The expressions (30-2)(30+2) and 30^2-2^2 are equivalent and can help us find the product of two numbers. which two numbers are they?

Answer:

the answer is 1/2 the first one

Step-by-step explanation:

Because a dice has 6 sides, 3 of the numbers are odd so 3/6 and that is equal to 1/2 when simplified.

The expression that represents the volume of the prism, in cubic centimetres is [tex]28.476(2x+1) \: \rm cm^3[/tex] approx

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross section is same as its base, then its volume is:

[tex]V = B \times h[/tex]
where h is the height of that prism and B is the area of the base of that prism.

For this case, we are provided a prism which has pentagon as its cross sections, and its height is [tex]2x + 1[/tex] units.

Let B be the area of those pentagons, then:
Volume of the prism = [tex]B(2x + 1) \: \rm cm^3[/tex]

It is provided that the apothem of the pentagon is 2.8 cm.

An n sided regular polygon has internal angles' sum as 180(n-2)°

Thus, each internal angle would be of  180(n-2)/n°

For n = 5, this comes as 108°

Since the line AO is bisecting the internal angle, the angle OAB is o of 108/2 = 54°

Using the tangent ratio, we get:

[tex]\tan(54^\circ) = \dfrac{|OD|}{|AD|}\\\\|AD| = \dfrac{2.8}{\tan(54^\circ)} \approx 2.034 \: \rm cm[/tex]

Thus, area of the triangle AOD = [tex]\dfrac{1}{2} \times |AD| \times |OD| \approx \dfrac{1}{2} \times 2.034\times 2.8 = 2.8476 \: \rm cm^2[/tex]

There are 10 such triangles, all congruent, thus:

Area of pentagon = [tex]B \approx 10 \times 2.8476= 28.476 \: \rm cm^2[/tex]

Thus, volume of the pentagonal prism is:

[tex]V = B \times h \approx 28.476(2x+1) cm^3[/tex]

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Answer:

14x^2+7x

B

Step-by-step explanation:

I did the test.

Answer:

4.2

Step-by-step explanation:

The square root of 18 is 4.24

So, on this number line, it should go about 1 cm away from 4 to indicate that it is not 4, but 4.2.

Put the dot where you think it would be appropriate to be labled as 4.2.

Also if you didnt know the x axis is the one on the bottom.

Answer:

18x + 15

Step-by-step explanation:

First, deal with the first part of the question:

5(4x+3)

We multiply the outside of the brackets with the inside. So, we do

5 x 4x = 20x

and 5 x 3 = 15

then put them together:

20x+15

Now, the second part:

- 2x

We cannot simplify this further so we put the two parts together:

20x + 15 - 2x

Collect like terms (20x - 2x) =

18x + 15

I hope this helped. If you have any further questions, do ask.

- profparis

Answer:

1.) you're going to subtract 4 from 46

46-4= 42

7x=42

Then you divide 7 from 42 and get 6..........x=6

2.) you're going to do the same thing for this one

17-9=8

4x=8

8÷4=2

x=2

3.) you're going to do the same thing

1-1=0

2x=0

0÷2=0

x=0

Step-by-step explanation:

Hope this helps:)....if not then sorry for wasting your time and may God bless you:)

Answer:

37.12

Step-by-step explanation:

Area of a Semi-circle = 3.14 x r to the 2nd power / 2

Area of a Triangle = b x h /2

3.14 times 4 to the 2nd power  divided by 2 is 25.12. 8 times 3 is 24, divided by 2 is 12. Add 25.12 and 12 together and get 37.12.

Answer:

(8π + 12) in.2 or B

Step-by-step explanation:

E2020

Answer: $212.52

Step-by-step explanation:

first we have to find the right equation for the problem. a "pen" is an enclosure for animals that is fenced in, meaning we have to find how much fencing we need.

the question gives us two values, 8 meters wide and 13 meters long. we can infer that this "pen" is in the shape of a rectangle meaning two sides will be 8 meters wide and the two others sides are 13 meters long.

this means we will be finding the perimeter of the pen, which is all the sides of a shape added together. for a rectangle the perimeter you use (lenght+width) *2.

when we add the given values we have (8+13)*2 → 21*2 → 42. we need 42 meters of fencing to complete the "pen."

since each meter of fencing is worth $5.06, we multiply the amount of fencing me need by the cost. 5.06*42= 212.52.

this means the farmer will need to spend $212.52 in order to make his goat pen with a perimeter of 42 meters.

