Answer:
33 1/3 L of the 40% solution, 16 2/3 L of the 25% solution
Step-by-step explanation:
Set up two equations...
Let x represent the number of Liters of the 40% solution
Let y represent the number of Liters of the 25% solution
We need 50 liters total, so
x + y = 50
and we need the 50 L to be 35% solution, so
0.4x = 0.25y = 0.35(50)
Solve the first equation for one variable...
x = 50 - y (subtract y from both sides in equation 1)
Now substitute that value into the second equation...
0.4(50 - y) + 0.25y = 17.5 (x becomes 50 - y, 0.35(50) = 17.5)
Now solve for y...
20 - 0.4y + 0.25y = 17.5
-0.15y = -2.5
y = 16.66666667
y = 16 2/3 L
So we need to plug that into the first equation to find 'x'
x + 16 2/3 = 50
x = 50 - 16 2/3
x = 33 1/3
Hello,
1. Since Angle C has the longest side for this triangle, it will have the largest degree value.
2. Use the Law of Cosines and inverse properties of “theta” to solve for Angle C. (Ensure that the calculator used is in “degree mode”, not “radian mode”.
c^2 = a^2 + b^2 - 2(a)(b)(cos (C))
15^2 = 11^2 + 14^2 - 2(11)(14)(cos(C))
225 - 317 = -2(11)(14)(cos(C))
-92 / -2(11)(14) = cos(C)
cos(C) becomes ->> cos^-1[92 /-2(11)(14)] = 72.62° ->> to the nearest degree is 73°
The answer for angle C, 73°, is logical because the triangle in the picture represents a 60-60-60 triangle, known as an equilateral triangle.
Good luck to you!
Answer:
The answer is 80.
Step-by-step explanation:
Firstly we add all of the stamps
118+83+4=205
She put 125 in first album so we have
205-125=80 stamps left
These 80 she needs to put in another album
<span>(a) Triangles ABC and PQR are similar triangles since they both share 2 congruent angles and therefore their 3rd angle is also congruent. So the triangles are similar due to the AAA similarity theorem.
(b) The area of triangle PQR is 1 million times larger than the area of triangle ABC. This can be shown since the area of a triangle is 1/2 base times height. You can show that the base of triangle PQR is 1000 times larger than the base of triangle ABC. And since all the sides are in proportion to each other, the height of triangle PQR is also 1000 times larger than the height of triangle ABC. And since 1000 times 1000 equals 1,000,000 or 1 million, the area of triangle PQR is 1 million times larger than triangle ABC.</span>
