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3 years ago

10. What is the solution to 5x2 - 7x + 3 = 0?

Mathematics

1 answer:

masya89 [10]3 years ago

3 0

Answer:

Bodmas rules first -7 multiplay by 3 and get -21 the 5 multiply by 2 and get 10 ..then +10 minus 21 and get -11

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The point (-3,-2) is rotated 180 degrees about the origin. what are the coordinates of its image?

den301095 [7]

Answer:

The coordinates of the image are (3,2)

Step-by-step explanation:

we know that

The coordinates of the pre-image are (-3,-2)

This point is located on III Quadrant

If the point is rotated 180 degrees about the origin

then

The image will be located on I Quadrant

The rule of the rotation is equal to

(x,y) ------> (-x,-y)

(-3,-2) -------> (3,2)

8 0

3 years ago

Read 2 more answers

Number graph ranging from negative one to seven on the x axis and negative four to four on the y axis. Two lines that are perpen

lys-0071 [83]

The solution for the system of lines is defined as follows,

x-Intercept for line a: (4,0)

y-Intercept for line a: (0,2)

x-Intercept for line b: (1.5, -0)

y-Intercept for line b: (0,-2)

Line a and b intersect at (2,1)

Solving the System of Lines:

Line a: x + 2y = 4

Line b: 3x – 2y = 4

From the graph,

Line a intersect x-axis at (4,0) and y-axis at (0,2)

Line b intersect x-axis at (-1.5,0) and y-axis at (0,-2)

x + 2y = 4

x = 4-2y

Since point P lies on bot the lines A and B, it will satisfy the equations of both a and b.

Thus, substituting x = 4-2y in the equation of line b, we get,

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

12 - 6y - 2y = 4

8y = 8

y = 1

Putting y=1 in the equation of line a, x = 4-2y, we get,

x = 4-2(1)

x = 4-2

x = 2

Hence, point P≡(2,1).

Learn more about a line here:

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3 0

2 years ago

Molly owes her brother $300.She works for $10 per hour as a checker at the local grocery store.Molly plans to repay her brother

gavmur [86]

Answer: The expression which represents the condition described is given as $4x=300$

Step-by-step explanation:

Since we have given that

Amount that Molly owes her brother = $300

Let the number of hours she worked as a checker be x

Cost of per hour = $10

Amount she get after doing work for x hours is given by

$10x$

Rate of tax are taken out = 80%

So, amount she left with is given by

$\frac{100-20}{100}\times 10x\\\\=\frac{80}{100}\times 10x\\\\=8x$

So, Molly plans to repay her brother half of what she earns is given by

$\frac{8x}{2}=4x$

According to question,

$4x=300\\\\x=\frac{300}{4}\\\\x=75\ hours$

So, the expression which represents the condition described is given as

$4x=300$

3 0

4 years ago

Read 2 more answers

(d). Use an appropriate technique to find the derivative of the following functions:

natima [27]

(i) I would first suggest writing this function as a product of the functions,

$\displaystyle y = fgh = (4+3x^2)^{1/2} (x^2+1)^{-1/3} \pi^x$

then apply the product rule. Hopefully it's clear which function each of f, g, and h refer to.

We then have, using the power and chain rules,

$\displaystyle \frac{df}{dx} = \frac12 (4+3x^2)^{-1/2} \cdot 6x = \frac{3x}{(4+3x^2)^{1/2}}$

$\displaystyle \frac{dg}{dx} = -\frac13 (x^2+1)^{-4/3} \cdot 2x = -\frac{2x}{3(x^2+1)^{4/3}}$

For the third function, we first rewrite in terms of the logarithmic and the exponential functions,

$h = \pi^x = e^{\ln(\pi^x)} = e^{\ln(\pi)x}$

Then by the chain rule,

$\displaystyle \frac{dh}{dx} = e^{\ln(\pi)x} \cdot \ln(\pi) = \ln(\pi) \pi^x$

By the product rule, we have

$\displaystyle \frac{dy}{dx} = \frac{df}{dx}gh + f\frac{dg}{dx}h + fg\frac{dh}{dx}$

