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2 years ago

Solve the system using the substituion method -4x+y=8 x-3y=9

1 answer:

3 0

Hi there!

x - 3y = 9
x = 9 + 3y

-4x + y = 8
-4(9+3y) + y = 8
-36 - 12y + y = 8
-36 - 11y = 8
-11y = 44
-y = 4
y = -4

x - 3y = 9
x - 3(-4) = 9
x + 12 = 9
x = 21

So, your answers are y = -4 and x = 21.

Hope this helps!

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Solve for x. 8(9x-4)-2=3+2

gavmur [86]

So first you have to move the -2 over to the opposite side.
8(9x-4)=3+2+2
Then you can simplify the right side
8(9x-4)=7
Then you distribute
8*9x=72x
8*-4=-32
so now you have...
72x-32=7
Then you move the 37 over
72x=39
Then you divide by 72 to isolate x
x=39/72 or x= 13/24 or x=0.54167

6 0

2 years ago

Wilhelmina wrote a check for $72 to pay her monthly Internet bill, but when

lesantik [10]

Answer:

her bank statement will show that she has $144 less than her checkbook balance

Step-by-step explanation:

let the amount of money in the bank before writing the check be x

after writing the check for $72, because she accidentally recorded this as a credit, here checkbook will reflect a balance of :$(x + 72)

However, the bank correctly records the debit of the $72, resulting a balance of: $(x-72)

Hence compared to her checkbook, the bank records will show an amount difference of :

(x-72) - (x + 72)

= x - 72 -x -72

= -144

i.e her bank statement will show that she has $144 less than her checkbook balance

3 0

2 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: $y'' = \frac{8}{(x+2)^3}$