Which values from the given replacement set make up the solution set of the inequality?

Multiply the a nagative to what is inside the paranthesis on the right side of the nagative sign then combine like variables. This will give you your answer.

Step-by-step explanation:

Multiply the a nagative to what is inside the paranthesis on the right side of the nagative sign then combine like variables. This will give you your answer.

8 0

3 years ago

A business was valued at £80000 at the start of 2013. In 5 years the value of this business raised to £95000. this is equivalent

Yuri [45]

the yearly increase of x% assumes is compounding yearly, so let's use that.

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\£95000\\ P=\textit{original amount deposited}\dotfill &\£80000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}$

$95000=80000\left(1+\frac{~~ \frac{r}{100}~~}{1}\right)^{1\cdot 5}\implies \cfrac{95000}{80000}=\left( 1+\cfrac{r}{100} \right)^5 \\\\\\ \cfrac{19}{16}=\left( 1+\cfrac{r}{100} \right)^5\implies \sqrt[5]{\cfrac{19}{16}}=1+\cfrac{r}{100}\implies \sqrt[5]{\cfrac{19}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[5]{\cfrac{19}{16}}=100+r\implies 100\sqrt[5]{\cfrac{19}{16}}-100=r\implies 3.5\approx r$

4 0

2 years ago

Mrs. Julien’s and Mrs. Castillejo’s classes are selling cookie dough for a school fundraiser. Customers can buy packages of maca

Oksi-84 [34.3K]

Answer: the cost of one package of macadamia nut chip cookie dough is $1.5

the cost of one package of triple chocolate cookie dough is $2.5

Step-by-step explanation:

Let x represent the cost of one package of macadamia nut chip cookie dough.

Let y represent the cost of one package of triple chocolate cookie dough.

Mrs. Julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $112.50. This means that

25x + 30y = 112.5 - - - - - - - - - - - - -1

Mrs. Castillejo’s class sold 8 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $124.50. This means that

8x + 45y = 124.5 - - - - - - - - - - -2

Multiplying equation 1 by 8 and equation 2 by 25, it becomes

200x + 240y = 900

200x + 1125 = 3112.5

Subtracting, it becomes

- 885y = - 2212.5

y = - 2212.5/- 885

y = 2.5

Substituting y = 2.5 into equation 1, it becomes

25x + 30 × 2.5 = 112.5

25x + 75 = 112.5

25x = 112.5 - 75 = 37.5

x = 37.5/25 = 1.5

The method used is the elimination method. It is more convenient to use.

8 0

4 years ago