Answer:

5a - 4b

Step-by-step explanation:

= 8a - 6b - 3a +2b

= 8a - 3a - 6b + 2b

= 5a - 4b

Hope it helps :)

Answer:

5a - 4b

Step-by-step explanation:

Sales tax amount:-

Price:-

Answer:

$17,280

Step-by-step explanation:

Given

Solving :

The distance between the two buildings is 844.23 feet apart, we go this answer by simply applying the SOH CAH TOA method

Given Data

Applying the SOH CAH TOA Approach we have

Tan  θ = Opp/Adj

Substituting our given data we have

Tan 35 = 400/x

0.4738 = 400/x

make x subject of the formula we have

x = 400/0.4738

x = 844.23 feet

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The largest exponent is the degree.

this only has one exponent so the degree would be 3

Answer:

Step-by-step explanation:

<A and <B are alternate interior angles. That means they are in the interior of the parallel lines and they are on opposite sides of the transversal.

When that happens <A = <B

8x + 78 = 2x + 114                      Subtract 2x from both sides.

8x - 2x + 78 = 2x - 2x + 114       Combine

6x + 78 = 114                              Subtract 78 from both sides

6x + 78 - 78 = 114 - 78

6x = 36                                       Divide by 6

6x/6 = 36/6

x = 6

I think you are asked for B

<B = 2x + 114

<B = 2*6 + 114

<B = 12 + 114

<B = 126

Answer:

B.

Step-by-step explanation:

Answer:

(2, -1)

Step-by-step explanation:

x = 2, y = −1

For zeroes i.e for value(s) of q and s, the given equations must be equal to 0, so let's start with first equation and then 2nd equation ;

[tex]{:\implies \quad \sf 6q^{2}-17q+12=0}[/tex]

[tex]{:\implies \quad \sf 6q^{2}-9q-8q+12=0}[/tex]

[tex]{:\implies \quad \sf 3q(2q-3)-4(2q-3)=0}[/tex]

[tex]{:\implies \quad \sf (3q-4)(2q-3)=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:3q-4=0\:\:\:or\:\:\: 2q-3=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:3q=4\:\:\:or\:\:\:2q=3}[/tex]

[tex]{:\implies \quad \bf q=\dfrac{3}{2},\dfrac43}[/tex]

Now, turning to the second equation ;

[tex]{:\implies \quad \sf 8s^{2}+2s-15=0}[/tex]

[tex]{:\implies \quad \sf 8s^{2}+12s-10s-15=0}[/tex]

[tex]{:\implies \quad \sf 4s(2s+3)-5(2s+3)=0}[/tex]

[tex]{:\implies \quad \sf (4s-5)(2s+3)=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:4s-5=0\:\:\:or\:\:\: 2s+3=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:4s=5\:\:\:or\:\:\:2s=-3}[/tex]

[tex]{:\implies \quad \bf s=\dfrac{5}{4},-\dfrac32}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

I am assuming you want to factor these expressions.

6q^2 - 17q + 12

We need 2 numbers whose product is (6*12) = 72 and whose sum is -17.

Theses are -9 and -8 so we write:

= 6q^2 - 9q - 8q + 12

= 3q(2q - 3) - 4(2q - 3)

= (3q - 4)(2q - 3)

If you want the solution of this expression = zero they are q = 4/3, 3/2.

8s^2 + 2s - 15

8 * -15 = -120.   -120 = -2 * 2 * 2 * 3 * 5 = +12 * -10 ( to give the +2s)

= 8s^2 + 12s - 10s - 15

= 4s(2s + 3) - 5(2s + 3)

= (4s - 5)(2s + 3)

If you want the solution of this expression = zero they are s = 5/4, -3/2.

Answer:

Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.

So he does 1/20 of the job per minute.

.

Rob can do the job in 30 min. His rate is 1/30 of the job per minute.

.

Working together how does it take?

.

1/20*x + 1/30*x = 1 job done

, where x = minutes.

.

Step-by-step explanation:

When Deshawn installs a shelf bracket, the width of the shelf that will fit without overhang will be 3 inches.

From the complete information, the other two sides have been given as 4 inches and 5 inches.

