If p+q+r = 1 and pq+qr+pr = -1, and pqr = -1, find the value of $p^(3)+ q^(3)+ r^(3)$

Answers

Answer 1

Answer: pq+qr+pr= pqr (because they are both equal to -1)
then you divide both sides by p to get
q+ qr/p + r = qr. then you divide both sides by q and get
r/p + r/q = r. so I divided both sides by r to get
P + q =0 therefore p= -q. putting that into the first equation allows you to get that r=1 because p and q cancel each other out. then I put that into pq+qr+pr=-1 so pq+q+p=-1 since p=-q the q+p gets canceled out and you're left with pq=-1 and since it is the product of the two numbers and q is the negative of p. q=-1 while p=1. therefore p=1 r=1 and q=-1

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B.
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Answers

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The blanco family is deciding between two lawn care services. Evergreen charges a $49 startup fee, plus $29 per month. Great Grass charges a $25 starup fee, plus $37 per month. In how many months will both lawn-care services cost the same? What will the cost be?

Answers

In three months their money will be equal and the amount is $136.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Given that, the Blanco family is deciding between two lawn care services.

Evergreen charges a $49 startup fee, plus $29 per month.

Let the number of months be x.

Here, 49+29x -----(i)

Great Grass charges a $25 starup fee, plus $37 per month.

So, 25+37x ------(ii)

Both lawn-care services cost the same

Equation (i) and (ii) are equal, we get

49+29x=25+37x

37x-29x=49-25

8x=24

x=3

Now, 49+29x=$136

25+37x=$136

Therefore, in three months their money will be equal and the amount is $136.

To learn more about an equation visit:

brainly.com/question/14686792.

#SPJ2

MATH!!!!!!!! Help please

Answers

Answer:

Step-by-step explanation:

f(3) means what is the value of f(x) when x = 3

From the table

When x = 3 then f(x) = 9

Thus f(3) = 9

4 1/2 + 5 2/4 i need work shown will give 15 points

Answers

Answer:

The answer is 10

Step-by-step explanation:

Hopefully this helps

If the terminal ray of β lies in the fourth quadrant and sin (β) = -√3/3 determine cos(β) in simplest form.

Answers

Answer:

$cos(\beta)=(√(6))/(3)}$

Step-by-step explanation:

we know that

If the terminal ray of β lies in the fourth quadrant

then

sin (β) is negative and cos (β) is positive

Remember the trigonometric identity

$sin^2(\beta)+cos^2(\beta)=1$

we have

$sin(\beta)=-(√(3))/(3)$

substitute

$(-(√(3))/(3))^2+cos^2(\beta)=1$

$(3)/(9)+cos^2(\beta)=1$

$cos^2(\beta)=1-(3)/(9)$

$cos^2(\beta)=(6)/(9)$

apply root square both sides

$cos(\beta)=(√(6))/(3)}$

A garden contains 20 different species of plants. Five of these plants are ferns. What percent of the garden is made up if ferns?

Answers

Answer:

25%

Step-by-step explanation:

A garden contains 20 different species of plants. Five of these plants are ferns.

Total number of species = 20

In that 20 species , 5 are ferns

WE need to find out how much percentage of 20 is 5

LEts make an equation. x be the percentage

x% of 20 is 5

$(x)/(100) \cdot 20 = 5$

$(x)/(5)= 5$

Now multiply both sides by 5

x= 25

So 25% of 20 species plans is equal to 5 ferns

5 out of 20 plants can be written as 5/20.

A percentage is just a fraction with the denominator being 100.
100 / 20 = 5.
5 X 5 = 25
25/100

25% of the garden is made up of ferns

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