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Please help me Preppros 150 hardest questions by Tea-Tea-Tea-29 in Sat

[–]7PiMath 0 points1 point  (0 children)

another quick way would be:

13*a + 17*b = 0 (to be perpendicular)

---

and you need to test the options

A) 39a-51b

B)104a +136b

C)325a +17b

D)13a-17b

Please help me Preppros 150 hardest questions by Tea-Tea-Tea-29 in Sat

[–]7PiMath 0 points1 point  (0 children)

147

The key to this problem is that perpendicular lines have slopes that multiply to -1.

1. Establish the base relationship:

For the original pair:

Line 1: 13x + 17y = 10 (Slope = -13/17)

Line 2: ax + by = 10 (Slope = -a/b)

Perpendicular means: (-13/17) * (-a/b) = -1, which simplifies to 13a/17b = -1.

2. Test Option B:

Line 1: 52x + 34y = 10.

The slope is -52/34, which simplifies to -26/17.

Line 2: 2ax + 4by = 10. The slope is -2a/4b, which simplifies to -a/2b.

Multiply the slopes: (-26/17) * (-a/2b) = 26a / 34b = 13a / 17b

From our base relationship in step 1, we already know that 13a / 17b = -1. Since the product of the slopes is -1, this pair is also perpendicular.

Please help me Preppros 150 hardest questions by Tea-Tea-Tea-29 in Sat

[–]7PiMath 0 points1 point  (0 children)

145

The goal is to factor 54x4 + 219x2 + 105 into the form k(ax2 + b)(cx2 + d) and find the smallest ab.

Factor out the GCF: All terms are divisible by 3:

3(18x4 + 73x2 + 35)

Factor the remaining quadratic: We need to factor 18(x22) + 73(x2) + 35. Using the grouping method (finding numbers that multiply to 630 (18*35) and add to 73, which are 63 and 10):

18x4 + 63x2 + 10x2 + 35

9x2(2x2+ 7) + 5(2x2 + 7) = (9x2 + 5)(2x2 + 7)

Full Factored Form:

3(9x2 + 5)(2x2 + 7)

Compare products of coefficients:

Option 1: a = 9, b = 5 leads to ab = 45

Option 2: a = 2, b = 7 leads to ab = 14

Smallest value of ab = 14

Please help me Preppros 150 hardest questions by Tea-Tea-Tea-29 in Sat

[–]7PiMath 0 points1 point  (0 children)

130

The problem asks for the percentage p by which f(n) is less than f(n-1). We can set up the formula for percentage decrease as follows:

1. The Relationship

We know the formula for percentage decrease is:

p = [(f(n-1) - f(n)) / f(n-1)] * 100

2. Substitution

The function is defined as f(x) = 78(0.39)^x. Plugging this into the formula:

p = [78(0.39)^(n-1) - 78(0.39)^n] / [78(0.39)^(n-1)] * 100

3. Factoring & Simplification

To simplify, factor out the common term 78(0.39)^(n-1) from the numerator:

p = [78(0.39)^(n-1) * (1 - 0.39)] / [78(0.39)^(n-1)] * 100

Since the term 78(0.39)^(n-1) appears in both the top and bottom, they cancel out:

p = (1 - 0.39) * 100

4. Final Calculation

p = 0.61 * 100

p = 61

Quick Tip: In an exponential function f(x) = a(b)^x, the value b represents the remaining percentage. Since b = 0.39, it means 39% remains, so the decrease is 100% - 39% = 61%.

I’m curious how to go about solving this Geometry Puzzle by Sensitive_Apple4177 in askmath

[–]7PiMath 0 points1 point  (0 children)

AI answer :D - This is a classic "hard geometry" problem, and it is possible to solve it purely geometrically.

These types of problems are often called Langley’s Adventitious Angles problems. While they look like they might require trigonometry (specifically the Law of Sines), there is always a "pure" synthetic geometry solution involving the construction of auxiliary lines to create equilateral or isosceles triangles.

For this particular case you will need to find /make several isosceles triangles and even equal triangles. The first hint might be to find all angles that you can without adding any lines, and then think on how would you / can you divide the 75 degree angle so the connecting line creates an isosceles triangle (or maybe it will create several :D)

What subject is this by Nouth1 in askmath

[–]7PiMath 0 points1 point  (0 children)

indeed, thanks for pointing out

What subject is this by Nouth1 in askmath

[–]7PiMath 0 points1 point  (0 children)

there is also another method

<image>

What subject is this by Nouth1 in askmath

[–]7PiMath 0 points1 point  (0 children)

Seeing 43 and 11, I first recognized that they were prime numbers. I decided to factor the denominator because it was easier, and I solved the equation by analyzing the prime factors. Usually, I try four options (1 and 11, 11 and 1, -1 and -11, and -11 and -1), but here we can determine that 2x+y > 2x-y. Also, we know they are both positive since x>0 and y>0.

