Answer:
20kg of 25% copper alloy
30kg of 60% copper alloy
Step-by-step explanation:
There are 2 kinds of metal, first metal(A) have 25% copper while the second metal(B) has 60% copper. The metalworker want to create 50kg of metal, which means the total weight of both metals is 50kg (A+B = 50). The metalworker also want the metal made of a 46% which is 23kg(0.25A + 0.6B = 0.46*50). From these sentences, we can derive 2 equations. We can solve this with substitution.
A+B = 50
A= 50-B
Let's put the first equation into the second.
0.25A + 0.6B = 0.46 *50
0.25(50-B) + 0.6B =23
12.5 - 0.25B + 0.6B =23
0.35B=23 -12.5
B= 10.5/ 0.35= 30
Then we can solve A
A= 50-B
A= 50-30
A=20
Answer:
So the model should represent either 
or
(its equivalent and simplified form.
Step-by-step explanation:
1) Originally the question wants to represent this quotient as tiles.
So,
We can still simplify it, but since we're dealing with 100 x 100 squares let's keep it this way
2) So the model should represent either or (its equivalent and simplified form.
A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
Answer: 
Step-by-step explanation:
Given
Max is driving at a speed of 
It took him three-quarters of a second i.e. 
Speed in meter per second is 
Distance is given by
Reaction distance is
