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2 years ago

The nth term of a sequence is given by 12 - 5n. Write down the first 3 terms of the sequence.

Mathematics

1 answer:

zysi [14]2 years ago

6 0

Answer:

$\bold{a_1=7\,,\quad a_2=2\,,\quad a_3=-3}$

Step-by-step explanation:

$a_n=12-5n\\\\\\a_1=12-5\cdot1=12-5=7\\\\a_2=12-5\cdot2=12-10=2\\\\a_3=12-5\cdot3=12-15=-3$

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A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0

2 years ago

Please help it would be much appreciated!

sergiy2304 [10]

Answer:

Part a) Option d

Part b) Option a

Step-by-step explanation:

Part a

if we look at the options given and the data available

Option a) x^4+9

Putting x= 2 we get (2^4) + 9 =25

Putting x= 3 we get (3^4) + 9 =90 but f(x) =125 so not correct option

Option b) (4^x)+9

Putting x= 2 we get (4^2) + 9 =25

Putting x= 3 we get (4^3) + 9 =73 but f(x) =125 so not correct option

Option c) x^5

Putting x= 2 we get (2^5) =32 but f(x) =25 so not correct option

Option d) 5^x

Putting x= 2 we get (5^2) =25

Putting x= 3 we get (5^3) =125

Putting x= 4 we get (5^4) =625

So Option d is correct.

Part (b)

3(2)^3x

can be solved as:

=3(2^3)^x

=3(8)^x

So, correct option is a

8 0

3 years ago

Find the present value of $10,000 payable in five years at 6% simple interest.

Svet_ta [14]

We know, I = P * R * T /100
Here, P = 10,000
R = 6%
T = 5

Substitute their values into the expression,
I = 10000 * 6 * 5 /100
I = 300000 / 100
I = 300

Final Amount = Initial Amount + Interest Amount
Final Amount = 10,000 + 300 = 10,300

So, your final answer is $10,300

Hope this helps!

6 0

3 years ago

Please help! Find all the missing angles ??

Natasha2012 [34]

Answer:

A 62°

B 118°

C 62°

D 118°

E 50°

F 58°

G 120°

H 120°

I 120°

J 60°

K 60°

L 60°

M 120°

N 120°

P 60°

Q 35.5°

R 49°

S 35.5°

T 109°

U 71°

V 109°

W 60°

5 0

3 years ago

Which term is a term in this expression? A. x+4 B. -7 C. -3 D. -3x

svp [43]

Answer: -3x is a term

Step-by-step explanation: Any number that has a variable after it is a term. Another way to look at it is any grouping of a number and a variable. If the number stands alone, it's not a term, and if it is being added to something, it is an equation.

7 0

3 years ago