what is the surface area of this triangular pyramid

Answer: [tex]70a^2b^2c^3[/tex] will be the answer.

Explanation:

Since Given expression is [tex]10abc^2\sqrt{49a^2b^2c^2}[/tex]

We can write, [tex]10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{7^2a^2b^2c^2}[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{(7abc)^2}[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^27abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10\times7abc^2abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70abc^2abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70a^2b^2c^3[/tex]

1. The simplified form of the expression [tex]10abc^2[/tex] is simply [tex]10abc^2[/tex] itself.

2. The simplified form of the expression [tex]\sqrt{49a^2b^2c^2}[/tex] is 7abc.

1. Since there are no like terms to combine, and no operations to perform, the expression remains unchanged.

2. The expression [tex]\sqrt{49a^2b^2c^2}[/tex] represents the square root of [tex]49a^2b^2c^2[/tex]. To simplify this, we need to find the square root of each term under the radical.

[tex]\sqrt{49a^2b^2c^2} = \sqrt{49} * \sqrt{a^2} * \sqrt{b^2} * \sqrt{c^2}[/tex]

The square root of 49 is 7, and the square root of any variable raised to the power of 2 is simply the variable itself. So, we have: [tex]\sqrt{49a^2b^2c^2} = 7 * a * b * c[/tex]

To know more about expression:

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Total housing expenses per month allowed will be $168.81.

To calculate how much you are allowed in housing expenses per month, we need to first determine your after-tax income.

You earn $6.80/hr plus tips averaging $2.30/hr, resulting in an hourly wage of

$6.80 + $2.30 = $9.10

Working 20 hours a week gives you a weekly income of

20 hours × $9.10/hr = $182

Monthly, this equates

$182  4 weeks = $728

The deductions are as follows: FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). These deductions total to

7.65% + 8.95% + 6.1% = 22.7%

To get the after-tax income, we calculate

$728 - (22.7% × $728)

≈ $562.69

This is your monthly take-home pay.

Financial experts often recommend spending no more than 30% of your take-home pay on housing. Therefore

$562.69 × 30%

= $168.81 houses expenses per month

To calculate the height of the cuboid, we convert the width to centimeters and use the volume formula. After conversion, we find the height by dividing the volume (1404cm³) by the product of the length (9cm) and width (13cm), resulting in a height of 12cm.

To find the height of the cuboid, we can use the formula for calculating volume, which is volume = length x width x height. The question gives us the volume of the cuboid as 1404cm³, the length as 9cm, and the width as 130mm. However, we need to ensure all units are the same, so let's convert the width from millimeters to centimeters: 130mm = 13cm (since 1cm = 10mm).

Now, using the formula for volume:

To find the height, we divide the volume by the product of the length and width:

Therefore, the height of the cuboid is 12cm.

Answer:

When you round to the nearest hundred:

150 or higher turns into 200, so you'd do add.

But when it's 149 or lower, you simply subtract it by 49.

Step-by-step explanation:

The equation to determine the number of bacteria in the colony after 6 hours is [tex]f(x) = 100(4)^x[/tex] and after 6 hours, there will be 409,600 bacteria in the colony.

To find the number of bacteria after 6 hours, one would substitute x with 6 in the exponential function [tex]f(x) = 100(4)^x[/tex].

This function models the growth of the bacteria colony, where the initial number of bacteria is 100 and they quadruple every hour.

The variable x represents the number of hours that have passed since the initial measurement at 9:00 a.m.

By substituting x = 6 into the function, we get:

[tex]f(6) = 100(4)^6[/tex]

Now, calculate the value of [tex](4)^6[/tex]:

[tex](4)^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096[/tex]

Then, multiply this by the initial number of bacteria, which is 100:

f(6) = 100 [tex]\times[/tex] 4096

Finally, calculate the total number of bacteria after 6 hours:

f(6) = 409600

Answer:

c

5

-10

Step-by-step explanation:

Two of the three side lengths are given.  To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle.  Use the Law of Cosines for this task.

a^2 = b^2 + c^2 - 2ac*cosA

Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or

         a^2 = 250000 + 572500 - 750000(-0.1736), or

                = 692264

Then a = +sqrt(692264) = 832 yds

Use Heron's Formula to find the area of the land.

First, calculate s=(a+b+c)/2:  (500+750+832)/2 = 1041=s

According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )

Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )

I will leave this calculation to you to complete.

Suppose the area of the land is A square yards.  Convert this to acres, using the fact that 1 acre = 4840 yd^2.

In acres, the area is 

         1 acre

A* ---------------- = (A/4840) acres

       4840 yd^2

How much will this cost?  Recall that the unit cost of the land is $2300/acre.

Then the total cost will be:

                            $2300

(A/4840) acres * ------------- = 0.475*A dollars.  (Substitute your value for A)

                             1 acre

1

the linear function f (x) = 0.05x + 3,

f(x) is the monthly fee and x is the price per minute

Brandon used 20 minutes of his long distance

So x is 20 minutes

We plug in 20 for x

f(x) = 0.05x + 3

f(20) = 0.05(20) + 3 = 4

So total bill is  $4 if Brandon used 20 minutes of his long distance service in a month

Rational Root Theorem:

If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:

[tex]P(x)=kx^{n}+...+m[/tex]

where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]

1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]

2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:

[tex]P(x)=(x-r)Q(x)[/tex]

3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.

Answer:

The answer is word SIMULTANEOUSLY.

Step-by-step explanation:

The alternative that fits best is " d.Simultaneously"

All at once, pandemonium broke loose. Simultaneously, the marching band came around the corner, dogs began barking, the horses pulling the Mayors carriage began to run.

This word maintains the coherence and cohesion of the given text.

Answer:

The alternative that fits best is  " d. Simultaneously"

Step-by-step explanation:

Thus, the complete sentence would read:  "All at once, pandemonium broke loose. Simultaneously the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!"

The explanation for this is that the word "Simultaneously" is the only one that fits the phrase, and maintains the coherence and cohesion of the text.  The words "anyway", "because", and "following", when embedded in the phrase, change the meaning of what the author wanted to go through.

Answer:

B is the answer

Step-by-step explanation:

i just took the test

Answer:

6

Step-by-step explanation:

Answer: The function would be,

[tex]f(x)=12(2)^x[/tex]

Step-by-step explanation:

Given,

Park rangers released 12 fish into a pond in year 0,

Thus, the initial number of fish = 12,

Also, there were twice as many fish as the year before,

⇒ After 1 year the number of fishes = 2(12) = 12(2),

Similarly,

After 2 years = 2(12(2))= 12(2)²,

After 3 years = 2(12(2)²) = 12(2)³,

................, so on,....

Thus, the number of fishes after x years would be,

[tex]12(2)^x[/tex]

Let f(x) represents the number of fish after x years,

[tex]\implies f(x) = 12(2)^x[/tex]

Which is the required function that the given scenario.

18 / n - 7 = 2  

18 / n =9  

18 = 9n  

2 = n  

18 / 2 - 7 = 2  

9 - 7 = 2  

2 = 2