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Answers

Answer 1

Answer: we have an geometric progression:
nth term=a₁r^(n-1)
nth term=y
a₁ is the first term=10
r=common ratio=a₂/a₁=20/10=2
n=x
nth term=a₁r^(n-1)

Therefore
y=10.2^(x-1)=(2*5)2^(x-1)=(5)2^(x-1+1)=(5)2^x

Answer: y=[5][(2)]^[x]

To check:
if x=1 ⇒y=(5)(2)=10
if x=2 ⇒y=(5)(4)=20
if x=3 ⇒y=(5)(8)=40

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Yoko paid $10.70 for stamps. She bought three times as many 25 cent stamps as 14 cent stamps, twice as many 2 cent stamps
as 25 cent stamps and the same number of one-cent stamps as
2 cent stamps. How many stamps of each type did Yoko buy?

Answers

Answer:

30 of 25 cent, 10 of 14 cent, 60 of 2 cent

Step-by-step explanation:

Note: it must be typo 10.70, changed to 10.10

Number of 25 cent stamps = x

Number of 14 cent stamps = y

Number of 2 sent stamps = z

Total = $10.10 = 1010 ¢
x = 3y
z = 2x ⇒ z = 6y

Solving equation

25x + 14y + 2z = 1010
25(3y) + 14y + 12y = 1010
75y + 26y = 1010
101y = 1010
y = 1010/101
y = 10

The finding x and z

x = 3*10 = 30
z = 6*10 = 60

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A bride wants to serve her 175 guests cheesecake instead of wedding cake. She purchases 14 cheesecakes that serve 12 people each. If each guest is served only one piece of cheesecake, how many guests will not get a piece?_________________ guests

Answers

seven guests will not get served

Your answer is 7 guests.

Hope this helps.

If f(x)=|x−4|+5, find f(1).

Answers

Answer:

Step-by-step explanation:

To find f(1), substitute x = 1 into the given function f(x)

(output values from an absolute value become positive)

$f(1) = |1-4|+5\nf(1)=|-3|+5\nf(1)=3+5\nf(1)=8$

Hope this helps!

An experiment consists of tossing a coin and drawing a card, with the card-drawing stage dependent on the result of the coin toss. If heads occurs, then a card is selected at random from the clubs and spades suits. If tails occurs, then a card is selected at random from the hearts and diamonds suits. What is the size of the sample space of this two-stage experiment?

Answers

well .5 for coin toss and with 52 cards in deck and clubs and spades makes it 26 so its 1/26 then those are your probabilities.

Answer:th answer is 7

Step-by-step explanation:

the answer is 7

True or false: Polar equations can describe graphs as functions, even when their equations in the rectangular coordinate system are not functions.

Answers

The statement above is true. Polar equations indeed can describe graphs as functions, even if when the equations in the rectangular coordinate system are not one of the functions. Polar equations can be graphed accurately using hands by using the Polar Coordinate System.

Answer:

The answer is true.

Step-by-step explanation:

A polar equation describes the relation between r and θ. Here 'r' is the distance from the origin to a point curve. 'θ' is the angle made by a point on a curve, the pole, and the positive x-axis.

So, the statement - Polar equations can describe graphs as functions, even when their equations in the rectangular coordinate system are not functions - is true.

Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? x(x2 + 4) + 5(x2 + 4) x2(x + 4) + 5(x + 4) x2(x + 5) + 4(x + 5) x(x2 + 5) + 4x(x2 + 5)

Answers

x²(x + 4) + 5(x + 4)

Further explanation

Factoring (also called factorization) is the reserve operation of multiplication. When we factor (or factorize) a polynomial, we write it as a product of its factors.

Grouping is one of the factoring methods. Other methods such as isolating common factors and identities.

Steps for grouping:

We group the terms with a common factor.
We can isolate a common factor and put it outside the parentheses.

Let’s start.

$\boxed{ \ x^3 + 4x^2 + 5x + 20 = \ ? \ }$

$\boxed{ \ = (x^3 + 4x^2) + (5x + 20) \ }$

$\boxed{\boxed{ \ = x^2(x + 4) + 5(x + 4) \ }}$

We can also group the terms as follows.

$\boxed{ \ x^3 + 4x^2 + 5x + 20 = \ ? \ }$

$\boxed{ \ = (x^3 + 5x) + (4x^2 + 20) \ }$

$\boxed{\boxed{ \ = x(x^2 + 5) + 4(x^2 + 5) \ }}$

We will get the same results from the two ways above. Let's see.

First group, $\boxed{ \ x^2(x + 4) + 5(x + 4) \ } \rightarrow \boxed{ \ (x + 4) (x^2 + 5) \ }$
Second group, $\boxed{ \ x(x^2 + 5) + 4(x^2 + 5) \ } \rightarrow \boxed{ \ (x^2 + 5) (x + 4) \ }$

Thus the part which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping is $\boxed{\boxed{ \ x^2(x + 4) + 5(x + 4) \ }}$

Learn more

Which expression is equivalent to the product of a binomial and a trinomial after it has been fully simplified brainly.com/question/1394854
The y-intercept of the quadratic function f(x) = (x – 6)(x – 2) brainly.com/question/1332667
Which is the graph of f(x) = (x - 1)(x + 4) brainly.com/question/2334270

Keywords: which shows, one way, to determine, the factors of x³ + 4x² + 5x + 20, by grouping, common factor, polynomial, identities

The correct option is $\fbox{\text{Option B}}$ that is ${x^2}\left( {x + 4} \right) + 5\left( {x + 4} \right)$ that shows one way to determine the factors of ${x^3} + 4{x^2} + 5x + 20$ .

Further explanation:

Factors are the numbers if we multiply them we get the original number.

Factorization is finding the numbers if we multiply them we get the original number.

Prime factorization is finding the numbers if we multiply them we get the original number.

Given:

The polynomial is ${x^3} + 4{x^2} + 5x + 20$ .

The options are,

A. $x\left( {{x^2} + 4} \right) + 5\left( {{x^2} + 4} \right)$ .

B. ${x^2}\left( {x + 4} \right) + 5\left( {x + 4} \right)$ .

C. ${x^2}\left( {x + 5} \right) + 5\left( {x + 5} \right)$ .

D. $x\left( {{x^2} + 5} \right) + 4x\left( {{x^2} + 5} \right)$

Explanation:

Consider the polynomial ${x^3} + 4{x^2} + 5x + 20$ as $P\left( x \right)$ .

Steps involve in finding the factors of ${x^3} + 4{x^2} + 5x + 20$ are as follows,

First we have to make the groups of the terms as,

$P\left( x \right) = \left( {{x^3} + 4{x^2}} \right) + \left( {5x + 20} \right)$

Now factorize the above 2 groups.

$\begin{gathered}P\left( x \right) = {x^2}\left( {x + 4} \right)+5\left( {{x^2}+4} \right)\n= \left( {{x^2}+5} \right)\left( {x+4} \right) \n\end{gathered}$

The factors of ${x^3} + 4{x^2} + 5x + 20\text{ } \text{are} \left( {{x^2} + 5} \right) \text{and} \left( {x + 4} \right)$ .

Option A is not correct as the first common factor is $x$ from group one but it not the highest common factor.

$\fbox{\text{Option B}}$ is correct as the factors are same as the factors of the polynomial.

Option C is not correct as the factors are not same as the factors of the polynomial.

Option D is not correct as the factors are not same as the factors of the polynomial.

Learn more:

1. Learn more about the polynomial brainly.com/question/12996944

2. Learn more about logarithm model brainly.com/question/13005829

3. Learn more about the product of binomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Polynomials

Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

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