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:
(a) x = 30°
(b) mRS = 30°
mST = 120°
mTU = 120°
mUR = 90°
Step-by-step explanation:
(a) In the picture attached, the diagram is shown.
Given that m arc RS = x, from the ratios:
m arc ST = 4x
m arc TU = 4x
m arc UR = 3x
The addition of the four arcs must be equal to 360°, then:
x + 4x + 4x + 3x = 360°
12x = 360°
x = 360°/12 = 30°
(b) m arc RS = x = 30°
m arc ST = 4x = 4*30° = 120°
m arc TU = 4x = 4*30° = 120°
m arc UR = 3x = 3*30° = 90°
Answer:
If line EF was dilated by a scale of 1/2 from the origin to get line E'F', then if line E'F' is dilated by a scale of 2 from the origin, EF is obtained. Also, the length of EF is double than the length of E'F'.
Dilation by a scale of 2 from the origin transforms point (x,y) into (2*x, 2*y)
E'(1,0) -> E(2,0)
F'(1, 3) ->F(2, 6)
length of E'F': 3
length of EF: 6
We need to know the definition of the "combined function" h(x). I'm going to guess--by looking at answers--that the function is
making it
This function is undefined wherever the denominator is equal to 0 (division by zero is undefined). Factor the denominator.
The two values of x that make the denominator 0 are 3 and -3, otherwise written
.
I can only assume that you meant, "Solve for x:"
Apply the exponent 3/2 to both sides of this equation. The result will be
3/2
343 = x/6.
Multiplying both sides by 6 isolates x:
3/2
6*343 = x Since 7^3 = 343, the expression for x
can be rewritten as
3/2
6*(7^3) = x which can be further simplified, as follows:
x = 6^(3/2)*7^(9/2), or:
x = 6^(3/2)*7^(8/2)*√7, or
x = 6^(3/2)*7^4*√7
