360 - 90 - 85 - 72 = 113
x = 113
Answer:
So the height is 12
Step-by-step explanation:
Let W be the width
Let W- 4 be the height
W2 +(W-4)2 = 400
So: W2 -4W-192 =0
One uses the quadratic solution:
W = (4 + (16 + 4*192).5)/2 = 16
Answer:
x=8
Step-by-step explanation:
5(x+2)=6x+3x-14
5x+10=6x+3x-14. distributive property
10+14=8x-5x. combine like term
24=3x. addition and subtraction property
24/3 = 3x/3. division property
8=x
> x = 8
Answer:
One could add "and in the same plane as that point and all other points"
It takes 3 points to define a plane.
All the points on a sphere are the same distance from one point but they do not define a circle.
Answer:
a. 87.5%
b. 30 g of 12 carat and 60 g of 21 carat.
Step-by-step explanation:
a. The percentage of gold in 21 carat is given by:
![gold_{21} = \frac{21}{24}*100 = 87.5 \%](https://tex.z-dn.net/?f=gold_%7B21%7D%20%3D%20%5Cfrac%7B21%7D%7B24%7D%2A100%20%3D%2087.5%20%5C%25)
b. Since the mass he wants to produce is 90 g, then the added mass of the 12 carat, "x", and the mass of the 21 carat "y", must be equal to that:
![x + y = 90](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2090)
The sum of gold on each carat type must be equal to the amount of gold on the final mixture, since a 12 carat has 50% gold and a 21 carat has 87.5% gold, then we have:
![0.5*x + 0.875*y = 0.75*90\\\\0.5*x + 0.875*y = 67.5\\](https://tex.z-dn.net/?f=0.5%2Ax%20%2B%200.875%2Ay%20%3D%200.75%2A90%5C%5C%5C%5C0.5%2Ax%20%2B%200.875%2Ay%20%3D%2067.5%5C%5C)
We now have a system of equations which we can solve to find the necessary mass of each type.
![x + y = 90 \text{ } *-0.5\\0.5*x + 0.875*y = 67.5\\\\-0.5*x - 0.5*y = -45\\0.5*x + 0.875*y = 67.5\\\\0.375*y = 22.5\\\\y = 60](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2090%20%5Ctext%7B%20%7D%20%2A-0.5%5C%5C0.5%2Ax%20%2B%200.875%2Ay%20%3D%2067.5%5C%5C%5C%5C-0.5%2Ax%20-%200.5%2Ay%20%3D%20-45%5C%5C0.5%2Ax%20%2B%200.875%2Ay%20%3D%2067.5%5C%5C%5C%5C0.375%2Ay%20%3D%2022.5%5C%5C%5C%5Cy%20%3D%2060)
![x = 90 - y = 90 - 60\\\\x = 30](https://tex.z-dn.net/?f=x%20%3D%2090%20-%20y%20%3D%2090%20-%2060%5C%5C%5C%5Cx%20%3D%2030)
He needs 30 g of 12 carat gold and 60 g of 21 carat gold.