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3 years ago

How many solutions exist for the given equation?

Mathematics

2 answers:

faust18 [17]3 years ago

8 0

Answer:

$\Huge \boxed{\mathrm{infinite \ solutions}}$

Step-by-step explanation:

$\sf 12x + 1 = 3(4x + 1) - 2$

Using distributive property.

$\sf 12x + 1 = 12x+3 - 2$

$\sf 12x + 1 = 12x+1$

Subtracting 1 from both sides.

$\sf 12x=12x$

Dividing both sides by 12.

$\sf x=x$

All real numbers are solutions.

There are infinite solutions.

Tpy6a [65]3 years ago

4 0

Answer:

infinitely many

Step-by-step explanation:

12x + 1 = 3(4x + 1) - 2

Distribute

12x + 1 = 12x + 3 - 2

Combine like terms

12x+1 = 12x +1

Subtract 12x from each side

1 =1

Since this is always true, we have infinite solutions

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The product of a number and 5 is atleast 45 write an equation for that

shtirl [24]

product means multiply, at least means greater than or equal to

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If asked to solve, divide 5 from both sides: n ≥ 9

Answer: 5n ≥ 45

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3 years ago

Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)

Citrus2011 [14]

Answer:

It is 3y = 4x + 10

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

${x}^{2} - xy + {y}^{2} = 7$

introduce dy/dx :

$\frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0$

make dy/dx the subject:

$2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1}$

At point (-1, 2):

$\frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3}$

but a tangent has the same slope as the curve:

$y = mx + c$

m is the slope

c is the y-intercept

At (-1, 2):

$2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3}$

equation:

$y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}$

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3 years ago

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Can you please help me with this I will mark the BRAINLIEST who ever can help thanks

son4ous [18]

$QUESTION:$

$WORK$ $OUT$ $THE$ $VALUE$ $OF$ $2^{6}$

Or 2 times 2 times 2 times 2 times 2 times 2 times 2

$ANSWER:$

So, 2^6 is:

Now, 7^4 is:

2,401

Hope it helps!

$Grace Rosalia$

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3 years ago

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Which strategy uses place value to correctly solve for 321 x 4?

Dmitry_Shevchenko [17]

Answer:

300x4 =1200

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1288

Step-by-step explanation:

Break apart 321 = 300+20+ 1

This is the hundreds, tens, and ones

Then multiply each by 4

Add all together to get answer

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3 years ago