Let f and e represent the amount of 40% and 80% solutions used...
We are told the f+e=20 which means that f=20-e and we can say that:
(.4f+.8e)/20=.7, using f=20-e in this equation we see that:
.4(20-e)+.8e=14
8-.4e+.8e=14
8+.4e=14
.4e=6
e=15, and since f=20-e then
f=5
So 15 quarts of 80% solution is mixed with 5 quarts of 40% solution to produce a 20 quart mixture of 70% solution.
Answer:
f(x) has a minimum value of -10.
Step-by-step explanation:
It will have a minimum value because the coefficient of x^2 is positive.
To find its value we convert to vertex form:
f(x) = 4x^2 - 16x + 6
= 4(x^2 - 4x) + 6
= 4[(x - 2)^2 - 4] + 6
= 4(x - 2)^2 - 16 + 6
= 4(x - 2)^2 - 10.
So the minimum value is -10.
Answer:
Robert Recorde.
Step-by-step explanation:
Robert Recorde was a Welsh known for vast knowledge and experience in the field of mathematics and physics. He was born in Tenby, Pembrokeshire, Wales during the Medieval period (c. 1512).
Robert Recorde was famously known for his work in the field of mathematics and most especially, the invention of the equal to (=) sign. He introduced it in his book titled "The Whetstone of Witte."
<em>Hence, Robert Recorde was the first english mathematician who first used the modern symbol of equality in 1557. </em>
Distributive property :))))
1) P=2w +2l
46=2w +14
32=2w
16= w or width
2) A=lw
A=7 x 12
A= 84
3) A= 12 x 21
A= 252
