What is 20 times greater than 0.08?

Answer:

less than $896.00

Step-by-step explanation:

A common rule is that housing expenses should not be more than 28% of your monthly income.

your monthly income = $3,200

so your housing expense should not be more than 28% of $3,200

= [tex]\frac{28}{100}[/tex] × 3,200

= 0.28 × 3,200 = $896.00

So you can spend less than $896.00 on housing expenses.

Answer:

The below attached graph shows the given inequality.

Step-by-step explanation:

Here, the given inequality,

x - 2y > -12

Since, related equation of the inequality,

x - 2y = -12

Which is a line passes through (-12, 0) and (0, 6)

Also, '>' represents dotted line,

So, join these two points by dotted line in the coordinate plan,

Now,

0 - 2(0) > -12 (True)

i.e. shade the region of the line that contains origin.

By the above explanation we will get the graph of given inequality ( shown below )

Answer:

Option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]

Step-by-step explanation:

[tex]y=3x+1[/tex]

For finding the inverse of this function, we will interchange x and y, then solve for y.

[tex]3y=x-1[/tex]

[tex]y=\frac{x-1}{3}[/tex]

Hence, option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]

Answer:

Let x represents the number of hours of labor and y represents the total charges.

Since, in the given situation,

The total charges = A fixed charge for house call + Extra charge per hours,

Fixed charge for house call = $ 45,

Extra charges for every hour = $ 25,

⇒ Extra charge for x hours = 25 x,

Thus, the total charges for x hours,

y = 45 + 25 x

Which is the required equation that will use to determine the amount to charge each customer.

By comparing this equation with y = mx + c,

m = 25

Answer: The answer is [tex]\dfrac{5}{8},~\dfrac{3}{2}[/tex] and no extraneous solution.

Step-by-step explanation: The given equation is

[tex]2|7-7x|=2x+4.[/tex]

We are given to solve this equation and also find its extraneous solution.

The solution is as follows:

[tex]2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=\dfrac{5}{8},~~~~~~~~~~~~~~~~~\Rightarrow x=\dfrac{3}{2}.[/tex]

now, for [tex]x=\dfrac{5}{8}[/tex], we have

[tex]L.H.S.=2|7-7\times \dfrac{5}{8}|=\dfrac{21}{4},\\\\R.H.S.=2\times\dfrac{5}{8}+4=\dfrac{21}{4}.[/tex]

So, this solution is not extraneous.

For [tex]x=\dfrac{3}{2}[/tex], we have

[tex]L.H.S.=2|7-7\times \dfrac{3}{2}|=7,\\\\R.H.S.=2\times\dfrac{3}{2}+4=7.[/tex]

So, this solution is also not extraneous.

Hence, the solution is [tex]\dfrac{5}{8},~\dfrac{3}{2}[tex] and there is no extraneous solution.

Triangle FBD in the given regular hexagon inscribed in a circle can be proven to be an equilateral triangle based on the equal lengths of radii and the angle of 60 degrees subtended at the center by the side of the hexagon.

To prove that triangle FBD is an equilateral triangle, we first need to understand a few properties of a regular hexagon and a circle. In a regular hexagon inscribed in a circle, every angle at the center of the circle subtended by the sides of the hexagon is 60 degrees because the total degree measure at the center of the circle is 360, and this is divided equally among the six sides of the hexagon.

Triangle FBD is formed by joining the center of the circle, O, and two consecutive vertices of the hexagon, B and F. As the hexagon is regular and inscribed in a circle, both OB and OF are radii of the circle. By definition, all radii of a given circle are equal in length. Therefore, OB = OF.

The angle BFO subtended at the center by the side BF of the hexagon is 60 degrees. Hence, triangle FBD is an equilateral triangle because it has two equal sides and the included angle is 60 degrees, which are the properties of an equilateral triangle.

