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3 years ago

What is the value of x? 3(x−2)+5x=18 X = ????

Mathematics

2 answers:

ikadub [295]3 years ago

6 0

3(x-2)+5x=18

the correct answer is x=3

first simply the equation

8x=18+6

Now rid of alike terms resulting in

8x=24

now divide 24 by 8

x=3

irakobra [83]3 years ago

3 0

3x-6+5x=18. 8x=24. X=3.

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What is number 61 and a step by step explaination please?

astra-53 [7]

1/3 ln(x) + ln(2) - ln(3) = 3

Recall that $m\log_b(n)=\log_b(n^m)$ , so

ln(x ¹ʹ³) + ln(2) - ln(3) = 3

Condense the left side by using sum and difference properties of logarithms:

$\log_b(m)+\log_b(n)=\log_b(mn)$

$\log_b(m)-\log_b(n)=\log_b\left(\dfrac mn\right)$

Then

ln(2/3 x ¹ʹ³) = 3

Take the exponential of both sides; that is, write both sides as powers of the constant e. (I'm using exp(x) = e ˣ so I can write it all in one line.)

exp(ln(2/3 x ¹ʹ³)) = exp(3)

Now exp(ln(x)) = x for all x, so this simplifies to

2/3 x ¹ʹ³ = exp(3)

Now solve for x. Multiply both sides by 3/2 :

3/2 × 2/3 x ¹ʹ³ = 3/2 exp(3)

x ¹ʹ³ = 3/2 exp(3)

Raise both sides to the power of 3:

(x ¹ʹ³)³ = (3/2 exp(3))³

x = 3³/2³ exp(3×3)

x = 27/8 exp(9)

which is the same as

x = 27/8 e ⁹

3 0

3 years ago

Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different

N76 [4]

Answer:

(a) As time increases, the amount of water in the pool increases.

11 gallons per minute

(b) 65 gallons

Step-by-step explanation:

From inspection of the table, we can see that as time increases, the amount of water in the pool increases.

We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.

The rate at which the water is increasing is the rate of change (which is also the slope of a linear function).

Choose 2 ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(8, 153)$

$\textsf{let}\:(x_2,y_2)=(12,197)$

Input these into the slope formula:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11$

Therefore, the rate at which the water in the pool is increasing is:

11 gallons per minute

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

$y-y_1=m(x-x_1)$