What is the value of x, given that the two pyramids are similar?

Mathematics

2 answers:

kiruha [24]3 years ago

7 0

Answer:

A 3

Step-by-step explanation:

big pic base length = 8

small pic base length = 4

8÷4 = 2

big pic height = 6

small pic height = 6÷2 =3

Dvinal [7]3 years ago

7 0

The pyramid is dilated by the scale factor of 2.

$8 \div 2=4$

$6 \div 2 = 3$

You might be interested in

Help it’s slope idk how to do it

Over [174]

a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

Finally, the equation of the line is:

$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

In this case, we have that:

The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
The y-axis represents the <em>Height of the Tree </em>in inches.

Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation: