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3 years ago

Solve the equation 3x-y=28 3x+y=14

Mathematics

1 answer:

Elis [28]3 years ago

3 0

Answer:

(x, y) = (7, -7)

Step-by-step explanation:

You can eliminate y by adding the two equations:

(3x -y) +(3x +y) = (28) +(14)

6x = 42 . . . . simplify

x = 7 . . . . . . divide by 6

You can eliminate x by subtracting the two equations:

(3x +y) -(3x -y) = (14) -(28)

2y = -14 . . . . simplify

y = -7 . . . . . . divide by 2

The solution is (x, y) = (7, -7).

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F(x) = 3x + x3

____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

$\frac{d}{dx}\left(3x+x^3\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

solving

$\frac{d}{dx}\left(3x\right)$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'$

$=3\frac{d}{dx}\left(x\right)$

$\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$=3\cdot \:1$

$=3$

now solving

$\frac{d}{dx}\left(x^3\right)$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$=3x^{3-1}$

$=3x^2$

Thus, the expression becomes

$\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

$=3+3x^2$

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 = 3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

Thus, the value of x will be:

$x=2,\:x=-2$

5 0

3 years ago

HELP! THIS IS DUE AT 10:40!!!!!!

katrin2010 [14]

Answer:

Yes

Step-by-step explanation:

Both quadrilaterals have two triangles. The triangles that coordinate with the triangles in the other quadrilateral are proven congruent by AAS and AA. That makes the quadrilaterals congruent.

3 0

3 years ago

Find the mean of each data set.<br> 1.9, 10, 11, 16, 12, 12,14

igor_vitrenko [27]

Answer:

Add all the values up and divide by 7 ( as there are 7 values in the data set)

Step-by-step explanation:

1.9 + 10 + 11 + 16 + 12 + 12 + 14 = 76.9

If you divide by 7, you will get 10.9857142857.

6 0

2 years ago

Read 2 more answers

He gave out half of the cookies in the morning. At lunch, he gave out 14 more. He then had 8 cookies left. How many cookies did

Vsevolod [243]

Answer:

44 cookies

Step-by-step explanation:

add the remaining cookies to the ones he gave away

(8+14)=22

double that

22x2

answer

3 0

3 years ago

There are only chickens and pigs in Henry's Barn Henry counted a total of Sixteen animal heads and a total of 50 animal feet.How

raketka [301]

Answer:

9 pigs

Step-by-step explanation:

We have the following numbers of heads:

pigs (p) + chickens (c) = 16 animal heads (1)

And the following numbers of feet:

4p + 2c = 50 animal feet (2)

From equation (1):

p = 16 - c (3)

By entering equation (3) into (2) we have:

4(16 - c) + 2c = 50

64 - 4c + 2c = 50

c = 7

Now, entering the value of c into equation (3) we have the next value of p:

p = 16 - c

p = 16 - 7

p = 9

Therefore, the number of pigs that Henry has is 9.

I hope it helps you!

4 0

3 years ago