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3 years ago

Solve (9x-4)^2=18 using the square root method

Mathematics

1 answer:

Damm [24]3 years ago

7 0

Answer:

x = 4/9 + sqrt(2)/3 or x = 4/9 - sqrt(2)/3

Step-by-step explanation:

Solve for x over the real numbers:

(9 x - 4)^2 = 18

Take the square root of both sides:

9 x - 4 = 3 sqrt(2) or 9 x - 4 = -3 sqrt(2)

Add 4 to both sides:

9 x = 4 + 3 sqrt(2) or 9 x - 4 = -3 sqrt(2)

Divide both sides by 9:

x = 4/9 + sqrt(2)/3 or 9 x - 4 = -3 sqrt(2)

Add 4 to both sides:

x = 4/9 + sqrt(2)/3 or 9 x = 4 - 3 sqrt(2)

Divide both sides by 9:

Answer: x = 4/9 + sqrt(2)/3 or x = 4/9 - sqrt(2)/3

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What does an increase in taxes and decrease in the money supply do to the supply and demand curves?

jok3333 [9.3K]

Answer:

The supply and demand curves will shift to the left i.e. there will be a decrease in demand and supply.

Step-by-step explanation:

First: Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

Secondly: Money supply is the total amount of monetary assets available in an economy at a specific time.

When tax is increased, this means individuals and businesses have to contribute more to the state revenue leaving both categories with lesser income or profit i.e. lesser to spend.

In the same way, when money supply decreases, there is lesser money available to both individuals and businesses

What this implies is that demand will decrease because income has decreased. Supply will also decrease because producers will not make as much profit given the increase in tax (tax is considered cost of production).

As a result of this, the demand curve shifts to the left, the supply curve also shift to the left because both demand and supply will decrease.

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3 years ago

(2_{1} + 4_{2})^{4} <br> ----------------------- = Plz answer<br> 2

Gnom [1K]

Answer: The answer is 1296

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3 years ago

A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body i

Over [174]

Answer:

a) $\frac{dC}{dt} = rC$

And for this case we can rewrite the model like this:

$\frac{dC}{C} = r dt$

If we integrate both sides we got:

$ln C = rt + k$

If we use exponentials for both sides we got:

$C = e^{rt} e^k = C_o e^{rt}$

For this case $C_o = 100 mg$ and r = -0.16

So then our model would be given by:

$C(t) = 100 e^{-0.16 t}$

Where t represent the number of hours

b) $C(5) = 100 e^{-0.16*5}= 44.9329$

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

$\frac{dC}{dt} = rC$

And for this case we can rewrite the model like this:

$\frac{dC}{C} = r dt$

If we integrate both sides we got:

$ln C = rt + k$

If we use exponentials for both sides we got:

$C = e^{rt} e^k = C_o e^{rt}$

For this case $C_o = 100 mg$ and r = -0.16

So then our model would be given by:

$C(t) = 100 e^{-0.16 t}$

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

$C(5) = 100 e^{-0.16*5}= 44.9329$

7 0

3 years ago

A fence must be built to enclose a rectangular area of 45 comma 000 ftsquared. Fencing material costs $ 3 per foot for the two s

Tatiana [17]

Answer:

150 feet by 300 feet.

Step-by-step explanation:

The fence is to enclose a rectangular area of 45,000 ft squared.

If the dimensions of the rectangle are x and y

Area of a rectangle = xy

xy=45000
$x=\frac{45000}{y}$

Perimeter of the Rectangle =2x+2y

Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides.

Cost of Fencing, C=$(6*2x+3*2y)=$(12x+6y)

Substitute $x=\frac{45000}{y}$ into the Cost to get C(y)

C=12x+6y

$C(y)=12(\frac{45000}{y})+6y\\C(y)=\frac{540000+6y^2}{y}$

The value at which the cost is least expensive is at the minimum point of C(y), when the derivative is zero.

$C^{'}(y)=\dfrac{6y^2-540000}{y^2}$

$\dfrac{6y^2-540000}{y^2}=0\\6y^2-540000=0\\6y^2=540000\\y^2=\frac{540000}{6} =90000\\y=\sqrt{90000}=300$

Recall,

$x=\frac{45000}{y}=\frac{45000}{300}=150$

Since x=150, y=300

The dimensions that will be least expensive to build is 150 feet by 300 feet.

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3 years ago

(6x+5)-(3x+10)<br> how to solve this question?

Sveta_85 [38]

Answer:

3x-5

Step-by-step explanation:

(6x+5)-(3x+10) = 6x+5-3x-10

= 3x-5

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2 years ago

Read 2 more answers