12

c = -7

Therefore the zeroes of the function will be

[tex]\rm \dfrac {-12 \pm \sqrt{12^2 -4*6*(-7)}}{2 *6}[/tex]

[tex]\rm \dfrac {-12 \pm \sqrt{312}}{12}[/tex]

[tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]

Therefore these are the two zeroes of the function.

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3. When using set builder notation, what does it mean to 'Define a set'?

Answers

Answer:

A set is a well-defined collection of distinct mathematical objects.

Make a tree diagram to show all possible arrangements of the letters in the word MAT. If each of the letters is ordered randomly, what is the fractional probability of M being the last letter?

Answers

If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We have to make a tree diagram to show all possible arrangements of the letters in the word MAT.

M ⇒ A ⇒ T

⇒ T ⇒ A

A ⇒ M ⇒ T

⇒ T ⇒ A

T ⇒ M ⇒ A

⇒ A ⇒ M

If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.

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Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.

What are the dimensions of the cropped photo?

8 inches by 8 inches
9 inches by 9 inches
12 inches by 12 inches
13 inches by 13 inches

Answers

Answer:

x = 9 or B

Step-by-step explanation:

Formula

(x + 2)^2 = 121

Comment

The easiest way to do this is to take the square root immediately, which is usually possible.

Solution

√(x + 2)^2 = √121 Take the square root

x + 2 = 11 Subtract 2 from both sides

x + 2 - 2 = 11 - 2

x = 9

Answer: B) 9 inches by 9 inches

Step-by-step explanation:

Edg 2022

Which of the following choices name the sides of DGF?

Answers

Answer:

Second choice GD and GF with the LINE symbol over each

Step-by-step explanation:

Angle named DGF means that G ( in the middle) is the vertex so GD would be a line starting at G going out toward D and G F would be a line starting at G going out to F

50/22 as a decimal rounded to the nearest hundreth

Answers

Step-by-step explanation:

the answer is 2.27. hope this helps

For each of the following research questions, determine whether an observational study, an
experiment, or neither should be used to answer the question. Note - each term on the right may be
used more than once or not at all.

Answers

The situations described can be classified as experiment, and observational study.

What is an experiment?

An experiment is a tool to test a hypothesis about the occurrence of a particular phenomenon. According to the above, it can be stated that student-centered instruction can be classified as an experiment because this method of education is used and it is verified whether it is effective or not.

What is an observational study?

An observational study is a methodology to identify the occurrence of an event in a particular situation. From the foregoing, it can be inferred that the participation of women in the 2016 election is the product of an observational study because only the number of voters should be counted and the number of women who participated should be identified.

Note: This question is incomplete because there is some information missing. Here is the information missing.

OPTIONS:

Does learner-centered instruction increase students' success rates in maths?

What proportion of registered women voters voted in the 2016 U.S. presidential election?

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Which expression represents a difference of squares?
A. t² +100
B. 4x² - 16x
C. 25k-64
D. 81-49y²

Answers

Answer:

D represents a difference of squares.

Answer: Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex]

Step-by-step explanation:

Hii, do you need to know which expression represents a difference of squares? No problem! (:

The Difference of Squares

Let's consider it for a moment. The "difference of squares" means we subtract two numbers squared, like [tex]\boldsymbol{a^2-b^2}[/tex].

Now let's check our choices and see where we subtract two numbers squared.

The only choice like that is Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex].

In choice A, we add 2 numbers; in choices B and C we don't subtract two numbers squared.

Voila! There's our solution, cheers! (:

Hope that this helped! Best wishes.

[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]

[tex]\frac{5}{x+5}(2x-5(2))[/tex]

Answers

Answer: 10

Step-by-step explanation:

[tex]\frac{5}{x+5} (2x-5(2))\\\frac{5}{x+5} (2x-10)\\\frac{10x-50}{x+5}\\\frac{10(x+5)}{x+5} \\\frac{10}{1} \\10[/tex]

If the sum of a number and eight is doubled the result is five less than the number find the number

Answers

Answer: -21

Step-by-step explanation:

Let the number be x.

Then, this means 2(x+8)+5=x.

2x+16+5=x [distributive property]2x+21=x [combine like terms]x+21=0 [subtract x from both sides]x= - 21 [subtract 21 from both sides]

1. Draw an appropriate Venn diagram to depict each of the following sets. U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbers. 1. Draw an appropriate Venn diagram to depict each of the following sets . U = The set of integers . A = The set of even integers . B = The set of odd integers . C = The set of multiples of 3 . D= The set of prime numbers .

Answers

The attached diagram represents the Venn diagram of the sets

How to draw the Venn diagram?

The sets are given as:

The universal set, U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbers

From the above representation, we have the following highlights:

Set A and set B will not intersect, because no number can be even and oddSet C and set D will intersect set A because they have common elements 6 and 2, respectivelySet C and set D will intersect set B because they have common elements 3 and 3, respectively

Using the above highlights, we can now draw the Venn diagram

See attachment for the Venn diagram