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2 years ago

Please help me with this problem

Mathematics

1 answer:

Rom4ik [11]2 years ago

6 0

y=x^2 + x - 2

x + y = 1

Replace y in the second equation:

x + x^2 + x -2 = 1

Simplify:

x^2 + 2x -2 = 1

Subtract 1 from both sides:

x^2 + 2x -3 = 0

Factor:

(x-1) (x+3) = 0

Solve for both x's:

x = 1 and x = -3

Now replace x in the second equation and solve for y using both x values:

1 + y = 1, y = 0

-3 + y = 1, y = 4

Now you have (1,0) and (-3,4) as solutions for (x,y)

XY = x times y:

1 x 0 = 0

-3 x 4 = -12

The answer would be -12

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I run a 10km race in 56 minutes.what is my average speed in kilometres per minute

Luden [163]

Hey there! I'm happy to help!

You ran a 10 kilometer race in 56 minutes (good job!). To find how much you ran in 1 minute, you simply divide by 56.

10/56=0.178571428

Therefore, you ran around 0.18 km/minute.

Have a wonderful day! :D

7 0

3 years ago

Find the solution set of this inequality|10x+20| ≤10

Pavlova-9 [17]

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

$|10x+20|\leq 10$

Firstly, we will find critical values

so, let's assume it is equal

$|10x+20|= 10$

now, we can break absolute sign

For $|10x+20|= -(10x+20)$ :

$-(10x+20)= 10$

we can solve for x

$-10x-20= 10$

Add both sides by 20

$-10x-20+20= 10+20$

$-10x= 30$

Divide both sides by -10

and we get

$x=-3$

For $|10x+20|= (10x+20)$ :

$(10x+20)= 10$

we can solve for x

$10x+20= 10$

Subtract both sides by 20

$10x+20-20= 10-20$

$10x= -10$

Divide both sides by 10

and we get

$x=-1$

so, critical values are

$x=-3$

$x=-1$

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For $(-\infty,-3)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

$|10\times -5+20|\leq 10$

$|-50+20|\leq 10$

$30\leq 10$

so, this is FALSE

For $[-3,-1]$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

$|10\times -2+20|\leq 10$

$|-20+20|\leq 10$

$0\leq 10$

so, this is TRUE

For $(-1,\infty)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

$|10\times 0+20|\leq 10$

$|0+20|\leq 10$

$20\leq 10$

so, this is FALSE

so, solution is

[-3,-1]

7 0

2 years ago

A) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s.

Fed [463]

Answer:

A) $a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

B) $a_{0} = a_{1} = 0$

C) for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

Step-by-step explanation:

A) A recurrence relation for the number of bit strings of length n that contain a pair of consecutive Os can be represented below

if a string (n ) ends with 00 for n-2 positions there are a pair of consecutive Os therefore there will be : $2^{n-2}$ strings

therefore for n ≥ 2

The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

b ) The initial conditions

The initial conditions are : $a_{0} = a_{1} = 0$

C) The number of bit strings of length seven containing two consecutive 0s

here we apply the re occurrence relation and the initial conditions

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

7 0

2 years ago

What is the area of a regular octagon with a side length of 4.6 meters and a length from the center to a vertex of 6 meters? HEL

Shtirlitz [24]

<span>What is the area of a regular octagon with a side length of 4.6 meters and a length from the center to a vertex of 6 meters?

Good Morning

The Correct Answer is c) 101.2

Hope I Helped

-Nullgaming650

</span>

6 0

2 years ago

A community sports league is raising money by making custom shirts to sell at league games. They plan to sell the shirts for $14

11111nata11111 [884]

Answer:

A. (14 – 7)n – 55

Step-by-step explanation:

it cost $14 to make so $14 - $7 to make then you have to advertise it AFTER and it takes more money to advertise so, -55 so the answer would be:

(14 – 7)n – 55

5 0

2 years ago

Please help me with this problem​

Please help me with this problem