MATHEMATICS HIGH SCHOOL

Which of the following choices is the common difference between the terms of this arithmetic sequence4x + 7y, 8x+ 2y ,12x -3y,16x-8y,20x-13y, ...

a. 5x+4y
b. 4x-5y
c. -5x-4y
d. 5x -4y
e. 4x +5y

Answers

Answer 1
Answer: Choice (b) that is 4x-5y

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Paul drove for one and a half hours at 65 mph before he realized he had forgotten his wallet. How far was he from home?

Answers

He drove for one and half hours = 1  1/2 = 1.5 hours.

Speed = 65 miles per hour.

Distance = Speed * Time

Distance = 65 miles/hour  * 1.5 hours

Distance = 97.5 miles

So Paul was 97.5 miles from home.

There are 229 people attending a convention. Each table seats 8 people. What is the least number of tables needed to seat everyone?__________ tables

Answers

29 tables will be needed.

Angelica is working on function machines. She has two machines g(x)=square root x-5 and h(x)= x^2-6. she wants to put them in order so that the output of the first machine becomes the input of the second. she wants to use a beginning input of 6.a) in what order must she put the machines to get a final output of 5.
b)is it possible for her to get a final output of -5? if so,show how she could do that. If not explain why not.

PLEASE HELP!

Answers

g(h(x))=√(x^2-6-5)=√(x^2-11)\ng(h(6))=√(6^2-11)=√(36-11)=√(25)=5

a)
h(x) is the input for g(x), so h(x) must be first

b)
It's impossible for g(h(x)=√(x^2-11), because its value is always non-negative for any x. Let's see what about h(g(x)).

h(g(x))=(√(x-5))^2-6=x-5-6=x-11

The result is a non-constant linear function, so its value can be any real number, including -5. You can calculate for what x it's equal to -5.

x-11=-5\nx=6

x-11=-5\nx=6

a) To get a final output of 5 , she must first input 6 into machine h(x) , then the result from machine h(x) is input back to machine g(x).

b) It is possible to get a final output of -5. It could be done by first input 6 into machine g(x) , then the result from machine g(x) is input back to machine h(x).

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

  • Linear Function → f(x) = ax + b
  • Quadratic Function → f(x) = ax² + bx + c
  • Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
  • Logarithmic function → f(x) = ln x
  • Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

This problem is about Composition of Functions.

Question a:

Given:

g(x) = √(x - 5)

h(x) = x^2 - 6

( h \circ g )( x ) = h ( g ( x ) )

( h \circ g )( x ) = h ( \sqrt {x - 5} )

( h \circ g )( x ) = (\sqrt {x - 5})^2 - 6

( h \circ g )( x ) = x - 5 - 6

( h \circ g )( x ) = x - 11

( h \circ g )( 6 ) = 6 - 11

\large {\boxed {( h \circ g )( 6 ) = -5 } }

( g \circ h )( x ) = g ( h ( x ) )

( g \circ h )( x ) = g ( x^2 - 6 )

( g \circ h )( x ) = \sqrt {( x^2 - 6 ) - 5 }

( g \circ h )( x ) = \sqrt { x^2 - 11 }

( g \circ h )( 6 ) = \sqrt { 6^2 - 11 }

( g \circ h )( 6 ) = \sqrt { 25 }

\large {\boxed {( g \circ h )( 6 ) = 5 } }

To get a final output of 5 , she must first input 6 into machine h(x) , then the result from machine h(x) is input back to machine g(x).

Question b:

From the results above , it is possible to get a final output of -5.

It could be done by first input 6 into machine g(x) , then the result from machine g(x) is input back to machine h(x).

Learn more

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic

How many halves are there in 14 and a halfhow many halves are there in 14 and a half

Answers

14, 1/2 = 29/2
14 x 2 since it's a half = 28 plus another half is 29 halves :)

How to do recurring decimal and fraction

Answers

Answer:

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A pattern of letter arrangements begins with the 3 steps below, A
ABA
ABCBA

what are the next 3 steps, how many letters are in the 3 above and how many letters are in the 10th step?

Answers

The 10th step have 19 letters.

What is Arithmetic Progression?

We can define an arithmetic progression (AP) in two ways:

  • An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.
  • An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term.

In first pattern

number of letters= 1

In second pattern

number of letters= 3

In third pattern

number of letters= 5

so,  we can create a series as

1,3,5,.....

a=1, d= 2

Now, for a_10= a+ 9d

=1 + 9*2

=1+18

=18

Hence, the 10th step have 19 letters.

Learn more Arithmeticprogression here:

brainly.com/question/20385181

#SPJ2


next 3 steps:

ABCDCBA
ABCDEDCBA
ABCDEFEDCBA

Patern: add 2 letters

1. 1
2. 3
3. 5
4. 7
5. 9
6. 11
7. 13
8. 15
9. 17
10. 19

The 10th step has 19 letters
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