HK high value SAT math

Pythagorean triple

a set of three positive integers that work in the pythagorean theorem

30-60-90 triangle

An acute angle in a right triangle has measure 30° if and only if the side opposite this angle is half the length of the hypotenuse. (Such a triangle is called a 30°-60°-90° triangle.)

see question

Choice A is correct. The intersection point (x, y) of the two graphs can be found by multiplying the second equation in the system 1.6x + 0.5y = −1.3 by 3, which gives 4.8x + 1.5y = −3.9 . The y-terms in the equation 4.8x + 1.5y = −3.9 and the first equation in the system 2.4x − 1.5y = 0.3 have coefficients that are opposites. Adding the left- and right-hand sides of the equations 4.8x + 1.5y = −3.9 and 2.4x − 1.5y = 0.3 produces 7.2x + 0.0y = −3.6 , which is equivalent to 7.2x = −3.6 . Dividing both sides of the equation by 7.2 gives x = −0.5 . Therefore, the x- coordinate

A circle in the ��xyx, y‑plane has equation (�+3)2+(�−1)2=25(x+3)2+(y−1)2=25left parenthesis, x, plus, 3, right parenthesis, squared, plus, left parenthesis, y, minus, 1, right parenthesis, squared, equals, 25. Which of the following points does NOT lie in the interior of the circle?

Hint #1 We can determine the center and radius of the circle from the equation, then find the point at a distance greater than the radius from the center. In the standard form equation of a circle, (�−ℎ)2+(�−�)2=�2(x−h)2+(y−k)2=r2left parenthesis, x, minus, h, right parenthesis, squared, plus, left parenthesis, y, minus, k, right parenthesis, squared, equals, r, squared, (ℎ,�)(h,k)left parenthesis, h, comma, k, right parenthesis represents the coordinates of the center and �rr represents the radius. For the circle with the equation (�+3)2+(�−1)2=25(x+3)2+(y−1)2=25left parenthesis, x, plus, 3, right parenthesis, squared, plus, left parenthesis, y, minus, 1, right parenthesis, squared, equals, 25: ℎ=−3h=−3h, equals, minus, 3 �=1k=1k, equals, 1 �=25=5r=25​=5r, equals, square root of, 25, end square root, equals, 5 This means the circle has a center at (−3,1)(−3,1)left parenthesis, minus, 3, comma, 1, right parenthesis and a radius of 555.

Pythagorean triple

Set of 3 nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem

The mean, median, range, and standard deviation define

mean median range

parabola formula

y=a(x-h)^2 +k (h,k)=vertex,intercept/width & direction