To find the x intercept of the function, we would find g(x) = 0
To do this, we would set each expression in the piecewise function to zero and solve for x. We have
For
x/3 + 2 = 0
let us multiply both sides of the equation by 3. We have
x/3 * 3 + 2 * 3 = 0 * 3
x + 6 = 0
x = - 6
- 6 is less than - 1
- 6 < - 1
It satisfies the inequality. Thus, x = - 6 is in the domain
For
4x - 2 = 0
adding 2 to both sides of the equation, we have
4x - 2 + 2 = 0 + 2
4x = 2
Dividing both sides of the equation by 4, we have
4x/4 = 2/4
x = 1/2
x = 1/2 is less than 1. It is not in the domain of this equation. Thus, there is no x interscept at x = 1/2
Therefore, the x intercept of the piecewise function is (- 6, 0)
Answer: k - 8
Step-by-step explanation:
4x = 7(x-3)
1. Distribute that multiplicand 7: 4x = 7x - 21
2. Group the x terms together: Subtract 4x from both sides: 0 = 3x - 21
3. Solve for x: Add 21 to both sides: 21 = 3x
4. Divide both sides by 3 to obtain x = 7 (answer)
Answer:
Step-by-step explanation:
If Quan had 15 and Kaden had 3 times as much, then Kaden had 15(3) = 45. If he spent 10 then he had 35 left. The amount of money Quan had after his mom gave him some was 4/5 the amount of Kaden's 35 (let x = the amount of money Quan has after his mom gives him some):
35 divides by the 5 in the denominator 7 times, and 7 times 4 is 28. That's how you get your 28 in part a.
For part b., he started with 15 and ended with 28, so his mom gave him 28-15=13. That's how you get the 13.
1/4 * 1/3 * 1/2 * 1/1 = 1/24 chance that all 4 letters are placed in the correct envelopes.
With the first envelope, there are 4 choices of letters, so the probability of picking the correct letter is 1/4.
With the second envelope, there are 3 remaining letters, so the probability of picking the correct letter is 1/3.
The same logic follows the the third and final letter.
