Answer:
The solution to the system of equations is:
Step-by-step explanation:
Given the system of equations
solving the system of equations
solve for y
Divide both sides by -23
Divide both sides by 10
Thus, the solution to the system of equations is:
The z-score associated with 14.3 is 0.84. 0.2995 of the population is between 12.2 and 14.3. 0.1894 of the population is less than 10.0.
The formula for a z-score is
z=(X-μ)/σ
With our data, we have:
z=(14.3-12.2)/2.5=0.84
The z-score associated with the mean is 0.5. To find the proportion of the population between the mean and 14.3, subtract 0.7995 (the proportion of population below the z-score of 0.84, using http://www.z-table.com) and 0.5:
0.7995 - 0.5 = 0.2995.
The z-score for 10.0 is
(10.0-12.2)/2.5 = -0.88. The proportion of the population less than this is 0.1894.
9^2 < 6^2 + 8^2
so its acute angled.
Answer:
1. AB ~= DF
2. Definition of Congruent
3. Reflexive Property of Congruency
4 BD=BD
6. AB+BD=AD; DF+BD=BF
7. Substitution Property of Equality
8. Definition of Congruent
Step-by-step explanation:
1. The given always goes first, and that's the first reason, so AB ~= DF must be the first statement (that should be the congruency symbol).
2. The definition of congruent is that if they are congruent then they are equal. Since that statement made two congruent lines equal, it must be the definition.
3. The reflexive property means something is congruent to itself, and BDis BD, therefore it is the reflexive property.
4. Remember if something is congruent then it is equal.
6. The segment addition postulate states that if we are given two points on a line segment, then AB+AC=AC.
7. In this statement AD was substituted for DF+BD. This can be done because of AB=DF and BD=BD as aforementioned.
8. If two things are congruent then they are equal by definition of congruency.
You cannot factor it any further as it is in its simplest factored form. There is no common factor in either the term (25x^2) or (9y^2) that you can pull out so it cannot be simplified. Hope this helps
