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
Let the slower cars speed equal X.
The faster cars speed would be X+5 ( 5 mph faster).
They traveled for 3 hours
Multiply the time of travel by speed to equal the number of miles traveled.
So you have:
3X + 3(X+5) = 267 miles
Simplify the left side:
3X + 3X+15 = 267
Combine like terms:
6x + 15 = 267
Subtract 15 from each side"
6x = 252
Divide each side by 6:
x = 252 / 6
X = 42
The slower car was traveling at 42 mph and the faster car was traveling at 47 mph.
Answer: Her measuring cup has 8.25 mL of medicine.
Step-by-step explanation:
As per given,
In 11 mL of medicine, there are 20 drops.
That means quantity in 1 drop = 
mL
Now , the quantity in 15 drops = 15 x quantity in 1 drop
= 
= 8.25 mL
Hence, her measuring cup has 8.25 mL of medicine.
Answer:
24.75/24¾
Step-by-step explanation:
148.5 ÷ 6 = 24¾ or 24.75
Answer: Each driver drove 24.75/24¾ miles
Answer:
31.13
Step-by-step explanation:
If you look carefully, you will find a semicircle and a triangle.
The total area is =
- r = 4 - 0 = 4
- base = |-4-0 | = 4
- height = 14 - 9 = 5
So if we put the values:
