MATHEMATICS HIGH SCHOOL

A pentagonal prism is cut by a plane perpendicular to the base. What is the shape of the cross section that is formed?a pentagon with one pair of equal sides
a trapezoid with one pair of parallel sides
a rectangle
a triangle
a hexagon

Answers

Answer 1
Answer:

The correct answer is:

a rectangle

Explanation:

In a right pentagonal prism, the bases are pentagons and the lateral faces are rectangles.

If we take a cross-section perpendicular to the base, this same cross-section will be parallel to the lateral faces. This means it will be the same shape as the lateral faces, which is a rectangle.
Answer 2
Answer:

Answer:

rectangle

Step-by-step explanation:

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What is the volume of 5 m 8m and 10.5m​

Answers

Answer:

Volume = 5×8×10.5 = 420 meters3

Step-by-step explanation:

5×8×10.5

Write the standard form of the equation of the hyperbola 4x2 − 9y2 − 16x − 36y − 56 = 0.

Answers

The standard form of the equation of the hyperbola:

((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1

How did we get the values?

To write the standardform of the equation of a hyperbola, you need to rearrange the given equation into the following form:

((x-h)^2)/(a^2) - ((y-k)^2)/(b^2) = 1

Where (h, k) is the center of the hyperbola, and "a" and "b" are positive constants related to the shape and size of the hyperbola.

Start by completing the square for both the x and y terms:

1. Group the x terms and y terms separately:

  4x² - 16x - 9y2 - 36y - 56 = 0

2. Complete the square for the x terms by adding and subtracting the appropriate constant inside the first bracket:

  4(x² - 4x + 4) - 9y² - 36y - 56 = 0

3. Complete the square for the y terms by adding and subtracting the appropriate constant inside the second bracket:

  4(x² - 4x + 4) - 9(y² + 4y + 4) - 56 + 36 = 0

4. Now, rewrite the equation and simplify:

  4(x² - 4x + 4) - 9(y² + 4y + 4) - 20 = 0

5. Factor the squares:

  4(x - 2)² - 9(y + 2)² - 20 = 0

6. Divide both sides by the constants to isolate the equation:

((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1

Now, you have the standard form of the equation of the hyperbola:

((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1

The center of the hyperbola is at (h, k) = (2, -2), "a" is the square root of 5, and "b" is the square root of 20/9.

learn more about standard form: brainly.com/question/19169731

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Answer:

(x-2)^2/3^2 - (y+2)^2/2^2 =1

Step-by-step explanation:

Plato

Factor this expression. Check by multiplying factors. 3ab+a+3b^2+b
whats the answer

Answers

The solution to the problem is as follows:

you have"a" as common so, you can write it as: a(3b+1) +3b^2 + b. from the remaining two terms, you have b common, so write it as a(3b+1) +b(3b+1).

This gives you (a+b)(3b+1)

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Two fourth is _____________ pieces of the whole

Answers

1/2 pieces of the hole because you can simplify 2/4 by dividing it by 2 and you'll get 1/2

A vegetable garden and a surrounding path are shaped like a square that together are 11 feet wide. The path is 2 feet wide. Fins the total area of the veget garden and path.

Answers

The area of a square is found by S^2 where S is the length of a side.


The garden and path are 11 feet wide, so the total area for both is 11^2 = 121 square feet.


The length of a side of just the garden would be 11 - 4 ( 2 feet of path on both sides) = 7 feet


The area of the garden would be 7^2 = 49 square feet.


the area of the path would be the total area minus the area of the garden: 121-49 = 72 square feet.

Write the equation of the line that passes through the point (-3, 4) and is parallel to the line y = -3× + 10.

Answers