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xeze [42]
1 year ago
5

Find the numbers of faces, edges, and vertices of the solid.

Mathematics
1 answer:
deff fn [24]1 year ago
7 0

Answer:

  • 7 faces
  • 15 edges
  • 10 vertices

Step-by-step explanation:

This is a counting problem. As with many counting problems, it is helpful to adopt a strategy that helps ensure you count everything only once.

__

<h3>Faces</h3>

There are two pentagonal faces and 5 rectangular faces for a total of ...

  7 faces

__

<h3>Edges</h3>

There are 5 edges around each of the pentagonal faces, and 5 edges connecting the top face to the bottom faces, for a total of ...

  15 edges

__

<h3>Vertices</h3>

There are 5 vertices on the top face, and 5 on the bottom face, for a total of ...

  10 vertices

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Two Parallel lines are cut by a transcersal and form a pair of alternate exterior angles. One angle measures (6x + 5) and the ot
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Answer:

11° is the measure of the exterior angles

Step-by-step explanation:

Theorem:   Alternate exterior angles are congruent when two parallel lines cut by a transversal.

First we solve for x using the theorem

6x + 5 = 7x + 4

x = 1

Substitute x = 1 into 6x + 5

6(1) + 5 = 6 + 5 = 11°

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Answer:

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Step-by-step explanation:

f(x) = 9(3)^x

f(-4) = 9(3)^{-4}

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30 points!!<br> What is the sum of the first six terms of the series?<br> 48 - 12 + 3 - 0.75 +...
Lunna [17]

Answer:

The sum of the first six terms is 38.39

Step-by-step explanation:

This is a geometric sequence since the common difference between each term is -\frac{1}{4}

Thus, r=-\frac{1}{4}

To find the sum of first six terms, we need to find the fifth and sixth term of the sequence.

To find the fifth term:

The general form of geometric sequence is a_{n}=a_{1} \cdot r^{n-1}

To find the fifth term, substitute n=5 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{5} &=(48) \cdot\left(-\frac{1}{4}\right)^{5-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{4} \\&=(48)\left(\frac{1}{256}\right) \\a_{5} &=0.1875\end{aligned}

To find the sixth term, substitute n=6 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{6} &=(48) \cdot\left(-\frac{1}{4}\right)^{6-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{5} \\&=(48)\left(-\frac{1}{1024}\right) \\a_{5} &=-0.046875\end{aligned}

To find the sum of the first six terms:

The general formula to find Sn for |r| is S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}

\begin{aligned}S_{6} &=\frac{48\left(1-\left(-\frac{1}{4}\right)^{6}\right)}{1-\left(-\frac{1}{4}\right)} \\&=\frac{48\left(1-\frac{1}{4096}\right)}{1+\frac{1}{4096}} \\&=\frac{48(0.95)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{47.9904}{5} \\&=38.39\end{aligned}

Thus, the sum of first six terms is 38.39

5 0
2 years ago
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