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To prove that triangle FBD is equilateral, one can show that the central angles corresponding to the three sides of the hexagon (angle AOB, angle BOC, and so on) are all equal. Therefore, demonstrating that angle FOB, angle BOD, and angle DOF are each 120 degrees will establish that triangle FBD is equilateral.

In a regular hexagon inscribed in a circle, the central angles formed by connecting the center of the circle (O) to consecutive vertices of the hexagon are all equal. Since each interior angle of a regular hexagon is 120 degrees, the central angles (e.g., angle AOB, angle BOC, etc.) are also 120 degrees. To prove that triangle FBD is equilateral, one needs to focus on the central angles corresponding to its sides.

The central angles associated with triangle FBD are angle FOB, angle BOD, and angle DOF. By demonstrating that each of these angles is 120 degrees, it can be concluded that triangle FBD is equilateral. The regularity of the hexagon ensures that the central angles are equal, making this an effective and straightforward way to prove the equilaterality of triangle FBD.

In conclusion, to establish the equilaterality of triangle FBD, one should emphasize the properties of central angles within the context of a regular hexagon. Specifically, showing that angle FOB, angle BOD, and angle DOF are each 120 degrees serves as a valid proof for the equilateral nature of triangle FBD within the given geometric configuration.

Answer:

-3/2 ≤ x < 5  

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x+5

Solve the inequality separately

2x-3 <x+2  and x+2≤ 3x+5

LEts solve one by one

2x-3 <x+2

Subtract x from both sides

x -3 < 2

add 3 on both sides

x< 5

x+2≤ 3x+5

Subtract 3x from both sides

-2x + 2 ≤ 5

Subtract 2 from both sides

-2x ≤  3

Divide both sides by -2

x ≥ -3/2

we got x>= -3/2 and x<5

so x lies between -3/2  and 5

-3/2 ≤ x < 5

The solution to the given inequality is -3/2 ≤ x < 5.

To solve the given inequality: 2x - 3 < x + 2 ≤ 3x + 5, we can break it down into two separate inequalities and solve them individually.

2x - 3 < x + 2:

Subtracting x from both sides:

2x - x - 3 < x - x + 2

x - 3 < 2

Adding 3 to both sides:

x - 3 + 3 < 2 + 3

x < 5

Now x + 2 ≤ 3x + 5:

Subtracting x from both sides:

x - x + 2 ≤ 3x - x + 5

2 ≤ 2x + 5

Subtracting 5 from both sides:

2 - 5 ≤ 2x + 5 - 5

-3 ≤ 2x

Dividing both sides by 2:

-3/2 ≤ x

Combining the results from both inequalities:

-3/2 ≤ x < 5

To learn more on Inequality click:

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To write a percent as a fraction in lowest terms,  first remember that a percent is a ratio that compares a number to 100. In this case, 40% can be written as the ratio 40 to 100 or [tex]\frac{40}{100}[/tex]. Notice however that [tex]\frac{40}{100}[/tex] is not in lowest terms so we need to divide the numerator and the denominator by 20 which gives us [tex]\frac{2}{5}[/tex].

Answer:-24.87 is the correct answer, i checked it!

Step-by-step explanation:

The marginal revenue for 100 units sold is 180 dollars per unit. We cannot precisely estimate the total revenue for 100 or 101 units sold without further information.

In this problem, we're dealing with the concept of marginal revenue. The marginal revenue function gives us the change in total revenue for each additional unit sold. That is given in this case as R'(q)=240-18√q.

To find the marginal revenue at 100 units, we simply substitute q = 100 into our function: R'(100)=240-18√100 = 240 - 18*10 = 180 dollars per unit.

The total revenue given a specific quantity is typically found by integrating the marginal revenue function. However, without the constants of integration or the original revenue function, we cannot accurately compute the total revenue for 100 or 101 units sold in this case.

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To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.

To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.

Therefore, the log expression that simplifies to 7^x = 64 is x = 6 * log7(2).

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