MATHEMATICS HIGH SCHOOL

What is the solution of the equation? eliminate any extraneous solutions. (−2x + 6)15= (−8 + 10x)15?

Answers

Answer 1
Answer: Divide both sides by 15:  -2x +6 = -8 + 10x
Add 2x to both sides:               6 = -8 + 12x
Add 8 to both sides:                14 = 12x
Divide both sides by 12:          14/12 = x
Reduce the fraction:                  7/6 = x

Answer: x = 7/6

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Divide 7/24 by 35/48 and reduce to lowest fraction

Answers

To divide fractions you multiply the reciprocal of the divisor.

7/24 ÷ 35/48 =
7/24 × 48/35 =
336/840

Now we have to reduce...

336/840 = 168/420 = 84/210 = 42/105 = 6/15 = 2/5

Answer is 2/5

Which fraction is less 2/10 or 5/8 or neither they are equal

Answers

2/10 is less, because with a common denominator they are 8/40 and 25/40.  Since 5/8 = 25/40, and 8/40 is smaller than that, 2/10 is smaller.

Answer:

2/10 is less than 5/8

Step-by-step explanation:

2/10 =0.20

5/8= 0.625

0.20<0.625

Write an equation of a line in slope-intercept form if the slope is ½ and the y-intercept is -2.

Answers

y = mx + b

y = 1/2x - 2

HOPE THIS HELPS!!!!!!

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Answers

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Kelly works in the clothing store where she earns a 20% commission on the clothes she sells. Last Saturday she sold $500 in merchandise. what is her commission for Saturday?

Answers

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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
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