great video! may i ask why we subtracted 8 -13 ? the question just stated that the sum of any two sides of a triangle must be greater than the length of the third side. shouldn’t we just add 8 + 13 together?
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. In this problem, to determine the possible range for the third side, x, when the other two sides are 8 and 13, we apply the theorem in three ways: 8 + 13 > x which simplifies to x < 21 8 + x > 13 which simplifies to x > 5 13 + x > 8 which is always true for positive x We subtracted 8 from 13 to find the lower limit of x because the theorem also implies that the difference between any two sides must be less than the length of the third side. This ensures that the sides can actually form a triangle. Hence, we found that x must be greater than 5 and less than 21. Combining these results gives us the range: 5 < x < 21 So, all the sides of the triangle must satisfy the theorem which is why I do those ranges in the video! Hope this clarifies and makes more sense! Let me know. Thank you =)
The more difficult module 2! The geometry and trigonometry questions didn't seem too difficult on June SAT....but this is what they were. Just want to help people and to see what was tested =)
You're welcome! Yes, calculator is allowed. Demos is built into the Bluebook app (where you take the exam). However, you can also bring you own calculator! Here is a list of the calculators allowed on DSAT: satsuite.collegeboard.org/sat/what-to-bring-do/calculator-policy =)
Hi! I see where you're coming from with the idea of solving 4y + 5 + x + y = 180 directly for x + y. However, there's an important reason why we need to use a system of equations instead of just that single equation. In this problem, x and y are related to each other in more than one way. First, you have the equation for the sum of the angles in triangle PQR, which gives you: (3x + 5) + (2x + 9) + (4y + 5) = 180 This simplifies to: 5x + 4y = 161 That's one equation involving both x and y. Next, there's an exterior angle PRS, which is equal to the sum of the two opposite interior angles P and Q. This gives you another equation: x + y = 5x + 14 Now, because we have two variables, x and y, we need two equations to solve for them. If you only used the equation 4y + 5 + x + y = 180, you would miss the second important relationship between x and y, and you wouldn't be able to find the correct values for both. That's why we need to use a system of equations to ensure that all the relationships and constraints are taken into account. Hope this helps clear things up! =) =)
This is awesome, great prep for august SAT!! Thank you so much keep it up
You're so welcome! Thank you!
Very helpful. Please keep up the good work.
Thank you! Glad it was helpful! ☺️👩🏫
Thanks so much
You're welcome!
great video! may i ask why we subtracted 8 -13 ? the question just stated that the sum of any two sides of a triangle must be greater than the length of the third side. shouldn’t we just add 8 + 13 together?
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side.
In this problem, to determine the possible range for the third side, x, when the other two sides are 8 and 13, we apply the theorem in three ways:
8 + 13 > x which simplifies to x < 21
8 + x > 13 which simplifies to x > 5
13 + x > 8 which is always true for positive x
We subtracted 8 from 13 to find the lower limit of x because the theorem also implies that the difference between any two sides must be less than the length of the third side. This ensures that the sides can actually form a triangle. Hence, we found that x must be greater than 5 and less than 21.
Combining these results gives us the range:
5 < x < 21
So, all the sides of the triangle must satisfy the theorem which is why I do those ranges in the video! Hope this clarifies and makes more sense! Let me know. Thank you =)
Ya why?
do you know what modules these were on?
The first one was in the second module but my numbers were slightly different.....
The more difficult module 2! The geometry and trigonometry questions didn't seem too difficult on June SAT....but this is what they were. Just want to help people and to see what was tested =)
Thanks for your feedback!
2 nd question did come on the june test . little bit changed but the same thing
Happy to hear this! 😎
thank you!!! very helpfull
is calculator allowed in DSAT? i know desmos is there but a calculator is faster for large Arithmetic calculations.
You're welcome! Yes, calculator is allowed. Demos is built into the Bluebook app (where you take the exam). However, you can also bring you own calculator! Here is a list of the calculators allowed on DSAT: satsuite.collegeboard.org/sat/what-to-bring-do/calculator-policy
=)
why does the first question need system of equations? Why can you not just solve 4y+5 + x +y = 180 for x+y and get 35?
Hi! I see where you're coming from with the idea of solving 4y + 5 + x + y = 180 directly for x + y. However, there's an important reason why we need to use a system of equations instead of just that single equation.
In this problem, x and y are related to each other in more than one way. First, you have the equation for the sum of the angles in triangle PQR, which gives you:
(3x + 5) + (2x + 9) + (4y + 5) = 180
This simplifies to:
5x + 4y = 161
That's one equation involving both x and y.
Next, there's an exterior angle PRS, which is equal to the sum of the two opposite interior angles P and Q. This gives you another equation:
x + y = 5x + 14
Now, because we have two variables, x and y, we need two equations to solve for them. If you only used the equation 4y + 5 + x + y = 180, you would miss the second important relationship between x and y, and you wouldn't be able to find the correct values for both. That's why we need to use a system of equations to ensure that all the relationships and constraints are taken into account.
Hope this helps clear things up! =) =)
Was this from the international or US SAT
A mix from both US and International!
Thanks so much