Answer:
The value of x and y that satisfy the equations is x = 2 and y = 1
Step-by-step explanation:
Given
2.5(x−3y)−3=−3x+0.5
3(x+6y)+4=9y+19
Required.
Find x and y
We start by opening all brackets
2.5(x−3y)−3=−3x+0.5 becomes
2.5x - 7.5y - 3 = -3x + 0.5
Collect like terms
2.5x + 3x - 7.5y = 3 + 0.5
5.5x - 7.5y = 3.5 ---- Equation 1
In similar vein, 3(x+6y)+4=9y+19 becomes
3x + 18y + 4 = 9y + 19
Collect like terms
3x + 18y - 9y = 19 - 4
3x + 9y = 15
Multiply through by ⅓
⅓ * 3x + ⅓ * 9y = ⅓ * 15
x + 3y = 5
Make x the subject of formula
x = 5 - 3y
Substitute 5 - 3y for x in equation 1
5.5(5 - 3y) - 7.5y = 3.5
27.5 - 16.5y - 7.5y = 3.5
27.5 - 24y = 3.5
Collect like terms
-24y = 3.5 - 27.5
-24y = -24
Divide through by - 24
y = 1
Recall that x = 5 - 3y.
Substitute 1 for y in this equation
x = 5 - 3(1)
x = 5 - 3
x = 2
Hence, x = 2 and y = 1
Answer:
First model gets the equation: y = 2 . 2^z
Second model gets the equation: y = 4^z
Third model gets the equation: y: = 4 . 2^z
Answer:
- 10√2 - 5√5
Step-by-step explanation:
- 2√50
√50 = √( 2 x 5 x 5 ) = 5√2
- 2√50
= - 2 x 5√2
= - 10√2
- √125
= - √( 5 x 5 x 5 )
= - 5√5
- 2√50 - √125
= - 10√2 - 5√5
Answer:
there are 9 quarters and 19 dimes
Step-by-step explanation:
Let x be the number of dimes and y the number of quarters
-dimes: 0.1x
-quarters: 0.25y
-the total amount of coins : x + y = 28
=> x = 28 - y
We have the equation:
0.25y + 0.1x = 4.15
0.25y + 0.1(28 - y) = 4.15
0.25y + 2.8 - 0.1y = 4.15
0.15y = 1.35
y = 9
x = 28 - y
= 28 - 9
= 19
