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Reika [66]
3 years ago
15

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. A solid right pyramid

has a regular hexagonal base with a radius of 2 x units and an apothem of x StartRoot 3 EndRoot units. Which expression represents the area of the base of the pyramid? x squared StartRoot 3 EndRoot units2 3 x squared StartRoot 3 EndRoot units2 4 x squared StartRoot 3 EndRoot units2 6 x squared StartRoot 3 EndRoot units2

Mathematics
2 answers:
Xelga [282]3 years ago
5 0

Answer:

6 x^2*\sqrt{3}

Step-by-step explanation:

The base of the pyramid we need to study is a hexagon.

Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.

Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")

Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.

We know the area of a triangle is the product of its base times its height, divided by 2: \frac{base*height}{2} = \frac{2x*height}{2}

We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures x\sqrt{3}, so replacing this value in the formula above for the area of one of the triangles:

\frac{2x*height}{2}= \frac{2x*x\sqrt{3} }{2}=x^2\sqrt{3}

Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):

Area of hexagon = 6x^2\sqrt{3}

which is the last option given in the list.

RUDIKE [14]3 years ago
3 0

Answer:

D

Step-by-step explanation:

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PLEASE HELPPP<br><br> Which expression is equivalent to
Anettt [7]

Answer:

Fourth option

Step-by-step explanation:

Given the expression in the picture:

Apply Power of Power Rule

\frac{64g {}^{9} h {}^{6}k {}^{12}  }{8g {}^{3} h {}^{2} }

8g {}^{6} h {}^{4} k {}^{12}

The left side of the equation option had this in the fourth option so the fourth option is right

7 0
3 years ago
You deposit 2000 in account A, which pays 2.25% annual interest compounded monthly. You deposit another 2000 in account b, which
stellarik [79]
To model this situation, we are going to use the compound interest formula: A=P(1+ \frac{r}{n} )^{nt}
where
A is the final amount after t years 
P is the initial deposit 
r is the interest rate in decimal form 
n is the number of times the interest is compounded per year
t is the time in years 

For account A: 
We know for our problem that P=2000 and r= \frac{2.25}{100} =0.0225. Since the interest is compounded monthly, it is compounded 12 times per year; therefore, n=12. Lets replace those values in our formula:
A=2000(1+ \frac{0.0225}{12} )^{12t}

For account B:
P=2000, r= \frac{3}{100} =0.03, n=12. Lest replace those values in our formula:
A=2000(1+ \frac{0.03}{12} )^{12t}

Since we want to find the time, t, <span>when  the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:
</span>2000(1+ \frac{0.0225}{12} )^{12t}+2000(1+ \frac{0.03}{12} )^{12t}=5000

Now that we have our equation, we just need to solve for t:
2000[(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}]=5000
(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}= \frac{5000} {2000}
(1.001875)^{12t}+(1.0025 )^{12t}= \frac{5}&#10;{2}
ln(1.001875)^{12t}+ln(1.0025 )^{12t}=ln( \frac{5} {2})
12tln(1.001875)+12tln(1.0025 )=ln( \frac{5} {2})
t[12ln(1.001875)+12ln(1.0025 )]=ln( \frac{5} {2})
t= \frac{ln( \frac{5}{2} )}{12ln(1.001875)+12ln(1.0025 )}
17.47

We can conclude that after 17.47 years <span>the sum of the balance in both accounts will be at least 5000.</span>
5 0
3 years ago
Mary bought these art supplies: 4 paint brushes @ $1.29 each, 6 dowel rods @ $1.49 each, a jar of paste @ $1.25, and 2 canvases
Sophie [7]

Answer:

Option (1) is correct

The amount she receives back from $40 is  $12.65

Step-by-step explanation:

Given: Mary bought the art supplies.

4 paint brushes @ $1.29 each, 6 dowel rods @ $1.49 each, a jar of paste @ $1.25, and 2 canvases @ $6.00 each.

We have to find the change she get from $40.

We first find the total cost of the art supplies.

Since, she brought 4 paint brushes @ $1.29 each,

Thus, cost of 4 paint brush is  1.29 × 4 = $5.16

Also, 6 dowel rods @ $1.49 each,

Thus, cost of 6 dowel rods is  1.49 × 6 = $8.94

Thus, cost of 1 jar of paste  is $1.25

and 2 canvases @ $6.00 each

Thus, cost of 2 canvases  is $12.00

Thus, total cost of art supplies = 5.16 + 8.94 + 1.25 + 12 =$27.35

Thus, amount she receives back from $40 is $40 - $12.35 = $12.65

4 0
3 years ago
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serious [3.7K]

Answer:

the slope is 23/1

Step-by-step explanation:

4 0
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Stels [109]

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Answer:

  40°

Step-by-step explanation:

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  ∠T = 40°

4 0
3 years ago
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