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2 years ago

Given f(x)=3x^3+2x+k and x+1 is a factor of f(x) then what is the value of k

Mathematics

1 answer:

yaroslaw [1]2 years ago

3 0

Answer:

k = 5

Step-by-step explanation:

Given that (x + 1) is a factor of f(x) then f(- 1) = 0

f(- 1) = 3(- 1)³ + 2(- 1) + k

= 3(- 1) - 2 + k

= - 3 - 2 + k

= - 5 + k

Then - 5 + k = 0 ( add 5 to both sides )

k = 5

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An Ontario lottery has the following structure, the first person drawn from the names wins $15 000. Each subsequent person drawn

elixir [45]

The first four terms are : 15000, 14850, 14700, 14550
a = 15000 ; d = -150
The explicit formula is : $a_{n} = - 150n \: + 15150$

The first term of the sequence, a = 15,000

Each subsequent winner gets $150 less

Hence, the common difference, d = - $150

The first four terms :

First term, a1 = $15000

Second term, a2 = a - d = $15000 - $150 = $14850

Third term, a3 = a2 - d = $14850 - $150 = $14700

Fourth term, a4 = a3 - d = $14700 - $150 = $14550

a, for the sequence is the first term = $15000

d, for the sequence is the common $150 (difference between successive wins).

Explicit formula for the general term :

$a_{n} \: = nd \: + c$

For n = 1

$15000 = 1( - 150) + c$

$15000 = - 150 + c$

$c = 15150$

Hence, the explicit formula for the nth term is :

$a_{n} \: = - 150n \: + 15150$

Learn more : brainly.com/question/12006170

3 0

2 years ago

A large cheese pizza costs $18. Each topping you add on costs $1.50. How much would it cost to get a large cheese pizza with cc

grigory [225]

Answer:

$\$18+\$1.50c$

Step-by-step explanation:

Let

y------> the total cost

c-----> the number of topping

we know that

$y=\$18+\$1.50c$ ----> linear equation that represent the situation

7 0

2 years ago

I need help, i do not understand, this is pythagorean theorem

ser-zykov [4K]

Answer:

11.2

Step-by-step explanation:

First draw an imaginary straight line to separate the two shapes.

You will have a side of 10 in the traingle

And a side of 13 - 8 =5

Then

Using pythagoras theorem

Sqrt(10^2+5^2)=11.180

5 0

2 years ago

What is the distance between the points (-4,2) and (3,-5)

34kurt

Answer:

7√2 units

Step-by-step explanation:

The distance between two points having coordinates (x1, y1) and (x2, y2) is given by,

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

Here, x1=-4 and y1=2

x2=3 and y2=-5

$\sqrt{ {(3 - ( - 4))}^{2} + {( - 5 - 2)}^{2} }$

$\sqrt{ {(3 + 4)}^{2} + {( - 7)}^{2} }$

$\sqrt{ {(7)}^{2} + {( - 7)}^{2} }$

$\sqrt{49 + 49} = 7 \sqrt{2}$

6 0

2 years ago

Read 2 more answers

Xanthe and Sarah do some fundraising for their local nursing home. Together they raised $$$302. If Xanthe raised $$$102 more tha

Dimas [21]

Given :

Xanthe and Sarah together raised $302 .

If Xanthe raised $102 more than Sarah .

To Find :

The amount raised by Sarah .

Solution :

Let , amount raise by Sarah is x .

So , by the relation given , price raised by Xanthe is 102 + x .

Now , sum of their amount raised is :

$x+(x+102)=302\\\\2x=302-102\\\\x=\$100$

Therefore , the amount raised by Sarah is $100 .

Hence , this is the required solution .

6 0

2 years ago