Answer:
The number of cards Frank has is 18 and the number of cards his friend has is 24.
Step-by-step explanation:
<u><em>The correct question is </em></u>
Two friends are collecting cards. Frank has 6 more than half the number of cards as his friend. Together they have 42 cards. How many cards does each friend have?
Let
x ----> the number of cards that Frank has
y ----> the number of cards that his friend has
we know that
Together they have 42 cards
----> equation A
Frank has 6 more than half the number of cards as his friend
---> equation B
Solve the system by substitution
Substitute equation B in equation A
solve for y
<em>Find the value of x</em>
therefore
The number of cards Frank has is 18 and the number of cards his friend has is 24.
Answer:
x = 1, y = 6
or
x = 5, y = 2.
Step-by-step explanation:
y=x2−7x+12
y=−x+7
Substitute for y in the first equation:
- x + 7 = x^2 - 7x + 12
x^2 - 7x + x + 12 - 7 = 0
x^2 - 6x + 5 = 0
(x - 1)(x - 5) = 0
x = 1, 5.
When x = 1, y = -1 + 7 = 6.
when x = 5, y = -5+7 = 2.
Answer:
The intermediate step are;
1) Separate the constants from the terms in x² and x
2) Divide the equation by the coefficient of x²
3) Add the constants that makes the expression in x² and x a perfect square and factorize the expression
Step-by-step explanation:
The function given in the question is 6·x² + 48·x + 207 = 15
The intermediate steps in the to express the given function in the form (x + a)² = b are found as follows;
6·x² + 48·x + 207 = 15
We get
1) Subtract 207 from both sides gives 6·x² + 48·x = 15 - 207 = -192
6·x² + 48·x = -192
2) Dividing by 6 x² + 8·x = -32
3) Add the constant that completes the square to both sides
x² + 8·x + 16 = -32 +16 = -16
x² + 8·x + 16 = -16
4) Factorize (x + 4)² = -16
5) Compare (x + 4)² = -16 which is in the form (x + a)² = b
