400

Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respective

kifflom [539]

233 base five = 2 x 5^2 + 3 x 5 + 3 x 1 = 2 x 25 + 15 + 3 = 50 + 18 = 68 base 10

11000 base two = 1 x 2^4 + 1 x 2^3 = 16 + 8 = 24 base ten

43E base twelve = 4 x 12^2 + 3 x 12 + 11 x 1 = 4 x 144 + 36 + 11 = 576 + 47 = 623 base ten

5 0

3 years ago

a language arts test is worth 100 points there is a total of 26 questions . there are spelling word questions that ae worth 2 po

natka813 [3]

10 question of spelling words and 16 questions of vocabulary are present

Solution:

Let "x" be the number of spelling word questions

Let "y" be the number of vocabulary word question

There is a total of 26 questions. Therefore, we get

number of spelling word questions + number of vocabulary word question = 26

x + y = 26 --------- eqn 1

There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each

The language arts test is worth 100 points

Therefore, we frame a equation as:

number of spelling word questions x 2 + number of vocabulary word question x 5 = 100

$x \times 2 + y \times 5 = 100$

2x + 5y = 100 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 26 - y ------- eqn 3

Substitute eqn 3 in eqn 2

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

3y = 100 - 52

3y = 48

Substitute y = 16 in eqn 3

x = 26 - 16

Thus 10 question of spelling words and 16 questions of vocabulary are present

4 0

3 years ago

Simplify -3x^3(2x^2+3)+9x^4

SIZIF [17.4K]

Answer:

ANSWER = −6x^5 +9x^4 − 9x^3

Step-by-step explanation:

Let's simplify step-by-step.

(−3x^3) (2x^2 + 3) + 9x^4

Distribute:

=(−3x^3) (2x^2) + (−3x^3) (3) + 9x^4

=−6x^5 + − 9x^3 + 9x^4

Answer:

= −6x^5 +9x^4 − 9x^3

3 0

3 years ago

If exactly 180 people sign up for a charter flight, Leisure World Travel Agency charges $298/person. However, if more than 180 p

lesantik [10]

Answer:

The max. revenue is $57,121.

This happens with 239 passengers.

The price of the ticket is $239 per person.

Step-by-step explanation:

Let the variable "P" denote the number of passengers.

If P=180, then the ticket cost is $298/person. Then the price is reduced by $1 for each additional person.

In general, if P=(180+x), then the ticket cost becomes (298-x) per person.

The revenue can be defined as the ticket cost multplied by the number of passengers:

$R=P*T=(180+x)(298-x)=53,640-180x+298x-x^2\\\\R(x)=-x^2+118x+53,640$

We can derive R and equal to zero to maximize the function.

$dR/dx=-2x+118=0\\\\x=118/2=59$

The amount of passengers is:

$P=180+x=180+59=239$

The price of the tickets is

$T=298-59=239$

The revenue is:

$R(59)=(180+59)(298-59)=239*239\\\\R(59)=57,121$

3 0

3 years ago

What is the solution to −4x+5y=−12 x−6y=22

lara31 [8.8K]

Answer:

The solution to the system is S= (-2, -4).

Step-by-step explanation:

Given the system

−4x+5y=−12

x−6y=22

The first step is to solve x from the first equation for example, and substitute the expression in the second equation.

1) -4x + 5 y = -12 ⇒ -4x = -12 - 5y ⇒ x = (-12 - 5y)/-4 ⇒ x = 3 + (5/4)y

2) x - 6y = 22 ⇒ (3 + (5/4)y) - 6y = 22 ⇒ 3 + (5/4)y - 6y = 22

⇒ 3 - (19/4)y = 22 ⇒ (-19/4)y = 22- 3 ⇒ y = 19/(-19/4) ⇒ y =-4.

Finally, with the value obtained for "y", you have to return to the original equations and replace it to obtain the "x" value.

-4x + 5y = -12 ⇒ -4x + 5(-4) = -12 ⇒ -4x - 20 = -12 ⇒ -4x = -12 + 20

⇒ -4x = 8 ⇒ x = 8/-4 ⇒ x = -2.

Summarizing, the solution to this system is S = (-2, -4).

7 0

3 years ago