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Inessa [10]
3 years ago
9

Solve the following equations for x. Show the step by step process.

Mathematics
1 answer:
kherson [118]3 years ago
6 0
1. 3x - 19 = 2
        +19    +19
           3x = 21
           ÷3   ÷3
          x= 7
2. 4x + 12x = 6² + 4(11)
            16x = 36 + 44
            16x = 80
           ÷16   ÷16
             x= 5
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Factor the given polynomial completely \. If the polynomial cannot be factored, say that is prime. y^4+10y^3+16y^2
Svetach [21]
I took out the greatest common factor, which is y^2 and factored from there
You’ll end up with y^2(y+2)(y+8)
Here’s my work :)

4 0
3 years ago
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Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio
JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

Initial =1\ million

6\ years\ later = 500,000

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

\frac{dA}{dt} = kA

Where k represents the constant of proportionality

\frac{dA}{dt} = kA

Multiply both sides by dt/A

\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}

\frac{dA}{A}  = k\ dt

Integrate both sides

\int\ {\frac{dA}{A}  = \int\ {k\ dt}

ln\ A = kt + lnC

Make A, the subject

A = Ce^{kt}

t = 0\ when\ A =1\ million i.e. At initial

So, we have:

A = Ce^{kt}

1000000 = Ce^{k*0}

1000000 = Ce^{0}

1000000 = C*1

1000000 = C

C =1000000

Substitute C =1000000 in A = Ce^{kt}

A = 1000000e^{kt}

To solve for k;

6\ years\ later = 500,000

i.e.

t = 6\ A = 500000

So:

500000= 1000000e^{k*6}

Divide both sides by 1000000

0.5= e^{k*6}

Take natural logarithm (ln) of both sides

ln(0.5) = ln(e^{k*6})

ln(0.5) = k*6

Solve for k

k = \frac{ln(0.5)}{6}

k = \frac{-0.693}{6}

k = -0.1155

Recall that:

\frac{dA}{dt} = kA

Where

\frac{dA}{dt} = Rate

So, when

A = 600000

The rate is:

\frac{dA}{dt} = -0.1155 * 600000

\frac{dA}{dt} = -69300

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

7 0
2 years ago
Which of the values in the set {2, 3, 4, 5} is a solution to the equation 2x + 4 = 10?
Mrac [35]
The answer is 3 because 2(3) + 4 = 10; 6 + 4 = 10
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x = number of people went to movies

equation

6.25x + 12 = 30.75

6.25x = 30.75 - 12

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answer

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3 0
3 years ago
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-5(-x + 1) -3x -1 = -12<br> Solve for x please
hjlf

Answer:

Hello,

-5(-x + 1) -3x -1 = -12 ⇔ 5x - 5 - 3x - 1 = -12 ⇔ 2x - 6 = -12 ⇔ 2x = -6 ⇔ x = -3

3 0
3 years ago
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