All categories

2 years ago

What is the solution of |2x+3|< 19

Mathematics

1 answer:

Alex2 years ago

6 0

Answer:

- 11 < x < 8

Step-by-step explanation:

inequalities of the type | x | < a have solutions of the form

- a < x < a

then

| 2x + 3 | < 19

- 19 < 2x + 3 < 19 ( subtract 3 from each interval )

- 22 < 2x < 16 ( divide each interval by 2 )

- 11 < x < 8

You might be interested in

Which equation illustrates the additive inverse property?

Minchanka [31]

Answer:

Step-by-step explanation:

A negative of the same value added to positive always gives you 0

negative is inverse of positive

7 0

3 years ago

Two friends go out to eat and order the same meal. They pay a 6% sales tax and a 20% tip on their meals. The total bill, includi

vova2212 [387]

Sales tax and tip will increase the price of an item.

The cost of each meal is: $10.89

Let the cost of both meals be x.

A 20% tip means that, the current price is:

$Price = x \times (1 + 20\%)$

A 6% sales tax on the meal means that, the current price is:

$Price = x \times (1 + 20\%) \times (1 + 6\%)$

So, we have:

$Price = x \times (1 + 0.20) \times (1 + 0.06)$

$Price = x \times (1.20) \times (1.06)$

$Price = x \times 1.272$

The amount paid is $27.72

So, the equation becomes

$27.72= x \times 1.272$

Make x the subject

$x = \frac{27.72}{1.272}$

$x = 21.78$

So, the cost of each meal is:

$Each= \frac{21.78}{2}$

$Each= 10.89$

Hence, the cost of each meal is: $10.89

Read more about sales tax at:

brainly.com/question/19715580

3 0

3 years ago

Find how long it takes a $ 900.00 investment to earn $ 120.00 in interest if it is invested at 6% compounded annually.

atroni [7]

So, we know the earned interest is 120, and we know the original deposited amount is 900 bucks, so, the accumulated amount will then be 900 + 120 or 1020 bucks.

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$1020\\
P=\textit{original amount deposited}\to &\$900\\
r=rate\to 6\%\to \frac{6}{100}\to &0.06\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years
\end{cases}$

$\bf 1020=900\left(1+\frac{0.06}{1}\right)^{1\cdot t}\implies \cfrac{1020}{900}=(1.06)^t\implies \cfrac{102}{90}=(1.06)^t
\\\\\\
log\left(\frac{102}{90} \right)=log(1.06^t)\implies log\left(\frac{102}{90} \right)=t\cdot log(1.06)
\\\\\\
\cfrac{log\left(\frac{102}{90} \right)}{log(1.06)}=t\implies 20.92 \approx t$

7 0

4 years ago

The annual tuition at a public two-year college last year was $3,200. For the new school year, Elizabeth’s first year in college

Korolek [52]

he tuition of $3,200 increased by 5% is: 3,200 + 0.05*3,200 = 1.05*3,200 = $3,360

Elizabeth saved equal amounts each month for 12 months the previous year thus we divide $3,360 by 12 to find how much she saved monthly:

$3,360 : 12 = $280

The minimum amount Elizabeth should have saved monthly is $280.

6 0

3 years ago

Use the remainder theorem to determine the remainder when d 4 + 2d 2 + 5d ? 10 is divided by d + 4

AURORKA [14]

\left[d \right] = \left[ 0\right][d]=[0] totally answer

5 0

3 years ago