Apple orchard sells Apple's in bags of 10. The orchard sold a total of 2,430 apples one day. How many bags of Apple's was this

Divide. Round to the nearest tenth if necessary. 11.4 divided by 19

Nana76 [90]

11.4 divided by 19 is 0.6

3 0

3 years ago

What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 in

EastWind [94]

Answer:

$6\sqrt{19} \approx 26.153$ inches.

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment $\mathsf{AG}$ .

In this diagram (not to scale,) $\mathsf{AB} = 26$ (length of prism,) $\mathsf{AC} = 2$ (width of prism,) $\mathsf{AE} = 2$ (height of prism.)

Pythagorean Theorem can help find the length of $\mathsf{AG}$ , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.

Start by finding the length of line segment $\mathsf{AD}$ . That's the black dotted line in the diagram. In right triangle $\triangle\mathsf{ABD}$ (second diagram,)

Segment $\mathsf{AD}$ is the hypotenuse.
One of the legs of $\triangle\mathsf{ABD}$ is $\mathsf{AB}$ . The length of $\mathsf{AB}$ is $26$ , same as the length of this prism.
Segment $\mathsf{BD}$ is the other leg of this triangle. The length of $\mathsf{BD}$ is $2$ , same as the width of this prism.

Apply the Pythagorean Theorem to right triangle $\triangle\mathsf{ABD}$ to find the length of $\mathsf{AB}$ , the hypotenuse of this triangle:

$\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}$ .

Consider right triangle $\triangle \mathsf{ADG}$ (third diagram.) In this triangle,

Segment $\mathsf{AG}$ is the hypotenuse, while
$\mathsf{AD}$ and $\mathsf{DG}$ are the two legs.

$\mathsf{AD} = \sqrt{26^2 + 2^2}$ . The length of segment $\mathsf{DG}$ is the same as the height of the rectangular prism, $2$ (inches.) Apply the Pythagorean Theorem to right triangle $\triangle \mathsf{ADG}$ to find the length of the hypotenuse $\mathsf{AG}$ :

$\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}$ .

Hence, the length of the longest line segment in this prism is $6\sqrt{19} \approx 26.153$ inches.

5 0

3 years ago

Im having a hard time on edge any tips?

slamgirl [31]

Answer:

Take deep breaths and focus, don't be afraid to ask for help.

Good luck!

5 0

3 years ago

Read 2 more answers

Given the function below, find x so that,<br> f(x)=10

ch4aika [34]

To find the slope and the -intercept of the line, first write the function as an equation, by substituting for

y=10
y=0x+10
y=0x+10 , m=0
y=0x+10 , m=0 , b=10

m=0 , b=10

The slope of the line is m=0 and the y-intercept is b=10

7 0

3 years ago

Which describes how to graph g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function?

ratelena [41]

Answer:

$f(x) =\sqrt[3]{x}$

Step-by-step explanation:

Hello!

Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:

$g(x) = \sqrt[3]{x-5}+7$

To have the the parent function, we must find the parent one, let's call it by f(x).

$f(x) =\sqrt[3]{x}$

This function satisfies the Domain of the given one, because the Domain is still $(-\infty, \infty)$ and the range as well.

Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.

4 0

3 years ago