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2 years ago

Simplify the radical expression. 3^ sqrt 125x^9

Mathematics

1 answer:

QveST [7]2 years ago

6 0

$\sqrt[3]{125x^9} = \sqrt[3]{(5x^3)^3} =5x^3$

The answer is 5x³

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3. Identify the transformation(s) that has taken place in the pictures below. Be as specific as possible!

GuDViN [60]

Answer:

A. Reflection

B. Rotation and Translation

C. Translation

Step-by-step explanation:

We are given the figures transformed to different figures.

According to the options,

A. We see that,

Triangle ABC is reflected about the line y=x to obtain the triangle A'B'C'.

B. In the second figure, we get,

Triangle RST is rotated clock-wise around the point T and then translated 2 units to the right to obtain R'S'T'.

C. We have,

Triangle EFD is translated 3 units downwards followed by translation of 2 units to the right to get E'F'D'.

5 0

3 years ago

Write as logarithm with base 4: 4 -5 2 -4

NeX [460]

Answer:

log_4(256)=4

log_4(1/1024)=-5

log_4(16)=2

log_4(1/256)=-4

Step-by-step explanation:

We want to write a number, x, such that

Log_4(y)=x.

In exponential form that is 4^x=y.

So first number is x=4.

4^4=256 which means log_4(256) is 4 as a logarithm with base 4.

The second number is x=-5.

4^-5=1/4^5=1/1024 which means log_4(1/1024) is -5 as a logarithm with base 4.

The third number is x=2.

4^2=16 so log_4(16) is 2 as a logarithm with base 4.

The fourth number is x=-4.

Since 4^4=256 then 4^-4=1/256 which means -4 as a logarithm with base 4 is log_4(1/256).

8 0

2 years ago

Marris decides to bake his parents a cookie in the shape of a regular dodecagon (12‑gon) for their 12-day anniversary.

allochka39001 [22]

Answer:

The answer to each question is:

A.) 403.2 $cm^{2}$
B.) 100. 8 $cm^{2}$

Step-by-step explanation:

A.) To obtain the area of the dodecagon, you can use the next formula:

Area of a dodecagon = 6 * apothem * edge

In the exercise, we have the edge (6 cm), but, to find the apothem of a dodecagon, that is the distance between the center of the polygon, and the middle point of each side, you can use the next formula:

Apothem = Edge * $\frac{2+\sqrt{3}}{2}$

If we replace the value of the edge, we obtain:

Apothem = 6 cm * $\frac{2+\sqrt{3}}{2}$
Apothem = 11.2 cm (approximately).

With this data, we can find the area:

Area of a dodecagon = 6 * apothem * edge
Area of a dodecagon = 6 * 11.2 cm * 6 cm
Area of a dodecagon = 403.2 $cm^{2}$

Then, the area of the dodecagon is 403.2 $cm^{2}$ approximately.

B.) As the area obtained is for 12 pieces, when the parents ate 9 pieces, just left 3 pieces, with these values you can make a rule of three.

If:

12 pieces = 403.2 $cm^{2}$
3 pieces = X

Then:

X = (3 * 403.2 $cm^{2}$ ) / 12
X = 1209.6 $cm^{2}$ / 12
X = 100. 8 $cm^{2}$

In this form, when the cookie has 3 pieces, its area is 100. 8 $cm^{2}$ approximately.

5 0

3 years ago

Find the volume of the figure

Charra [1.4K]

8*10*14 = 1120
10*8*10 = 800
1120+800 = 1920
volume =1920 cm3

7 0

3 years ago

Can somebody give the answer and help explain how they got it?

beks73 [17]

When all three are put together you get a rectangle. Therefore we can use this formula to solve it:
A=lw
=(10.5+12)×15
=22.5×15
=337.5 ft^2

This means C is the answer. Hope this helps.

4 0

3 years ago

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