All categories

2 years ago

What is the volume of the triangle prism? ( HELP PLEASE )

Mathematics

1 answer:

worty [1.4K]2 years ago

3 0

Answer:

270 km³

Step-by-step explanation:

the volume = ½×9×6×10 = 270 km³

You might be interested in

Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.

Nezavi [6.7K]

Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4

2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = x² - 12x + 34

$y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}$

*******************************************************************************************

2) x = y² + 2y - 1

$x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}$

4 0

3 years ago

A factory needs to produce 1,800 jars of peanut butter on a certain day.

finlep [7]

Answer:

Step-by-step explanation:

because in 2 they make 600 and 600 times 3 is 1,800 then do 2 times 3 witch is 6 so 6 hours after 10:30 is 3:30. I hope that makes sense <3

7 0

2 years ago

Find the slope of the line that contains the following points. R(-3, 5), S(3, -2) 7/6 7/6 undefined

Musya8 [376]

Answer:

-\frac{7}{6}

Step-by-step explanation:

We can use the slope formula for the segment that joins any two points $(x_1, y_1)$ and $(x_2, y_2)$ :

$slope=\frac{y_2-y_1}{x_2-x_1}$

which in our case gives:

$slope=\frac{y_2-y_1}{x_2-x_1} = \frac{-2-5}{3-(-3)}=\frac{-7}{6} =-\frac{7}{6}$

5 0

2 years ago

How do you say 750 in words

Agata [3.3K]

750 in word form:

Seven Hundred Fifty

8 0

2 years ago

Read 2 more answers

Which number satisfies the inequality 9h + 15 > 55?

zalisa [80]

When you say "Which number ...", I expect to see a list of choices at the
end of the question, and I get very upset when there's nothing there.

9h + 15 > 55

Subtract 15 from each side: 9h > 40

Divide each side by 9 : <em> h > 40/9</em>

Any number greater than (4 and 4/9) satisfies the inequality.

5 0

3 years ago

Read 2 more answers