S the difference of 2 squares:-
a^2 - b^2 = (a + b)(a - b)
so her it is (2y + z)(2y - z)
Answer:
The two angles ADB and BDC are congruent since they are both right angles.
The segment AD and CD are congruent since D is the midpoint of AC.
Segment BD is in common for the two triangles.
The triangles ABD and BCD are congruent by SAS. In particular, Angle A is congruent to angle C (they are opposite to congruent sides), QED
Answer:
2/6 of a pound
Step-by-step explanation:
Answer:
p = 1.5 and q = 9
Step-by-step explanation:
Expand the right side then compare the coefficients of like terms on both sides, that is
4(x + p)² - q ← expand (x + p)² using FOIL
= 4(x² + 2px + p²) - q ← distribute parenthesis
= 4x² + 8px + 4p² - q
Comparing coefficients of like terms on both sides
8p = 12 ( coefficients of x- terms ) ← divide both sides by 8
p = 1.5
4p² - q = 0 ( constant terms ), that is
4(1.5)² - q = 0
9 - q = 0 ( subtract 9 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9
So if the standard deviation is 6 bpm, and the mean = 180, then +1s = 186, +2s = 192, -1s = 174, -2s = 168
a. The % less than 187 are all, including and less than, +1s. So 50% + 34.1% (1s) = 84.1% of the puppies
b. The % between 170 and 187 would be between -1.5s and +1s. So (34.1% × 2) + (13.6/2) = 68.2% + 6.8% = 75% of the puppies
c. Since in a) we said that the % for less than 187 bpm was 84.1%, we just take that % of 500: .841×500 = 420.5, so we'd expect between 420 and 421 puppies
d. 10% of all.puppies will have a heart rate greater than? This is asking what deviation above the mean corresponds to 10%.
This will be around those above around +1.5s, so around 188 bpm