14. 1.5, 10 <- Answer
15. 5,1 <- Answer
Proof 14
Solve the following system:
{2 x - y = -7 | (equation 1)
4 x - y = -4 | (equation 2)
Swap equation 1 with equation 2:
{4 x - y = -4 | (equation 1)
2 x - y = -7 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x - y = -4 | (equation 1)
0 x - y/2 = -5 | (equation 2)
Multiply equation 2 by -2:
{4 x - y = -4 | (equation 1)
0 x+y = 10 | (equation 2)
Add equation 2 to equation 1:
{4 x+0 y = 6 | (equation 1)
0 x+y = 10 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 3/2 | (equation 1)
0 x+y = 10 | (equation 2)
Collect results:
Answer: {x = 1.5
y = 10
Proof 15.
Solve the following system:
{5 x + 7 y = 32 | (equation 1)
8 x + 6 y = 46 | (equation 2)
Swap equation 1 with equation 2:
{8 x + 6 y = 46 | (equation 1)
5 x + 7 y = 32 | (equation 2)
Subtract 5/8 × (equation 1) from equation 2:{8 x + 6 y = 46 | (equation 1)
0 x+(13 y)/4 = 13/4 | (equation 2)
Divide equation 1 by 2:
{4 x + 3 y = 23 | (equation 1)
0 x+(13 y)/4 = 13/4 | (equation 2)
Multiply equation 2 by 4/13:
{4 x + 3 y = 23 | (equation 1)
0 x+y = 1 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = 20 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 5 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = 5 y = 1
Answer:
Federcio's age possible values are those that are greater than 14 i.e 15, 16, 17 and so on
Step-by-step explanation:
Let Federico's age = x
Three times the difference of Federico’s age, and 4 means:
3(x - 4)
Increased by 7:
3(x - 4) + 7
Is greater than 37:
3(x - 4) + 7 > 37
Solving the inequality:
3x - 12 + 7 > 37
3x - 5 > 37
3x > 37 + 5
3x > 42
x >42/3
x > 14
Federcio's age possible values are those that are greater than 14
Answer:
{d,b}={4,3}
Step-by-step explanation:
[1] 11d + 17b = 95
[2] d + b = 7
Graphic Representation of the Equations :
17b + 11d = 95 b + d = 7
Solve by Substitution :
// Solve equation [2] for the variable b
[2] b = -d + 7
// Plug this in for variable b in equation [1]
[1] 11d + 17•(-d +7) = 95
[1] -6d = -24
// Solve equation [1] for the variable d
[1] 6d = 24
[1] d = 4
// By now we know this much :
d = 4
b = -d+7
// Use the d value to solve for b
b = -(4)+7 = 3
Solution :
{d,b} = {4,3}
60/ (30/100)
= 60* (100/30)
= 200
The final answer is 200~
The perimeter of a rectangle is 62m. find the length of its sides if it is known that the area of the rectangle is 1980000 cm².