The Pythagoras theorem will be used in this case and it goes thus:

4² + Width² = 5²

Width² = 5² - 4²

Width² = 25 - 16

Width² = 9

Width = ✓9

Width = 3

In conclusion, the width is 3 inches.

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The expression of the unit rate was defined with all parameters rightly inputed the Molly's unit rate is 2.5 pages per minutes

Given Data

The speed/ rate is defined as the number of pages read per minutes passed

Hence the expression for the unit rate is given as

Unit Rate = Number of pages/Time Taken

Substituting our given Parameters

Unit Rate = 75/30

Unit Rate = 2.5 pages per minutes

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Answer:

To find the volume of this figure, we must find the base area(pentagon) and multiply it by the figure's height.

Formula for area of a pentagon:-

A = 1/2 x p x a

Where 'p' represents the perimeter, and 'a' represents the apothem.

First, let's figure out the perimeter of the base pentagon.

One side of this pentagon is 10cm, and there are 5 side lengths of 10cm to this pentagon. So it'll result in (5 x 10) = 50cm altogether.

The apothem is given, 6.9cm.

So, we plug these into our formula:-

A = 1/2 x p x a

A = 1/2 x 50 x 6.9

A = 50/2 x 6.9

A = 25 x 6.9

A = 172.5cm, is the area of the pentagon.

Now we find the height of this figure and multiply it by the base area we've found(pentagon).

Our height is 17cm.

172.5(17)

= 2,932.5 cubic centimetres, is our volume.

Answer:

LOWER UPFRONT COSTS

Step-by-step explanation:

you're welcome ;)

- 6/17 = (-6) / 17 (2nde solution)

         = - (6/17) (4th solution)

         = 6/(-17) (last solution)

Answer: 83 degrees

Step-by-step explanation:

In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:

[tex]cos(x)=\frac{2}{16} =\frac{1}{8}[/tex]

[tex]arccos(cos(x))=arccos(\frac{1}{8} )=x[/tex]

Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:

[tex]x=arccos(\frac{1}{8} )[/tex]

[tex]x=83[/tex]

Answer: I think its 8

Step-by-step explanation:

Answer:

[tex]f(x) = 2000 * 1.05^x[/tex]

Step-by-step explanation:

The key to this question is interpreting the graph and then modelling it into an exponential function.

You are given 2 key characteristics of this graph. 1 characteristic being that it intercepts the y-axis at (0,2000), and another characteristic being that it goes through the point (1,2100)

Now refer to the standard form of an exponential function.

[tex]y = a * b^x[/tex]

Since you know that when x = 0, y = 2000, a must be 2000. Because [tex]b^0 = 1[/tex], 2000 * 1 = 2000

So you got your a value. Sub it into the equation and now you got.

[tex]y = 2000 * b^x[/tex]

You still need to solve for b, so this is where you do some algebra. Pick your key point, (1,2100), sub in those values for x and y, and solve for b.

[tex]2100 = 2000 * b^1\\\frac{2100}{2000} = b\\ 1.05 = b[/tex]

Now you have your a and b values. Now you can express using a function:

[tex]f(x) = 2000 * 1.05^x[/tex]

A dot plot or for chart is a statistical plot consisting of data points that are plotted on a scale using dots.

Your information is incomplete. Therefore, an overview of a dot plot will be given. A dot plot is a data visualization where the day points are plotted as dots on the graph.

Dot plots are used for relatively small data sets. It uses the dots to show where the data values in the distribution are.

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Hope this helps!! :)

Answer:

926% and I'm pretty sure the other one is 0.7

Step-by-step explanation: For a you have to remove the decimal. for b you have to remove the %

Answer:

57,700.10

Step-by-step explanation:

To solve, we use the equation [tex]17,600(1.16)^8[/tex]

we set it to the power of 8, since it is compounding quarterly this means it compounds 4 times a year, and since there is 2 years, we get 8 compounds.

please rate and mark as brainlest

Answer:

35.4

Step-by-step explanation:

divide 72.8 by 6.5 to get the other two sides. Then you will have all four sides. From there you can add all four sides. 6.5 + 6.5 + 11.2 + 11.2 = 35.4. Hope that helps!

Answer:

It is squash

Step-by-step explanation:

This is because for every 3 tomatoes there is one squash. 1 squash times 3 is 3. 3 tomatoes times 3 is 9.