2x + 4y + 2 = 3y + 5
2x + 4y - 3y + 2 - 5 = 0
2x + y - 3 = 0
Answer:
500 pennies
Step-by-step explanation:
Given that
Carmen saved 592 pennies.
Her sister saved 128 pennies.
Together, they put 250 pennies in wrappers and took them to the bank
We need to find out the total number of pennies Carmen and her sister have left
So,
= 592 pennies + 128 pennies - 250 pennies
= 470 pennies
= 500 pennies
Answer:
- Infinitely many solutions
Step-by-step explanation:
<u>Given system:</u>
<u>Divide the first equation by 2 and rearrange:</u>
- 2y/2 = 14/2 - 2x/2
- y = 7 - x
- y = -x + 7
We got the same equation with the second one. It means we have two of the same lines overlapping.
This gives us infinitely many solutions.
Example 1
Write y = x2 + 4x + 1 using function notation and evaluate the function at x = 3.
Solution
Given, y = x2 + 4x + 1
By applying function notation, we get
f(x) = x2 + 4x + 1
Evaluation:
Substitute x with 3
f (3) = 32 + 4 × 3 + 1 = 9 + 12 + 1 = 22
Example 2
Evaluate the function f(x) = 3(2x+1) when x = 4.
Solution
Plug x = 4 in the function f(x).
f (4) = 3[2(4) + 1]
f (4) = 3[8 + 1]
f (4) = 3 x 9
f (4) = 27
Example 3
Write the function y = 2x2 + 4x – 3 in function notation and find f (2a + 3).
Solution
y = 2x2 + 4x – 3 ⟹ f (x) = 2x2 + 4x – 3
Substitute x with (2a + 3).
f (2a + 3) = 2(2a + 3)2 + 4(2a + 3) – 3
= 2(4a2 + 12a + 9) + 8a + 12 – 3
= 8a2 + 24a + 18 + 8a + 12 – 3
= 8a2 + 32a + 27
Answer : X^2+6x+9
(X+3)(x+3)