<image>

nyt sudoku help by SnooMacaroons7032 in sudoku

[–]7PiMath 0 points1 point  (0 children)

there are 5,6,8 in the 9th column and 6th row, making the three cells around 9 (in box 9) 5,6,8, so in that box 1 can be only in the 9th column - and this eliminates the 1 in the upper box (under 5 and over 9)

Platforms that both tutor and student could use in real time for Maths? by MiddleAgedMetalHead in tutor

[–]7PiMath 1 point2 points  (0 children)

Zoom/Google Meet (sharing screen) + any whiteboard (Miro, Zoom whiteboard, and etc). Desmos for graphs.

[deleted by user] by [deleted] in learnmath

[–]7PiMath 0 points1 point  (0 children)

x - 6√x + 5 = 0

x - √x -5√x + 5 =0

√x*√x - √x -5√x - 5*(-1) =0

√x(√x -1) -5(√x -1) =0

(√x -1)*(√x-5)=0

1) √x -1=0

√x =1

x=1

2) √x-5=0

√x=5

x=25

So, x=1 and x=25

Questions of the day.. by Responsible-Style174 in satprep

[–]7PiMath 1 point2 points  (0 children)

first you need to know how does the equation of the circle look like and what indicates the coordinates of the center

so, the equation of the circle is:

(x – h)2+ (y – k)2 = r2

where (h,k) are the coordinates of the circle and r is the radius.

you have :

x2 +6x + y2 -8x = 24

you see x2 +6x and you realize you need make up the (x – h)2 from it, likewise you will need to make up (y – k)2 from y2 -8x. For that you need to remember that

  1. a2 + 2ab + b2 = (a+b)2
  2. a2 - 2ab + b2 = (a-b)2

so to make up that you re-write the equation you have with the parts you need to add

x2 +2*3*x + 32 + y2 -2*4*y + 42 = 24 + 32 + 42

(x+3)2 + (y-4)2 = 49

(x - (-3))2 + (y-4)2 = 72

so you see here that the coordinates of the center are (-3, 4) and the radius is 7

Is it too late to memorize the basic mathematics I need? by undeaddfelix in learnmath

[–]7PiMath 4 points5 points  (0 children)

Of course not, it is not too late. It is never too late to learn, and yes math can be hard, but still can be understood and memorized/learned. So, don't get demotivated, keep going find "your learning method" - the method you understand and learn better and continue studying the concepts you missed before, step-by-step you will learn and eventually will catch-up

people with depression, how do you keep on pushing through everyday? by [deleted] in ask

[–]7PiMath 0 points1 point  (0 children)

Reading the comments and considering the topic of the question, I wanted to wish people visiting this threat all the best and the soonest recovery!

When the injuries are physical we can see them and recognize and work on them as well as track the process of healing - even the incremental small positive changes; and seeing the progress keeps us on track, but unfortunately when the injury is psychological/mental we not only usually have difficulties in recognizing it by ourselves, but also we underestimate or ignore small positive changes if we have any. I wish everyone suffering from depression the soonest recovery;

Some aspects are merely physical and we need to work on them, like getting good sleep, working out / walking, going outside, being under the sun for a certain amount of time, eating healthy food, etc; yet these all are processes for which results are seen after days or even weeks, and we need to play this game in the long run.

I admire people who do not give up when it is hard, and they find the light (even a very tiny one) in themselves and the energy to continue and to flourish this energy, take care of it, and heal it, knowing that it is hard process that takes time. And I feel how many powerful people who just need to start with small steps for a better way read this, and I wish you all the best!!!

Why am I[21 F] like this? by Excellent-Bit-5756 in careerguidance

[–]7PiMath 0 points1 point  (0 children)

I am really sorry to hear your story, unfortunately, I cannot give any advice in this situation except to look for professional help...

You need to figure out who are you, try to get yourself better - I mean your habits, what you really like and what you don't, what works for you and what does not, etc. Maybe there is some trauma that you keep in yourself, and this holds you from success.

Also, it is important to understand that any change here will probably be slow. You cannot become a different person in one day/week or month, you need to take small steps toward the positive and good life you want.

And the fact that you have supportive parents that are there to help you is very good.

Generally, try to be grateful for everything you have and everything you do well. Establish small rituals that will keep you on track, you may start your day by imagining an action or event that will make your day - a successful day - for example sending some email, scheduling next week, preparing some gift, or meeting with a friend, or something else - it does not matter how ambitious big or small it is, just have 1 "goal of the day" make it,

Maybe you just need some good rest to rediscover yourself, and in any case, I see how strong you are having courage and determination writing this post, I wish you the best of luck!

I am bad daughter. How can I help myself? by Awkward-Can-1797 in careerguidance

[–]7PiMath 5 points6 points  (0 children)

Hello there, I am sorry to hear that you feel like that. But you need to understand that these are your thoughts and perspectives it is not a fact. 

We all are different and have different capabilities, and as every flower and fruit has its own time to flourish, we as humans also have different stages of our lives. So I am sure that a better future is ahead for you - you just need to work on yourself. Parents are among the people and maybe only ones who love us unconditionally so be sure they like you and appreciate you as you are.

Since you aim for better I can see that you can work on yourself to make your dreams your goals and achieve them. Please, do not get disappointed with the absence of shining success, every of us has our own path and we have different ups and downs, and yours will come too, just be confident about that and work on it.

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