Well, first since i split this up into 3 shapes. Then I multiplied 4x8 which was 32 and since there were two,it would be another 32. Then I multiplied 12x4 which was 48. Then I added 32+32+48 which equaled 112 square feet.
An angle of 90 degrees to a given line, plane or surface
Answer: 490 grams of the first alloy should be used.
30 grams of the second alloy should be used.
Step-by-step explanation:
Let x represent the weight of the first alloy in grams that should be used.
Let y represent the weight of the second alloy in grams that should be used.
A chemist has two alloys, one of which is 15% gold and 20% lead. This means that the amount of gold and lead in the first alloy is
0.15x and 0.2x
The second alloy contains 30% gold and 50% lead. This means that the amount of gold and lead in the second alloy is
0.3y and 0.5y
If the alloy to be made contains 82.5 g of gold, it means that
0.15x + 0.3y = 82.5 - - - - - - - - - - - -1
The second alloy would also contain 113 g of lead. This means that
0.2x + 0.5y = 113 - - - - - - - - - - - - -2
Multiplying equation 1 by 0.2 and equation 2 by 0.15, it becomes
0.03x + 0.06y = 16.5
0.03x + 0.075y = 16.95
Subtracting, it becomes
- 0.015y = - 0.45
y = - 0.45/- 0.015
y = 30
Substituting y = 30 into equation 1, it becomes
0.15x + 0.3 × 30 = 82.5
0.15x + 9 = 82.5
0.15x = 82.5 - 9 = 73.5
x = 73.5/0.15
x = 490
Answer:
SAS Similarity Theorem
Step-by-step explanation:
we know that
<u>SAS Similarity Theorem</u>: States that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar
In this problem
∠HJZ=∠RJW ----> by vertical angles
and
WJ/HJ=JR/JZ
substitute the values
8/4=6/3
2=2 ----> is true
so
Two sides of triangle HJZ are proportional with the two corresponding sides of triangle WJR and the included angle is congruent
therefore
Triangles are similar by SAS Similarity Theorem
7 + 6 = 13
13 - 6 = 7 or 13 - 7 = 6
