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Murrr4er [49]
3 years ago
9

3x - 4y = -16 2x - 4y = -8 what is x and y

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
4 0

Answer:

x = -8 , y = -2

Step-by-step explanation:

Solve the following system:

{3 x - 4 y = -16 | (equation 1)

2 x - 4 y = -8 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{3 x - 4 y = -16 | (equation 1)

0 x - (4 y)/3 = 8/3 | (equation 2)

Multiply equation 2 by 3/4:

{3 x - 4 y = -16 | (equation 1)

0 x - y = 2 | (equation 2)

Multiply equation 2 by -1:

{3 x - 4 y = -16 | (equation 1)

0 x+y = -2 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x+0 y = -24 | (equation 1)

0 x+y = -2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = -8 | (equation 1)

0 x+y = -2 | (equation 2)

Collect results:

Answer: {x = -8 , y = -2

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If the gradient of the tangent to
Marizza181 [45]

Answer:

Point A(9, 3)

General Formulas and Concepts:

<u>Pre-Algebra</u>  

Order of Operations: BPEMDAS  

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties  

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Algebra I</u>  

  • Coordinates (x, y)
  • Functions
  • Function Notation
  • Terms/Coefficients
  • Anything to the 0th power is 1
  • Exponential Rule [Rewrite]:                                                                              \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Rule [Root Rewrite]:                                                                     \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}  

<u>Calculus</u>  

Derivatives  

Derivative Notation  

Derivative of a constant is 0  

Basic Power Rule:  

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle y = \sqrt{x}<em />

<em />\displaystyle y' = \frac{1}{6}<em />

<em />

<u>Step 2: Differentiate</u>

  1. [Function] Rewrite [Exponential Rule - Root Rewrite]:                                   \displaystyle y = x^{\frac{1}{2}}
  2. Basic Power Rule:                                                                                             \displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}
  3. Simplify:                                                                                                             \displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}
  4. [Derivative] Rewrite [Exponential Rule - Rewrite]:                                          \displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}
  5. [Derivative] Rewrite [Exponential Rule - Root Rewrite]:                                 \displaystyle y' = \frac{1}{2\sqrt{x}}

<u>Step 3: Solve</u>

<em>Find coordinates of A.</em>

<em />

<em>x-coordinate</em>

  1. Substitute in <em>y'</em> [Derivative]:                                                                             \displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}
  2. [Multiplication Property of Equality] Multiply 2 on both sides:                      \displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}
  3. [Multiplication Property of Equality] Cross-multiply:                                      \displaystyle \sqrt{x} = 3
  4. [Equality Property] Square both sides:                                                           \displaystyle x = 9

<em>y-coordinate</em>

  1. Substitute in <em>x</em> [Function]:                                                                                \displaystyle y = \sqrt{9}
  2. [√Radical] Evaluate:                                                                                         \displaystyle y = 3

∴ Coordinates of A is (9, 3).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

7 0
3 years ago
Choose all items where the equation matches the given table
sdas [7]

Answer:

1st, 3rd, 4th

Step-by-step explanation:

1st one: 43 x

multiply x by 43

7 x 43 = 301

7 x 43 = 258

10 x 43 = 430

3 x 43 = 129

4 x 43 = 172

(correct)

2nd one: 12x

multiply x by 12

2 x 12= 32

we know that 2 x 12 is 2 so this equation does not work

(incorrect)

3rd one: 202x

multiply x by 202

6 x 202 = 1212

4 x 202 = 808

10 x 202 = 2020

3 x 202 = 606

8 x 202 = 1616

(correct)

4th one: 13x

multiply x by 3

9 x 13 = 117

2 x 13 = 26

7 x 13 = 91

3 x 13 = 36

10 x 13 = 130

(correct)

3 0
2 years ago
Carl wants to plant a garden that is 1 1/2 yards long and has an area of 3 1/2 yd.² how wide should the Garden be
lesya692 [45]
L= length= 1 1/2 yards
A= area= 3 1/2 yards^2
w= width

Area= length * width
plug in numbers you know
3 1/2= (1 1/2)(w)
convert to improper fractions
(3*2+1)/2= ((1*2+1)/2)(w)
7/2= 3/2w
divide both sides by 3/2
7/2 ÷ 3/2= w
to divide fractions, multiply by the reciprocal/inverse of 3/2
7/2 * 2/3= w
(7*2)/(2*3)= w
14/6= w
reduce by 2
7/3= width as improper fraction
OR
2 1/3= width as mixed fraction

ANSWER: The width should be 2 1/3 yards wide (or 7/3 yards wide).

Hope this helps! :)
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I’m not sure what the answer is but I hope someone helps you. Have a nice day‼️12
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