Answer:
She uses 200 milliliters of solution B
Step-by-step explanation:
Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:
Amount of solution A to be used = A
Amount of solution B to be used = B
So, since we need to find two unknowns, we need to create a system of two equations to solve them.
Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:
A = 2 B
The second equation we can build from the information of the amount of alcohol in each solution that combined will add up to 104 milliliters of alcohol in the mixture. Knowing the percent of alcohol in each solution, we can write an equation for the amount of alcohol:
0.19 A + 0.14 B = 104
Now we can use our first equation to substitute A in terms of B in the second equation:
0.19 (2 B) + 0.14 B = 104
0.38 B + 0.14 B = 104
0.52 B = 104
B = 104 / 0.52
B = 200 milliliters
The <em><u>correct answer</u></em> is:
AAS
Explanation:
AAS stands for "angle-angle-side." This states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.
In these triangles, we have ∠CAB ≅ ∠CDB given to us to begin with. Throughout the proof, we find that ∠ABC ≅ ∠DCB. We also have that CB is congruent to itself. This is two angles and a side not included, so this is AAS.
139 + 30d = 13 + 51d
139 - 13 = 51d - 30d
126 = 21d
126/21 = d
6 = d
now lets check..
139 + 30d = 139 + 30(6) = 319
13 + 51d = 13 + 51(6) = 319
so on day 6, they will both cost $ 319
We call x the 4 points-worth problems and y the 3 points-worth problems
You know that x+y = 32
4x+3y = 111
You know that the difference from the x and y is 32 so write:
x = 32-y
Substitute at x the value of 32-y
4(32-y)+3y = 111
128-4y +3y = 111
-4y+3y = 111-128
-y = -17
y = 17
