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Angelina_Jolie [31]
3 years ago
14

Dan invests £18790 into his bank account. He receives 5.3% per year simple interest. How much will Dan have after 7 years?

Mathematics
1 answer:
Neko [114]3 years ago
8 0

Answer: 55

Step-by-step explanation:

67

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A function f(x)=3x+12.
seraphim [82]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2822258

_______________


•  Function:   f(x) = 3x + 12.


A.  Finding the inverse of f.

The composition of f with its inverse results in the identity function:

(f o g)(x) = x

f[ g(x) ] = x

3 · g(x) + 12 = x

3 · g(x) = x – 12

              x – 12
g(x)  =  ⸺⸺
                 3

               x 
g(x)  =  ⸺  –  4    <———    this is the inverse of f.
               3

________


B.  Verifying that the composition of f and g gives us the identity function:

•  \mathsf{(f\circ g)(x)}

\mathsf{=f\big[g(x)\big]}\\\\\\ \mathsf{=3\cdot \left(\dfrac{x}{3}-4\right)+12}\\\\\\&#10;\mathsf{=\diagup\hspace{-7}3\cdot \dfrac{x}{\diagup\hspace{-7}3}-3\cdot 4+12}\\\\\\&#10;\mathsf{=x-12+12}\\\\&#10;\mathsf{=x\qquad\quad\checkmark}


and also

•  \mathsf{(g\circ f)(x)}

\mathsf{=g\big[f(x)\big]}\\\\\\ \mathsf{=\dfrac{f(x)}{3}-4}\\\\\\ \mathsf{=\dfrac{3x+12}{3}-4}\\\\\\&#10;\mathsf{=\dfrac{\diagup\hspace{-7}3\cdot (x+4)}{\diagup\hspace{-7}3}-4}\\\\\\&#10;\mathsf{=x+4-4}\\\\&#10;\mathsf{=x\qquad\quad\checkmark}

________


C.  Since f and g are inverse, then

f(g(– 2))

= (f o g)(– 2)

= – 2          <span>✔
</span>

•  Call h the compositon of f and g. So,

h(x) = (f o g)(x)

h(x) = x


As you can see above, there is no restriction for h. Therefore, the domain of h is R (all real numbers).


I hope this helps. =)

5 0
3 years ago
As part of his retirement strategy, John plans to invest $210,000 in two different funds. He projects that the moderately high r
Maslowich

Answer:

Therefore he invested $60,000 at 9% per year and $(210,000-60,000)=$150,000 at 4% per year.

Step-by-step explanation:

Given John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, overtime 9% per year,while low risk investments should return about 4% per year.

He wants a supplemental income of$11,400 a year.

Let , he invested $x at 9% per year and $(210,000-x) at 4% per year.

interest=\frac{prt}{100}   p = principle , r = rate of interest and t = time

The interest earns at 9% per year= \frac{x\times 9\times 1}{100}

The interest earns at 4% per year=\frac{(210,00-x)\times 4 \times 1}{100}

According to the problem,

\frac{x\times 9\times 1}{100}+\frac{(210,00-x)\times 4 \times 1}{100}= 11400

\Leftrightarrow 9x+840000-4x=11400 \times 100

\Leftrightarrow 5x=1140000-840000

\Leftrightarrow x=\frac{300000}{5}

\Leftrightarrow x=60,000

Therefore he invested $60,000 at 9% per year and $(210,000-60,000)=$150,000 at 4% per year.

7 0
3 years ago
What is the answer to y=2x-9
stiv31 [10]

Sorry to break it to you, but...

That's a line equation my dude. There's no answer.

5 0
3 years ago
Read 2 more answers
How do you find the turning point on this graph
USPshnik [31]

Answer:

It is found when the line starts moving up or down.

Step-by-step explanation:

5 0
3 years ago
In the given diagram abc is a right angle with DG CB segment AB is divided into four equal parts . The coordinates of point F ar
pickupchik [31]

Answer:

E(3.75,-2.5)

G(-0.75,-3)

Step-by-step explanation:

Point E is the midpoint of the segment AB, then it has coordinates

\left(\dfrac{-3+6}{2},\dfrac{-1+(-3)}{2}\right)=\left(\dfrac{3}{2},-2\right).

Point F is the midpoint of the segment EB, then it has coordinates

\left(\dfrac{\frac{3}{2}+6}{2},\dfrac{-2+(-3)}{2}\right)=\left(\dfrac{15}{4},-\dfrac{5}{2}\right)=(3.75,-2.5).

Let S be the midpoint of segment CB, then it has coordinates

\left(\dfrac{-3+6}{2},\dfrac{-3+(-3)}{2}\right)=\left(\dfrac{3}{2},-3\right).

Point G is the midpoint of segment CS, then its coordinates are

\left(\dfrac{\frac{3}{2}+(-3)}{2},\dfrac{-3+(-3)}{2}\right)=\left(-\dfrac{3}{4},-3\right)=(-0.75,-3).

6 0
3 years ago
Read 2 more answers
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