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3 years ago

7x+1=3x+9 basic equations

Mathematics

2 answers:

babymother [125]3 years ago

8 0

Answer:27

Step-by-step explanation:

goldenfox [79]3 years ago

5 0

Answer:

= 2

Step-by-step explanation:

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Angle 2 is 60. Find angle 8. Options: 140 100 40 60

pav-90 [236]

Angle 8 is 60 too
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5 0

3 years ago

Jackie has a jar of 54 coins consisting of dimes and quarters. If she has a total of $10.05, how many dimes does she have?

Jlenok [28]

31 dimes and 23 quarters

8 0

4 years ago

. A businessman invested a total of Rs. 9,000 in two savings accounts. One account earns 8% interest per year and the other earn

Alex17521 [72]

Answer:

amount invested in the account that earns 10% interest = Rs 3500

amount invested in the account that earns 8% interest =Rs 5500

Step-by-step explanation:

Two equations can be derived from the question

x + y = 9000 equation 1

0.08x + 0.1y = 790 equation 2

x = amount invested in the account that earns 8% interest

y = amount invested in the account that earns 10% interest

multiply equation 1 by 0.08

0.08x + 0.08y = 720 equation 3

subtract equation 3 from 2

0.02y = 70

divide both sides of the equation by 0.02

y = 70 / 0.02

y = 3500

Substitute for y in equation 1

x + 3500 = 9000

x = 9000 - 3500 = 5500

3 0

3 years ago

Calculus 2 Master needed, show steps with partial fraction decomposition <img src="https://tex.z-dn.net/?f=%5Cint%283x%5E2-26x%2

Vladimir79 [104]

Answer:

-ln|x−5| + 2 ln(x²+4) + 3 tan⁻¹(x/2) + C

Step-by-step explanation:

The fraction will be split into a sum of two other fractions.

The first fraction will have a denominator of x − 5. The numerator will the a polynomial of one less order, in this case, a constant A.

The second fraction will have a denominator of x² + 4. The numerator will be Bx + C.

$\frac{3x^{2}-26x+26}{(x-5)(x^{2}+4)}=\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}$

Combine the two fractions back into one using the common denominator.

$\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}=\frac{A(x^{2}+4)+(Bx+C)(x-5)}{(x-5)(x^{2}+4)}$

This numerator will equal the original numerator.

$A(x^{2}+4)+(Bx+C)(x-5)=3x^{2}-26x+26\\Ax^{2}+4A+Bx^{2}-5Bx+Cx-5C=3x^{2}-26x+26\\(A+B)x^{2}+(C-5B)x+(4A-5C)=3x^{2}-26x+26$

Match the coefficients.

$A+B=3\\C-5B=-26\\4A-5C=26$

Solve the system of equations.

$A=-1\\B=4\\C=-6$

So we can rewrite the integral as:

$\int {(\frac{-1}{x-5}+\frac{4x-6}{x^{2}+4}) } \, dx$

Solving:

$\int {\frac{-1}{x-5}\, dx + \int {\frac{4x}{x^{2}+4}} \, dx - \int {\frac{6}{x^{2}+4} } \, dx$

$-\int {\frac{1}{x-5}\, dx + 2\int {\frac{2x}{x^{2}+4}} \, dx - 6\int {\frac{1}{x^{2}+4} } \, dx$

$-ln|x-5| + 2ln(x^{2}+4) - 6(\frac{1}{2} tan^{-1}(\frac{x}{2} )) + C$

$-ln|x-5| + 2ln(x^{2}+4) - 3 tan^{-1}(\frac{x}{2} ) + C$

5 0

3 years ago

translated 3 units right and 2 units up. Then it is rotated 270 counterclockwise about the origin resulting in quadrilateral PQR

Daniel [21]

Because the shape is not undergoing a dilation, the perimeter of the original image and the new image is the same. The only thing that is changing is the placement of the original figure.

I hope this helps! :)

4 0

3 years ago