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2 years ago

A hexagonal pyramid is cut by a plane as shown in the diagram. What is the shape of the resulting cross section? see diagram

Mathematics

2 answers:

Alenkasestr [34]2 years ago

9 0

From the diagram you can see that plane cuts each lateral face of hexagonal pyramid and do not cut the base. A hexagonal pyramid has six lateral faces. The intersection of each of these lateral faces with given cutting plane is segment. The figure which consists of these segments is hexagon. This hexagon is not the same as base and even is not similar to the base because the cutting plane is not parallel to the base.

Answer: resulting cross section is a hexagon, correct choice is option 4.

Elan Coil [88]2 years ago

4 0

Cutting a hexagonal pyramid by a plane parallel to the base would result to a cross section with a shape of hexagon which would be same with its base. A cross section is a plane that results from cutting an object using a plane.

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8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the comm

denpristay [2]

Answer:

Step-by-step explanation:

We can express the 8th term as x and the 12th term as y.

This would mean that 8x=12y

Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y

Now we can use this to substitute y with x in the first equation. This would give us:

8x=12(x-8)

Which we can expand and solve:

8x=12x-96

-4x=-96

Therefore x=24

This means the 8th term is 24 and the 12th term is 16 (24-8).

To test if this is correct we can do:

8x24=12x16

Which indeed are equal, both sides multiply to 192.

Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)

24+14=38.

The first term is 38.

Hope this helped!

3 0

2 years ago

Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35

Brums [2.3K]

So for this, this can be written into the equation $y=50x+35$ (x = number of months, y = total cost).

To solve this problem, we need to plug in 1325 into the y-variable and solve from there.

$1325=50x+35$

Subtract 35 on each side to get $1290=50x$

Then just divide by 50 on each side, and your answer should be $25.8=x$

And because we cannot go past budget, we will have to round down to 25. In context, the maximum amount of months Abbey can do is 25 months.

8 0

2 years ago

Read 2 more answers

Write the expression 6^7/12 in radical form.

Marat540 [252]

$In\\general
\\ a^{ \frac{x}{y} } = \sqrt[y]{a^{x}} 

For our example,

\\ \\6^{ \frac{7}{12} = \sqrt[12]{6^{7}}$

4 0

1 year ago

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Consider the inverse function. Which conclusions can be drawn about f(x) = x2 + 2? Select three options. f(x) has a limited rang

PolarNik [594]

Answer:

f(x) has a limited range

f(x) has a maximum at the point (0, 2)

f(x) has a y-intercept at the point (0, 2).

Step-by-step explanation:

Given the function;

f(x) = x^2+2

The domain is the value of the input variables for which the function will exist. According to the expression given, the function exists on all real values of x. The same goes with range which deals with the output values. It also exists on all real values from 2 and above.

Hence f(x) have a limited range (since values less than 2 are not included compare to domain that exists on all real values) and does not have a restricted domain.

For the x intercept, x intercept occur at y = 0

substitute y = 0 into the function and get y

if y = f(x)

y = x^2+2

0 = x^2 + 2

x^2 = -2

x = 2i

Hence f(x) does not have an x-intercept of (2, 0)

For the y intercept, y intercept occur at x = 0

substitute x = 0 into the function and get y

if y = f(x)

y = x^2+2

y = 0^2 + 2

y = 2

Hence f(x) has a y-intercept at point (0, 2)

f(x) is at maximum if d(fx))/dx = 0

d(fx))/dx = 2x

since d(fx))/dx = 0

0 = 2x

x = 0

substitute x = 0 into the function

f(x) = x^2 + 2

y = 0^2+2

y = 2

Hence f(x) has a maximum at the point (0, 2)

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1 year ago

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Choose the most accurate statement based on the graph shown.

Eddi Din [679]

The most accurate would be the second statement: <span>The graph is misleading because it uses 3-dimensional bars.

The vertical range is just enough. It only appears small because the bars are in 3D. It should have been in 2D so that we could directly trace it to how much frequency each category is. Even the axes are in 3D also.</span>

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1 year ago

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