S9193331ashrafidn
Answered

Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Get step-by-step guidance for all your technical questions from our knowledgeable community members.

Andrea's record label released her new album. Andrea wants to know when she has sales of at least $20,000 per week. She uses the related equation below to determine when sales will be at least this amount, where t represents time in weeks.

please finish the other half

Andreas Record Label Released Her New Album Andrea Wants To Know When She Has Sales Of At Least 20000 Per Week She Uses The Related Equation Below To Determine class=

Sagot :

Mhanifaidn

Answer:

  • 10 ≤ t ≤ 20 or t ∈ [10; 20]

----------------------------

The other half is:

  • t - 15 ≥ - 5
  • t  ≥ - 5 + 15
  • t  ≥ 10

The answer, considering both halves, is:

  • 10 ≤ t ≤ 20

or

  • t ∈ [10; 20]
Semsee45idn

Answer:

[tex]10 \leq t \leq 20[/tex]

Step-by-step explanation:

Given absolute value inequality:

[tex]1000(-2|t-15|+30) \geq 20000[/tex]

Isolate the absolute value on one side of the equation:

[tex]\implies \dfrac{1000-2|t-15|+30)}{1000} \geq \dfrac{20000}{1000}[/tex]

[tex]\implies -2|t-15|+30 \geq 20[/tex]

[tex]\implies -2|t-15|+30-30 \geq 20-30[/tex]

[tex]\implies -2|t-15|\geq -10[/tex]

[tex]\implies \dfrac{-2|t-15|}{-2}\geq \dfrac{-10}{-2}[/tex]

[tex]\implies |t-15|\leq 5[/tex]

[tex]\textsf{Apply absolute rule:\quad {If} $|u| \leq a, \;a > 0$ \;then\; $-a \leq u \leq a$}[/tex]

[tex]\implies -5 \leq t-15\leq 5[/tex]

Solve both equations:

[tex]\begin{aligned}\underline{\sf Equation\;1} && \underline{\sf Equation\;2}\\t-15 &\geq -5 \quad & t-15& \leq 5\\t-15+15& \geq-5+15 &\qquad t-15+15& \leq 5+15\\t&\geq10 & t &\leq20\end{aligned}[/tex]

Merge the overlapping intervals:

[tex]10 \leq t \leq 20[/tex]

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.