Part 3: Construct a prism from the above regular hexagon. The height of the hexagonal prism is 5 feet. Find the surface area and the volume of this prism.

Step-by-step explanation:

Any prism volume is V = BH where B is area of base and H is height of prism, so find area of the base by B = 1/2 h(b1+b2), then multiply by the height of the prism.

This equation cannot be factorised, at least not easily. It would require decimals and that's not worth the time. Instead you can use the quadratic formula to solve for x, which works for any quadratic equation:

[tex]\frac{-b + or - \sqrt{b^{2} - 4ac} }{2a}[/tex]

a being the x^2 coefficient

b the x coefficient

and c the constant

here a = 21

b = -55

c = -14

let's solve this one:

You can simply input this into a calculator to find the answer, or you can work it out mentally.

= 2.852740993

Now, since this is a quadratic we need to possible values of x. So we just redo the same formula, but this time with a negative square root:

[tex]\frac{-(-55) - \sqrt{(-55)^{2} - 4(21)(-14)} }{2(21)}[/tex]

= -0.2336933736

You can round these answers however you like, but I would recommend doing to either 3 significant figures, either 2 or 3 decimal places.

Answer:

[tex]\displaystyle [7x - 2][3x - 7][/tex]

Step-by-step explanation:

Find two quantities that when summed to 55, they also multiply to 294. Those will be 6 and 49. The TINIER quantity gets the plus sign because the B-value is −55, therefore 49 gets the minus sign, leaving 6 with the plus sign. In extension, sinse we have a leading coefficient greater than one, we need to take extra procedures. Here is how it is done:

[tex]\displaystyle 21x^2 - 55x + 14 \\ \\ [21x^2 + 6x] - [49x + 14] \\ 3x[7x - 2] - 7[7x - 2] \\ \\ \boxed{[7x - 2][3x - 7]}[/tex]

I am joyous to assist you at any time.

**For all you moderatours out there, this user made a typographical errour with the symbol of the C-value. It was supposed to be 14, not −14. BELIEVE ME.

Answer:

The width is 8 meters.

Step-by-step explanation:

30-6=24

24/3=8

width=8 meters

The equivalent expression at the point where it is undefined is ∞

Given the trigonometry expression

tanαcos(2α)

From trigonometry identity;

tanα = sinα/cosα

The expression above will become:

tanαcos(2α) = sinαcos(2α)/cosα

The function is undefined at the point where cosα = 0

cosα = 0

α = arccos(0)

α = 90degrees

Substitute α = 90degrees into the expression;

tanαcos(2α) =  tan 90 cos(180)
tanαcos(2α) = ∞

Hence the equivalent expression at the point where it is undefined is ∞

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Answer:

Step-by-step explanation:

Rule

The sin of any angle = cos(90  -  the angle used for the sine)

Sin(64) = cos(90 - 64)

Sin(64) = cos(26)

Check

Sin(64) = 0.8988

Cos(26) = 0.8988

sin (90-x)=cos (x) ( Trigonometry Indentity)

So, sin (90-26)= cos (26) = sin (64)

Cosine and Sine values appear to be related complementary, as in the above answer. If you’ve seen the pattern such as

cos (0) = sin (90)

cos (30) = sin (60)

cos (45) = sin(45)

cos(60) = sin (30)

cos (90) = sin (0),

The sum of the angles equal 90 degrees.

The angle the tent pole makes with the sides of the tent is 39.6 degrees

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let Ф represent the angle the tent pole makes with the sides of the tent. Hence:

cosФ = 20/26

Ф = 39.6 degrees

The angle the tent pole makes with the sides of the tent is 39.6 degrees

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Answer:

The central pole forms a right triangle with the floor of the tent. The

of the missing angle is the ratio of the length of the central pole to the length of the side of the tent, which is

. Applying

, we find that the angle the tent pole makes with the sides of the tent is

.

Step-by-step explanation:

Each of the terms here (64, a^3, b^15, c^6) have a cube root.

The cube root of 64 is 4, the cube root of a^3 is a, the cube root of b^15 is b^5, and the cube root of c^6 is c^2.

You end up with the square root of 4 times a times b^5 times c^2

√4ab⁵c²

Answer:

61.875

length 3

width 2.5

hight 8.25

Answer:

Nicholas.

Step-by-step explanation:

2/3 is also 10/15

3/5 is also 9/15

10/15 is more, so 2/3 is more

Hope this helped :D

Answer:

Nick, drank 1/15 more

Step-by-step explanation:

1. Create Equation

2/3-3/5

2. Solve

2/3-3/5

10/15-9/15

1/15

Both circles are similar, therefore:

The area of circle B is: 33.75 sq. units.

The ratio of the area of circle A to that of circle B = 9/16 = 0.75

The ratio of the area of similar circles = ratio of the square of their scale factor.

