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Anna71 [15]
3 years ago
15

Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon. You need to purchase at least 9 gallons of drinks for a n

eighborhood picnic, but have at most $55 to spend. Model the scenario with a system of inequalities. Which of the following options represents a possible solution to the system of inequalities?
Mathematics
1 answer:
jekas [21]3 years ago
8 0
The answer is (10,-5)
You might be interested in
“encontrar la integral indefinida y verificar el resultado mediante derivación”
Oliga [24]

I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx

Haz la sustitución:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C

Para confirmar el resultado:

\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}

I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx

Sustituye:

y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx

\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C

(Te dejaré confirmar por ti mismo.)

I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx

Sustituye:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C

I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}

Sustituye:

u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}

\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C

Podemos hacer que esto se vea un poco mejor:

\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}

\implies I=-\dfrac{(t+1)^4}{4t^4}+C

4 0
3 years ago
Stan says that the least common multiple of 6 and 8
Kazeer [188]
Then the lest multiple of 6 and 8 are 5 and 7 duh
5 0
3 years ago
Work out 1 3/4 x 4 1/6
sattari [20]

Convert mixed number to improper fraction:

1\dfrac{3}{4}=\dfrac{1\cdot4+3}{4}=\dfrac{4+3}{4}=\dfrac{7}{4}\\\\4\dfrac{1}{6}=\dfrac{4\cdot6+1}{6}=\dfrac{24+1}{6}=\dfrac{25}{6}\\\\1\dfrac{3}{4}\times4\dfrac{1}{6}=\dfrac{7}{4}\times\dfrac{25}{6}=\dfrac{7\times25}{4\times6}=\dfrac{175}{24}=\dfrac{168+7}{24}=7\dfrac{7}{24}

8 0
4 years ago
!!!! PLEASEEE HELP ME, IDK WHAT TO DO PLEASE !!!!
Helga [31]

Answer:

  The first question is A.

  The second question is C.

   The thid question is B., I think i'm not quit sure sorry

4 0
3 years ago
On Wednesday, James slept for <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D" id="TexFormula1" title="\frac{3}{8}" alt=
Hatshy [7]

Answer:

I believe he slept for 9 hours of the day

Step-by-step explanation:

⅜ of 24

24 ÷ 8 = 3

3 × 3 = 9

8 0
3 years ago
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