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2 years ago

If y=3x and 2x−4y=3 , then x=

Mathematics

2 answers:

tatiyna2 years ago

3 0

Answer:

x = -3/10

Step-by-step explanation:

Solve for x by substituting y = 3x into the other equation:

2x - 4y = 3

2x - 4(3x) = 3

Simplify and solve for x:

2x - 12x = 3

-10x = 3

x = -3/10

So, x = -3/10

riadik2000 [5.3K]2 years ago

3 0

Answer:

$x=-\frac{3}{10}$

Step-by-step explanation:

2x - 4y = 3

y = 3x

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

2x - 4(3x = 3)

2x - 12x = 3

- 10x = 3

- 10x ÷ - 10 = 3 ÷ - 10

$x=-\frac{3}{10}$

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3 years ago

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If m∠ATB = 20°, m∠BTD = 72°, and m∠CTD = 38°, what is m∠ATC?

Ber [7]

Answer: m∠ATC = 54°

Step-by-step explanation:

Ok, we know that:

m∠ATB = 20° and m∠BTD = 72°

then we must have that the angle between A and D, is equal to the sum of the angles between A and B, and B and D, or:

m∠ATD = m∠ATB + m∠BTD = 20° + 72° = 92°

Now, we also know that m∠CTD = 38°

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3 years ago

3(x - 2) + 48 = -3x

kow [346]

Answer: X=-7

Step-by-step explanation:

Using PEMDAS;

Step 1: Distribute the "3" in the part of the equation "3(x-2)"

3x - 6

Step 2: Consider the equation as a whole with the newly part of the equation from step 1, as it is a part of the equation

Therefore, re-written as,

3x - 6 + 48 = -3x

Step 3: Evaluate the re-written equation

Using basic mathematics skills, we can evaluate the following,

3x - 6 + 48 = -3x ➡ -6 + 48 = -6x ➡ 42 = -6x ➡ -7 = x

As shown, the answer is x=-7.

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3 years ago

Point C is located 8 inches from point A and 6 inches from point B. Points A and B are 2 inches apart.

marshall27 [118]

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Step-by-step explanation:

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2 years ago

The curve

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

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

Algebra I

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]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

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:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$