$\displaystyle \frac{dy}{dx} = \frac{3x}{(4+3x^2)^{1/2}} (x^2+1)^{-1/3} \pi^x - (4+3x^2)^{1/2} \frac{2x}{3(x^2+1)^{4/3}} \pi^x + (4+3x^2)^{1/2} (x^2+1)^{-1/3} \ln(\pi) \pi^x$

$\displaystyle \frac{dy}{dx} = \frac{3x}{(4+3x^2)^{1/2}} \frac{1}{(x^2+1)^{1/3}} \pi^x - (4+3x^2)^{1/2} \frac{2x}{3(x^2+1)^{4/3}} \pi^x + (4+3x^2)^{1/2} \frac{1}{ (x^2+1)^{1/3}} \ln(\pi) \pi^x$

$\displaystyle \frac{dy}{dx} = \boxed{\frac{\pi^x}{(4+3x^2)^{1/2} (x^2+1)^{1/3}} \left( 3x - \frac{2x(4+3x^2)}{3(x^2+1)} + (4+3x^2)\ln(\pi)\right)}$

You could simplify this further if you like.

In Mathematica, you can confirm this by running

D[(4+3x^2)^(1/2) (x^2+1)^(-1/3) Pi^x, x]

The immediate result likely won't match up with what we found earlier, so you could try getting a result that more closely resembles it by following up with Simplify or FullSimplify, as in

FullSimplify[%]

(% refers to the last output)

If it still doesn't match, you can try running

Reduce[<our result> == %, {}]

and if our answer is indeed correct, this will return True. (I don't have access to M at the moment, so I can't check for myself.)

(ii) Given

$\displaystyle \frac{xy^3}{1+\sec(y)} = e^{xy}$

differentiating both sides with respect to x by the quotient and chain rules, taking y = y(x), gives

$\displaystyle \frac{(1+\sec(y))\left(y^3+3xy^2 \frac{dy}{dx}\right) - xy^3\sec(y)\tan(y) \frac{dy}{dx}}{(1+\sec(y))^2} = e^{xy} \left(y + x\frac{dy}{dx}\right)$

$\displaystyle \frac{y^3(1+\sec(y)) + 3xy^2(1+\sec(y)) \frac{dy}{dx} - xy^3\sec(y)\tan(y) \frac{dy}{dx}}{(1+\sec(y))^2} = ye^{xy} + xe^{xy}\frac{dy}{dx}$

$\displaystyle \frac{y^3}{1+\sec(y)} + \frac{3xy^2}{1+\sec(y)} \frac{dy}{dx} - \frac{xy^3\sec(y)\tan(y)}{(1+\sec(y))^2} \frac{dy}{dx} = ye^{xy} + xe^{xy}\frac{dy}{dx}$

$\displaystyle \left(\frac{3xy^2}{1+\sec(y)} - \frac{xy^3\sec(y)\tan(y)}{(1+\sec(y))^2} - xe^{xy}\right) \frac{dy}{dx}= ye^{xy} - \frac{y^3}{1+\sec(y)}$

$\displaystyle \frac{dy}{dx}= \frac{ye^{xy} - \frac{y^3}{1+\sec(y)}}{\frac{3xy^2}{1+\sec(y)} - \frac{xy^3\sec(y)\tan(y)}{(1+\sec(y))^2} - xe^{xy}}$

which could be simplified further if you wish.

In M, off the top of my head I would suggest verifying this solution by

Solve[D[x*y[x]^3/(1 + Sec[y[x]]) == E^(x*y[x]), x], y'[x]]

but I'm not entirely sure that will work. If you're using version 12 or older (you can check by running $Version), you can use a ResourceFunction,

ResourceFunction["ImplicitD"][<our equation>, x]

but I'm not completely confident that I have the right syntax, so you might want to consult the documentation.

3 0

2 years ago

Alguien me ayuda? Who can help me?

enyata [817]

The solving of the fractions simply shows that the value of 1 2/3 + 3 1/2 is 5 1/6.

<h3>How to solve the fraction?</h3>

The first fraction give is:

= 1 2/3 + 3 1/2

= 1 4/6 + 3 3/6

= 4 7/6

= 4 + 1 1/6

= 5 1/6

Also 3/4 - 5/7 will be:

= 3/4 - 5/7

= 21/28 - 20/28

= 1/8

It should be noted that when solving fractions, it's important to have a common denominator.

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5 0

2 years ago