1. MULTIPLE CHOICE Suppose y varies directly as x.

A swimming pool is represented on a coordinate grid with the following vertices: Vertex A is at (−2,−3) . Vertex B is at (−2,

Semmy [17]

Answer:

26 yards.

Step-by-step explanation:

We can find the distance walked by Jared by finding the distances between each of the given vertex of swimming pool. We will use distance formula to find the distances between each vertex.

$\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2--2)^{2}+(-3-5)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2+2)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(0)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{64}=8$

Now let us find distance between vertex B and vertex C.

$\text{Distance between vertex B and vertex C}=\sqrt{(-2-3)^{2}+(5-5)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{(-5)^{2}+(0)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{25}=5$

Now let us find distance between vertex C and vertex D.

$\text{Distance between vertex C and vertex D}=\sqrt{(3-3)^{2}+(5--3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{(0)^{2}+(5+3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{64}=8$

Now let us find distance between vertex D and vertex A.

$\text{Distance between vertex D and vertex A}=\sqrt{(3--2)^{2}+(-3--3)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{(3+2)^{2}+(-3+3)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{(5)^{2}+(0)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{25}=5$

Now let us add all these distances to find the total distance walked by Jared.

$\text{Total distance walked by Jared}=8+5+8+5$

$\text{Total distance walked by Jared}=26$

Since we have been given that one unit on the grid equals 1 yard, therefore, Jared walked a distance equal to 26 yards.

3 0

3 years ago

The region bounded by the curve y = 2/(1 + e−x), the x- and y-axes, and the line x = 10 is rotated about the x-axis. Use Simpson

sp2606 [1]

Answer:

21 darted to the nearest 10

Step-by-step explanation:

idk lol, sorry please don't report have great night or day where ever you live :D

4 0

2 years ago

6. Calculate the area of the octagon in the figure below.

Kryger [21]

Answer:

$41\text{ [units squared]}$

Step-by-step explanation:

The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.

The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:

4 triangles (corners)
3 rectangles (one in the middle, two on top after you remove triangles)

Formulas:

Area of rectangle with length $l$ and width $w$ : $A=lw$
Area of triangle with base $b$ and height $h$ : $A=\frac{1}{2}bh$

Area of triangles:

All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.

Thus, the total area of one is $A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}$

The area of all four is then $2\cdot 4=8$ units squared.

Area of rectangles:

The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of $3\cdot 2=6$ units squared, and the both of them have a total area of $6\cdot 2=12$ units squared.