9514 1404 393
Answer:
z° = 44°
Step-by-step explanation:
The sum of angles in a triangle is 180°.
44° +52° +z° +40° = 180°
z° = 44° . . . . . . . . . . . . . . . . subtract 136° from both sides
The value of z is 44.
_____
There is no "x".
Answer:
4 ducks
12 chickens
Step-by-step explanation:
Ducks to Chicken (ducks : chicken) ratio
= 1 : 3
Ducks to Chicken ratio, if chickens = 12
= ? : 12
1 : 3 = ? : 12
Find the scale factor of the ratios by dividing the number of chickens to the ratio of chickens.
12 ÷ 3 = 4
To find the number of ducks, multiply the ratio of ducks by the scale factor.
1 X 4 = 4
Therefore, there are 4 ducks and 12 chickens on the farm.
Ratios can also be written like fractions. Use this to check the answer:
1/3 = 4/12
4/12 can be reduced by dividing both the top and the bottom by 4.
4/4 = 1 Same as original ratio top
12/4 = 3 Same as original ratio bottom
A: 49
B:45
C: 20.1
D:114
(3x-11)+(6x-10)+x=180
10x-21=180
10x=201
x=20.1
(I think I did that right)
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:
375 = 3 · 5³
1000 = 2³ · 5³
Step-by-step explanation:
