Ben bought 1/2 pound if cheese for 3 sandwiches. If he puts the same amount of cheese on each sandwich, how much cheese will each sandwich have?

Answers

Answer 1

Answer: Given:
1/2 pound of cheese
3 sandwiches

To need to divide the 1/2 pound of cheese by 3 sandwiches to get the equal amount of cheese each sandwich must have.

1/2 ÷ 3 = 1/2 * 1/3 = 1/6 pound per cheese

Each sandwich contains 1/6 pound of cheese from the 1/2 pound of cheese available.

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What is the slope and y-intercept of this line?y = –3x + 9
A. slope: 3, y-intercept: –9
B. slope: –3, y-intercept: 9
C. slope: 1, y-intercept: –3
D. slope: 9, y-intercept: –3

Answers

The slope and y-intercept of the given line are -3 and 9 respectively.

What is equation of a line?

The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers.

When we represent the equation geometrically, we always get a straight line.

Given that, an equation of a line y = -3x+9, we need to determine the slope and the y-intercept of this line,

The slope of a line tell about the steepness and the y-intercept tells the point where it intersects the y-axis,

The slope-intercept form of the equation of a line is given by ;

y = mx+c

Here, m is the slope and c is the y-intercept,

So, the given equation is y = -3x+9

Comparing with the slope-intercept form,

m = -3 and y-intercept = 9

Hence, the slope and y-intercept of the given line are -3 and 9 respectively.

Learn more about equation of a line, click;

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Slope is -3
Y-intercept is 9

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

Inverse of Function : brainly.com/question/9289171
Rate of Change : brainly.com/question/11919986
Graph of Function : brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic

If g(y) = 5y, then solve g(-10)

Answers

Answer:

-50

Step-by-step explanation:

g(y) = 5y

Let y= -10

g(-10) = 5*-10

= -50

In the xy -plane, what is the y -intercept of the graph of theequation y =2(x+ 3)(x- 4)?
A. 24
B. 12
C. 2
D. 12

Answers

I don't think the correct y-intercept is offered as one of the choices.

   y = 2 (x + 3) (x - 4)

Where the graph crosses
the y-axis, x=0 : y = 2 (0 + 3) (0 - 4)

   y = 2 ( 3 ) ( -4 )

   y = 2 ( -12 ) = -24

How are equivalent fractions used when subtracting unlike fractions

Answers

they are used because when fractions Come you have to multiple and divide and subtract

Translate the sentence into an equation.
Seven times the sum of a number and 5 equals 2.

Answers

Answer: 7(x + 5) = 2

Step-by-step explanation:

Use the variable x to represent the number

7(x +5) = 2

Answer:

7(x+5)=2 x= -33/7

Step-by-step explanation:

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