Let 
be the number of liters of the 10% solution to be used, and 
the number of liters of the 4% solution. The chemist wants to end up with a 4 liter solution, so
For each liter used in the mixture, a concentration of either 10% or 4% acid will be contributed, and the goal is to make a 4L solution whose concentration is 7%, which means
Solving for 
gives 
, so 2L of both solutions is needed.
<span>First note that y cannot equal -7 or -1 as division by zero is undefined. So that if it comes up in our solution we know that it is not a real solution.
[(y+4)/(y+7)]+1=(y+3)/(y+1) make the left side have a common denominator
(y+4+y+7)/(y+7)=(y+3)/(y+1) combine like terms on left side
(2y+11)/(y+7)=(y+3)/(y+1) cross multiply
(2y+11)(y+1)=(y+3)(y+7) expand
2y^2+13y+11=y^2+10y+21 subtract y^2 from both sides
y^2+13y+11=10y+21 subtract 10y from both sides
y^2+3y+11=21 subtract 21 from both sides
y^2+3y-10=0 expand so factoring is easier
y^2-2y+5y-10=0 factor
y(y-2)+5(y-2)=0 which is equal to
(y+5)(y-2)=0
y=-5 or 2</span>
Answer:
22
Step-by-step explanation:
The standard form for an equation of a circle is 
, where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius of the circle. Therefore, the radius of this circle squared is 121, meaning that the radius of the circle is 11. Since the diameter of a circle is twice the radius, the radius of this circle is 22. Hope this helps!
1.2625 i dunno if this is correct though on my calculations
Answer:
ABCD is a parallelogram
Step-by-step explanation:
Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a
parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC
1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.
definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3.
alternate interior angles are congruent 4. AC ≅ AC 4.
reflexive property 5. △CAD ≅ △ACB 5. SAS congruency
theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.