Given the following:

Area of circle A = 45 sq. units.

Scale factor = 3/4

The area of circle B = 45 × 3/4 = 33.75 sq. units.

The ratio of the area of circle A to that of circle B = (3/4)² = 9/16 = 0.75

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Answer: 81%

Step-by-step explanation:

From the question, we are informed that a student received the following test scores: 71%, 89%, 72%,

84% and 83% in 5 tests and the student wants to maintain an average of 80%.

The lowest score/grade they can receive on the next test to maintain at least an 80% average first thus:

First, to make it easy we can remove the percent sign. Then we multiply 80 by 6 since we're calculating for 6 tests scores. This will be:

= 80 × 6

= 480

We then add all the 5 test scores. This will be:

= 71 + 89 + 72 + 84 + 83

= 399

We then subtract the values gotten. This will be:

= 480 - 399

= 81

This means the student must get at least 81%

Answer:

In Geometry, “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles.

A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point. Thus, we can say, a perpendicular bisector always divides a line segment through its midpoint. The term bisect itself means dividing equally or uniformly.

Hope it helps!

Have a nice day!

Answer:

C. the same

Step-by-step explanation:

4.80 divided by 12 equals .40

6.40 divided by 16 equals .40

Answer: s = 12 degrees

Step-by-step explanation:

We know that the sum of angles in a triangle is 180 degrees.

So we can set up an equation to find s given that:

7s + 4s + s + 36 = 180

Combine like terms:

12s + 36 = 180

Subtract 36 from both sides:

12s = 144

Divide both sides by 12:

s = 12

Answer:

[tex]9 - 4m = 19 \\ 4m = 9 - 19 \\ 4m = -10 \\ m = \cancel{\frac{-10}{4} } \\ \\ m = \frac{-5}{2} \\ \\ m = - 2.5[/tex]

hope helpful~

Answer:

m=-2.5

Step-by-step explanation:

Answer:

7.071

Step-by-step explanation:

Hope this helps (:

Answer:

y=2x+1

Step-by-step explanation:

Y intercept is 1 and slope is 2/1

While solving the equation 5(2x - 8) = 20, we used the distributive, combining like terms and Division property but commutative property is not part of the solution process, option D is correct.

The given equation is 5(2x - 8) = 20.

Using the distributive property, we get:

10x-40=20

Add  40 from both sides:

10x-40+40=20+40

Combining like terms:

10x=60

Divide both sides by 10 to isolate the variable:

10x/10=60/10

x=5

Hence, for solving the equation we have not used the commutative property. option D is correct.

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Answer:

A = $129,659.95

Step-by-step explanation:

the equation used for compound is  A = Pe^rt, where p= principle, r=rate(interest) e=2.71828, and t=time. first convert the rate into a decimal, then plug in the numbers into the equation.

A = 81,200.00(2.71828)^(0.036)(13)

Answer:

13

Step-by-step explanation:

6x2=12+13=25-15=10+3=13

The correct answer is

c) Neither person is correct because light does not change frequency when it travels through different media

we have given that The column on the right is labeled speed of light in meters per second and are all times 10 Superscript 8 Baseline with entries 2. 25, 2. 99, 1. 97, 1. 24.

light changes both wavelength and speed when it travels through different media, but the frequency remains the same

light changes both wavelength and speed when it travels through different media, but the frequency remains the same.

Therefore the option c is correct that

Neither person is correct because light does not change frequency when it travels through different media

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Answer:

The answerb is c

Step-by-step explanation:

Neither person is correct because light does not change frequency when it travels through different media.

Answer:

B

Step-by-step explanation:

If the screws stay the same then u multiply both sides by 20

Answer:

Option 2

Step-by-step explanation:

If the screw : bolt ratio is 4 : 7 to make a metal table,

then the correct option is :-

It would be A.15ft

Step-by-step explanation:

Answer:

7 = 84

Step-by-step explanation:

3 + 4 = 7

36 + 48 = 84

7 = 84

Hope this helps :)

Answer:

first question : solve for m: multiply both sides by n

m/n=p

m*(n)/n=p*n

m= p*n

Step-by-step explanation:

to solve for m in the first part, you have to get rid of the extras next to m. in this case because m is divided by n, if we multiply both sides by n, both n on the m side will cancel out n/n=1 . this will leave m*1= n*p

because we can ignore the coefficient 1, the solution of ot will give you m=n*p

this also answers the question that's asked in the first place. in the first question, you have to multiply both sides by n in order to get the answer.

Answer:

They will provide a warranty that guarantees a replacement if the calculator stopsworking within the specified time frame, and are trying to ...

Step-by-step explanation:

make me as brain liest

Answer:

this is hard-

Step-by-step explanation:

Hello

the same colour = ( RR- BB)

= 3/7 x  3/7  + 4/7 x 4/7

= 9/49 + 16/49

= 25/49