GYanggg

I that case, I guess that works too!

Nice job!

Hey tertre, I don't understand how you got 3 just from moving 21 to the other side. 

I'm pretty sure that's not how you solve a quadratic. 

Are you just guess and checking?

Hey GM!

We can factor this quadratic:

\(x^2-10x+21=(x-7)(x-3)=0\)

I'm not going to explain how to factor the quadratic, but you can learn here:

https://www.mathsisfun.com/algebra/factoring-quadratics.html

We then get x = 7 and x = 3. 

7 is the larger root, 

I hope this helped,

Gavin

If you want me to prove these statements, here is the proof:

(a) is not true, all we need to do is show an example that doesn't satisfy these claims to counter the statement. 

We say a = -2 and b = 3

\(|(-2)+3|=1\), \(|-2|+|3|=5\)

\(1\ne5\), therefore (a) is not true. 

(b) 

We once again can plug in numbers. 

a = 0 and b = 2

0 + 4c = 0 + 2c

4 is not equal to 2, so (b) is not true. 

(c)

This is true

The next palindrome after 45954 is 46064. 

Speed is distance divided by time. 

We already know the time, two hours, we just need to calculate the distance. 

46064 - 45954 = 110.

110 / 2 = 55

55 miles per hour, 

I hope this helped,

Gavin

4. 

y is only an integer when \(x\sqrt2\) is an integer. 

If x is an integer, \(x\sqrt2\), is only an integer when x = 0.

Therefore, there is only one lattice points on the graph.

Here is the line:https://www.desmos.com/calculator/mmw7vprxhx 

The one lattice point is: (0, -1)

\(y=0\cdot\sqrt2-1=-1\)

I hope this helped,

Gavin

3. 

Once we commonize the denominator, we achieve:

\(\frac{1}{\tan{x}}+\frac{1}{\cot{x}}=\frac{\tan{x}+\cot{x}}{\tan{x}\cdot\cot{x}}\)

Since, the problem gives us the numerical value:

\(\tan{x}+\cot{x}=\frac{144}{25}\),

we just need to solve for: 

\(\tan{x}\cdot\cot{x}\).

Since \(\tan{x}\) and \( \cot{x}\) are recipricals, \(\tan{x}\) is opposite over adjacent and \( \cot{x}\) is adjacent over opposite, their product is equal to 1. 

So our final expression becomes:

\(\frac{\frac{144}{25}}{1}\) , you can simplify. 

I hope this helped,

Gavin

B, RDF is a right triangle. 

Angle RDF is right, so triangle RDF must be a right triangle.

The proof is here: https://www.youtube.com/watch?v=z3YXznrwtp8 

I hope this helped,

Gavin

You can translate it 4 units to the left and 10 units down. 

The transformation rule is (-4, -10)

Then you can dilate it using a scale factor is 1/2. This is because the radius of Circle 1 is twice the radius of Circle 2. 

I hope this helped,

Gavin

Hey bigguy1989!

The longest stick that will fit is from on corner to the opposite corner. 

To calculate that diagonal, we use the pythagorean theorem:

s^2 = a^2 + b^2 + c^2

a, b, and c are 24, 18, and 12

s^2 = 24^2 + 18^2 + 12^2

s^2 = 1044

s = 6√29

I hope this helped,

Gavin