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3 years ago

How to solve: 3*9^(2n) = (3^(n +1))^3

2 answers:

8 0

3×9
n+1
−9×3
2n

=
3×3
2n+3
−(3
2
)
n+1

3×(3
2
)
n+1
−3
2
×3
2n

=
3
1+2n+3
−3
2n+2

3
1+2n+2
−3
2+2n

=
3
4+2n
−3
2n+2

3
3+2n
−3
2+2n

=
3
2n
(3
4
−3
2
)
3
2n
(3
3
−3
2
)

=
81−9
27−9

=
72
18

=
4
1

mixer [17]3 years ago

3 0

Answer:

Step-by-step explanation:

3*9^(2n) = (3^(n +1))^3

= 3×9^0^3

= 3×9^0

= 3×1

= 3

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Use the drop-down menus to solve the system using the 5-step process you just learned. x + 6y = 29 2x - 4y = -6 1) Solve for x i

Genrish500 [490]

We have the following system of linear equation:

(1) $x+6y=29$
(2) $2x-4y=-6$

Let's apply elimination method by multiplying (1) by -2, then:

$-2(x+6y)=-2(29)$
∴ $-2x-12y = -58$

Next let's subtract (1) and (2):

(1) $-2x-12y = -58$
(2) $2x-4y=-6$
_______________________
$-16y=-64$
∴ $y=4$

Finally, substituting this value in (1) we have that:

$x+6(4)=29$
∴ $\boxed{x=5}$

5 0

3 years ago

Read 2 more answers

5. Solve the following equations for the indicated variable.

wlad13 [49]

Answer:a) x =−1

B) x=1/2y+12

C) m=13

D) x=2

Step-by-step explanation:a) Let's solve your equation step-by-step.

5(3x+7)=20−2(x+1)

Step 1: Simplify both sides of the equation.

5(3x+7)=20−2(x+1)

(5)(3x)+(5)(7)=20+(−2)(x)+(−2)(1)(Distribute)

15x+35=20+−2x+−2

15x+35=(−2x)+(20+−2)(Combine Like Terms)

15x+35=−2x+18

Step 2: Add 2x to both sides.

15x+35+2x=−2x+18+2x

17x+35=18

Step 3: Subtract 35 from both sides.

17x+35−35=18−35

17x=−17

Step 4: Divide both sides by 17.

17x/17=−17/17

x=−1

B) Let's solve for x.

2x−y=24

Step 1: Add y to both sides.

2x−y+y=24+y

2x=y+24

Step 2: Divide both sides by 2.

2x/2=y+24/2

x=1/2y+12

C) Let's solve your equation step-by-step.

m(3−4m)=7+4(8−m2)

Step 1: Simplify both sides of the equation.

−4m2+3m=−4m2+39

Step 2: Add 4m^2 to both sides.

−4m2+3m+4m2=−4m2+39+4m2

3m=39

Step 3: Divide both sides by 3.

3m/3=39/3

m=13

D) Let's solve your equation step-by-step.

5x(x+3)=x(5x−3)+36

Step 1: Simplify both sides of the equation.

5x2+15x=5x2−3x+36

Step 2: Subtract 5x^2 from both sides.

5x2+15x−5x2=5x2−3x+36−5x2

15x=−3x+36

Step 3: Add 3x to both sides.

15x+3x=−3x+36+3x

18x=36

Step 4: Divide both sides by 18.

18x/18=36/18

x=2

3 0

3 years ago

Arlene has raised $56 for her class field trip. This is $14

yan [13]

Assuming Adams amount is x, three times his amount will be 3x. $14 more than the times Adam's amount will be 14 +3x.

Therefore if Arlene's money is $56 which is $14 more than three times Adam's amount, then the equation will be ;

14+3x=56

7 0

3 years ago

4b. A cell phone plan costs $200 to start. Then there is a $50 charge each

Kisachek [45]

The answer is 50x+200

6 0

3 years ago

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What is are the solutions to | x+4 |= 3x-5?

bonufazy [111]

Answer:

x = $\frac{9}{2}$

Step-by-step explanation:

The absolute value always returns a positive value but the expression inside can be positive or negative, that is

x + 4 = 3x - 5 ( subtract 3x from both sides )

- 2x + 4 = - 5 (subtract 4 from both sides )

- 2x = - 9 ( divide both sides by - 2 )

x = $\frac{9}{2}$

-(x + 4) = 3x - 5

- x - 4 = 3x - 5 ( subtract 3x from both sides )

- 4x - 4 = - 5 ( add 4 to both sides )

- 4x = - 1 ( divide both sides by - 4 )

x = $\frac{1}{4}$

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

| $\frac{9}{2}$ + 4 | = | $\frac{17}{2}$ | = $\frac{17}{2}$

right side = $\frac{27}{2}$ - 5 = $\frac{17}{2}$

left side = right side , thus x = $\frac{9}{2}$ is a solution

check second solution

| $\frac{1}{4}$ + 4 | = | $\frac{17}{4}$ | = $\frac{17}{4}$

right side = $\frac{3}{4}$ - 5 = - $\frac{17}{4}$

right side ≠ left sides, hence not a solution

7 0

4 years ago