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3 years ago

How to write the inverse of 3x+4y=12 in f^-1 (x)?

1 answer:

8 0

3x+4y=12

4y=12-3x

y=(12-3x)/4 <---------- This is f(x)

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

3x+4y=12

3x=12-4y

x=(12-4y)/3

Therefore:

f⁻¹(x)=(12-4x)/3

=[4(3-x)]/3

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Please Help!!!

alekssr [168]

A) About 25% of the fishermen caught between 25 and 30 fish.
>Since the boxplot looks symmetric, the parts are each 25%.

B) The spread is symmetrical about the median.
>The median is 20.
20-15 = 5; 15-10 = 5
25-20 = 5; 30-25 = 5

E) The range is 20 fish.
> The largest data is 30, smallest data is 10
Range = largest - smallest = 30-10 = 20

4 0

3 years ago

90 POINTS PLEASE HELP

11111nata11111 [884]

$sin\alpha = - 0.8$

Step-by-step explanation:

We have , $cos\alpha = \frac{3}{5}$ , where $\alpha$ is located in IV quadrant! Let's find out value of $sin\alpha$ :

$sin\alpha = \sqrt{1-(cos\alpha )^2$

⇒ $sin\alpha = \sqrt{1-(cos\alpha )^2$

⇒ $sin\alpha = \sqrt{1-(\frac{3}{5} )^2$

⇒ $sin\alpha = \sqrt{1-(\frac{9}{25} )$

⇒ $sin\alpha = \sqrt{(\frac{25-9}{25} )$

⇒ $sin\alpha = \sqrt{(\frac{16}{25} )$

⇒ $sin\alpha = \pm {(\frac{4}{5} )$

Value of $sin\alpha$ is dependent on which quadrant it is . Since, in question it's given that $\alpha$ is located in IV quadrant , So $sin\alpha$ is negative i.e.

⇒ $sin\alpha = - {(\frac{4}{5} )$

⇒ $sin\alpha = - 0.8$

Therefore, $sin\alpha = - 0.8$ .

4 0

3 years ago

Read 2 more answers

What sum will amount to rupees 4000 in 3 years at 6% p.a. compound interest

natali 33 [55]

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Given:}}}}}}}\end{gathered}$

⇢ Principle = Rs.4000
⇢ Rate = 6%
⇢ Time = 3 year

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{To Find:}}}}}}}\end{gathered}$

⇢ Amount

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Using Formula:}}}}}}}\end{gathered}$

${\dag{\underline{\boxed{\sf{Amount ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\dag{\underline{\boxed{\sf{Compound \: Interest = Amount- Principle }}}}$

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Solution:}}}}}}}\end{gathered}$

${\bigstar \:{\underline{\pmb{\frak{\red{Firstly,Finding \: the \: Amount }}}}}}$

$\quad {:\implies{\sf{Amount = \bf{P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

Substituting the values

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg(1 + \dfrac{6}{100}{\bigg)}^{3}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg(1 \times 100 + \dfrac{6}{100}{\bigg)}^{3}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg( \dfrac{100 + 6}{100}{\bigg)}^{3}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg( \dfrac{106}{100}{\bigg)}^{3}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg({\cancel{\dfrac{106}{100}}{\bigg)}}^{3}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg( \dfrac{53}{50}{\bigg)}^{3}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg( \dfrac{53}{50} \times \dfrac{53}{50} \times \dfrac{53}{50}{\bigg)}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000{\bigg( \dfrac{148877}{125000}{\bigg)}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4000 \times \dfrac{148877}{125000}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4{\cancel{000}} \times \dfrac{148877}{125{\cancel{000}}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{\dfrac{148877 \times 4}{125}}}}}$

$\quad {:\implies{\sf{Amount = \bf{\dfrac{595508}{125}}}}}$

$\quad {:\implies{\sf{Amount = \bf{\cancel{\dfrac{595508}{125}}}}}}$

$\quad {:\implies{\sf{Amount = \bf{4764.064}}}}$

$\begin{gathered} \dag{\boxed{\textsf{\textbf{\underline{\color{green}{Amount = {Rs.4764.064}}}}}}}\end{gathered}$

Hence, The Amount is Rs.4764.064

$\begin{gathered}\end{gathered}$

${\bigstar \:{\underline{\pmb{\frak{\red{ Now,Finding \: The \: Compound \: Interest }}}}}}$

$\quad{: \implies{\sf{Compound \: Interest = \bf{Amount- Principle }}}}$

Substituting the values

$\quad{: \implies{\sf{Compound \: Interest = \bf{4764.064- 4000 }}}}$

$\quad{: \implies{\sf{Compound \: Interest =\bf{764.064}}}}$

$\begin{gathered} \dag{\boxed{\textsf{\textbf{\underline{\color{green}{Compound Interest = Rs.764.064}}}}}}\end{gathered}$

Henceforth,The Compound Interest is Rs.764064

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Learn More:}}}}}}}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered} \dag \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Amount = Principle + Interest}} \\ \\ \dashrightarrow \sf{ P=Amount - Interest }\\ \\ \dashrightarrow \sf{ S.I = \dfrac{P \times R \times T}{100}} \\ \\ \dashrightarrow \sf{P = \dfrac{Interest \times 100 }{Time \times Rate}} \\ \\ \dashrightarrow \sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}} \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}$

8 0

3 years ago

The largest prime number that is a factor of 35 is multiplied by the smallest prime number

Lubov Fominskaja [6]

Answer:

the largest factor of 35 is 35 and the smallest prime number is 2 so 35 times two is 70

Step-by-step explanation:

6 0

2 years ago

Please show work and help me please

Gnesinka [82]

Answer:

31.4 in

Step-by-step explanation:

the formula for circumference is 2* $\pi$ *radius. Since the diameter (which is the radius multiplied by 2) is labeled we can divide 10 by 2 to get the radius. 10/2 is 5. Since pi is an infinite number, we round it to 3.14. Then, plug in the numbers. The expression will be 2*3.14*5. 2* = 10 and 10 * 3.14 you can just move the decimal so the answer is 31.4.

6 0

3 years ago