Looking for an algebraic equAtion answer.. 2x + y = 1 4x

a recipe calls for a total of 3 2/3 cups of flour and sugar. it the recipe calls for 1/4 cup of sugar, how much flour is needed?

zavuch27 [327]

Answer:

This is very detailed as I wish to make some principles about fractions clear.

3

5

12

Explanation:

This question boils down to

3

2

3

−

1

4

A fractions structure is that of:

count

size indicator of what you are counting

→

numerator

denominator

You can not directly add or subtract the counts (numerators) unless the size indicators (denominators) are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider

3

2

3

Write as

3

+

2

3

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its true value

[

3

×

1

]

+

2

3

[

3

×

3

]

+

2

3

9

3

+

2

3

=

11

3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Putting it all together

3

2

3

−

1

4

→

11

3

−

1

4

But the size indicators are not the same. I chose to make them become 12

11

3

−

1

4

→

[

11

3

×

1

]

−

[

1

4

×

1

]

→

[

11

3

×

4

]

−

[

1

4

×

3

]

→

44

12

−

3

12

Now we may subtract the counts

→

44

−

3

12

=

41

12

But this is the same as

12

+

12

+

12

+

5

12

=

1

2

+

2

1

2

+

2

1

2

+

5

12

=

3

5

12

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

6 0

3 years ago

Read 2 more answers

5y + 3 > −7y + 13 Multi-step linear inequalities

Artemon [7]

Answer:

y > $\frac{5}{6}$

Step-by-step explanation:

Given

5y + 3 > - 7y + 13 ( add 7y to both sides )

12y + 3 > 13 ( subtract 3 from both sides )

12y > 10 ( divide both sides by 12 )

y > $\frac{10}{12}$ , that is

y > $\frac{5}{6}$

3 0

3 years ago

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16

jolli1 [7]

To find the time at which both balls are at the same height, set the equations equal to each other then solve for t.
h = -16t^2 + 56t
h = -16t^2 + 156t - 248
-16t^2 + 56t = -16t^2 + 156t - 248
You can cancel out the -16t^2's to get
56t = 156t - 248
=> 0 = 100t - 248
=> 248 = 100t
=> 2.48 = t
Using this time value, plug into either equation to find the height.
h = 16(2.48)^2 + 56(2.48)
Final answer:
h = 40.4736
Hope I helped :)

6 0

4 years ago

Read 2 more answers

TIMED I REALLY NEED HELP/////////

leva [86]

It will be 3:45. You can find this by going ahead 3 hours, then going ahead a half an hour.

5 0

3 years ago

Read 2 more answers

Looking for an algebraic equAtion answer.. 2x + y = 1 4x - 2y = 6 Can you help?