Factorizar

1. (a+ b)^3 − 27

2. 2x^2+7x+3

Answer:

Step-by-step explanation:

Let the initial point on the line segment be O. If point A is located at 50 and point B is located at 104, then OA = 50 and OB = 104. Using the vector notation;

AO+OB = AB

(-OA)+OB = AB

-50+104 = AB

AB = 54

If point P divides the segment AB in a ratio 1:5, them AP:PB = 1:5

AP = 54/6

AP = 9

PB = 54-9

PB = 45

Hence the point P is located at 9 units from A and 45 units from B

The fundamental counting principle states that the total number of outcomes for any compound event is found my multiplying the total number of possible outcomes for each event. The spinner has 8 possible outcomes which are the  integers from 1 to 8, each of the two coins has two possible outcomes, a head and a tail.

By the fundamental counting principle, there total number of outcome is calculated as shown below,

There are 32 possible outcomes.

Answer:

Using the fundamental counting principle, the total possible outcomes are:

                                 32

Step-by-step explanation:

The spinner is spun, and 2 coins are flipped.

Now when a spinner is spin then total 8 outcomes are possible.

Since any of the 8 numbers could be obtained on the spin( 1 to 8)

and when a coin is flipped then there are only two possible outcome i.e.

either Head or Tail.

Hence, the total number of possible outcomes are:

                                8×2×2=32

( since the first possibility 8 is possible from spinner and the  '2' outcomes are possible from each of the flip of a coin  )

              Hence, the answer is:

                          32

Answer:

The cost function that represents this scenario is c(x) = 2 + 0.50x .

Option (b) is correct .

Step-by-step explanation:

As given

Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie.

if x equals the number of nights Laura has the movie.

Than the cost function that represents this scenario .

c(x) =  Flat fee + Cost for  x equals the number of nights Laura has the movie.

c(x) = 2 + x × 0.50

c(x) = 2 + 0.50x

Therefore the cost function that represents this scenario is c (x) = 2 + 0.50x .

Option (b) is correct .

Answer:

a = √a b = √5 c = √10

ac/b = (√a)(√10)/√5

= √ 10 × a /√5

= √10a / √5

Rationalize the surd

√10a ×√5/(√5)²

= √50a /5

= 5√2a/ 5

= √2a

The final answer is √2a

Hope this helps

Final answer:

You need to substitute the given values into the ac/b equation. After substitization and simplification, the equation ac/b simplifies to √2.

Explanation:

The equation that we need to evaluate is ac/b, using the variables a, b, and c given in the question. So, substituting the given values, we get:

a * c / b = √a * √10 / √5

Since a is equal to √a, we can replace a with √a in the equation, so it then becomes:

√a * √10 / √5 = √(a*10) / √5

Since a is √a, a*10 is therefore √10, so the equation becomes:

√10 / √5

That simplifies to √2 in its simplest form.

Learn more about Square Roots here:

brainly.com/question/1540542

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Answer:

(C) (2,-1)

Step-by-step explanation:

The given system of equations is :

                           (1)

and                  (2)  

Multiply equation (1) with 2 and then subtract equation (2) from it, we get

⇒

⇒

⇒

Substitute the value of x=2 in equation (1), we get

⇒

⇒

⇒

Therefore, x=2 and y=-1. that is (2,-1).