Answer:
an equation of the first degree in any number of variables.
Step-by-step explanation:
Answer:
3/4 cups of flour are needed.
Step-by-step explanation:
(3 2/3)/1=(2 3/4)/x
(11/3)/1=(11/4)/x cross multiply.
11x/3=11/4 cross multiply.
4*11x=3*11
44x=33
x=33/44
x=3/4
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:
The correct answer is D) (-2, -1)
Step-by-step explanation:
In order to solve this system of equations, start by multiplying the entire first equation by 2. Then add the two equations together. This will get the y's to cancel and allow you to solve for x.
-4x + 2y = -10
3x - 2y = 12
---------------------
-x = 2
x = -2
Now that we have the value for x, we can find y by plugging the x value into either equation.
-2x + y = -5
-2(2) + y = -5
-4 + y = -5
y = -1
Answer:
2.777777 and -7/3
Step-by-step explanation:
2.7182818459 cannot be written in fraction form therefore it is irrational.
2.777777 is rational because it can be written as the fraction 25/9
The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.
-7/3 is rational because it is already in fraction form.
