Let x be the number of weeks; therefore, the two linear equations are
![\begin{gathered} T=2+7x \\ \text{and} \\ C=11+4x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20T%3D2%2B7x%20%5C%5C%20%5Ctext%7Band%7D%20%5C%5C%20C%3D11%2B4x%20%5Cend%7Bgathered%7D)
Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then
![\begin{gathered} T=C \\ \Rightarrow2+7x=11+4x \\ \Rightarrow3x=9 \\ \Rightarrow x=\frac{9}{3}=3 \\ \Rightarrow x=3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20T%3DC%20%5C%5C%20%5CRightarrow2%2B7x%3D11%2B4x%20%5C%5C%20%5CRightarrow3x%3D9%20%5C%5C%20%5CRightarrow%20x%3D%5Cfrac%7B9%7D%7B3%7D%3D3%20%5C%5C%20%5CRightarrow%20x%3D3%20%5Cend%7Bgathered%7D)
Thus, substitute the value of x=3 into the first equation,
![\begin{gathered} x=3 \\ \Rightarrow T=2+7\cdot3=23 \\ \Rightarrow T=23 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D3%20%5C%5C%20%5CRightarrow%20T%3D2%2B7%5Ccdot3%3D23%20%5C%5C%20%5CRightarrow%20T%3D23%20%5Cend%7Bgathered%7D)
Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.
Answer:
27/14
Step-by-step explanation:
you can cross multiply and simplify before you start. that way it makes it a lot easier
Given:
f(x) = 4x² + 1
g(x) = x² - 5
Then
(f + g)(x) = 4x² + 1 + x² - 5
= 5x² - 4
Answer: 5x² - 4
Answer:
225 m
Step-by-step explanation:
Since we know they are similar triangles
8 15
---------- = -----------
120 bridge
Using cross products
8 * bridge = 15* 120
8* bridge = 1800
Divide each side by 8
8/8* bridge = 1800/8
bridge = 225
2a + 2c - 5b - c - b
2a + c - 5b - b
2a - 6b + c