MATHEMATICS HIGH SCHOOL

A cylindrical pail that has the base area of 9 pi inches squared and a height of 10 inches. One friend bought a pyramid mold with a square base with edge length of 4 inches and height of 7 inches. The other friend bought a cone with a radius of 2.5 inches and the height of six inches. What is the volume of these three objects?

Answers

Answer 1
Answer:

Answer:

  • cylinder — 90π in³
  • pyramid — 37 1/3 in³
  • cone — 12.5π in³

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = Bh . . . . . where B is the base area and h is the height

The volume of a pyramid or cone is given by ...

  V = (1/3)Bh . . . . . where B is the base area and h is the height

The area of a square of side length s is ...

  A = s²

The area of a circle of radius r is ...

  A = πr²

___

Using these formulas, the volumes of these objects are ...

  cylinder: (9π in²)(10 in) = 90π in³

  square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³

  cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid
Answer 2
Answer:

Answer:

12.5

Step-by-step explanation:

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At a store, ice cream cones cost $1.80 and sundaes cost $3.30. One day the receipts for a total of 148 cones and sundaes were $360.90. How many cones were sold? How many sundaes?

Answers

X= cones; y= sundaes

1.80x + 3.30y = 360.90 -------(i)

x + y = 148 -----------(ii)

from (ii) y= 148-x

1.80x + 3.30(148-x) = 360.9

1.80x + 488.4 + 3.30x = 360.9

1.5x = 127.5

x  = 85 cones

Find an equivalent function to f(x) = 5(3)3x. f(x) = 125x(27)x
f(x) = 152x
f(x) = 5(27)x
f(x) = 135x

Answers

If you would like to find an equivalent function to f(x) = 5(3)^(3x), you can do this using the following steps:

f(x) = 5(3)^(3x) = 5(3^(3x)) = 5(27)^x = 5(27)x

The correct result would be f(x) = 5(27)x.

Answer:

The correct result would be f(x) = 5(27)x.

Step-by-step explanation:

Cecil is buying almonds and cashews. A bag of almonds costs $7.00 and a bag of cashews costs $9.00. Cecil has $60 to spend on the nuts. Cecil wants to purchase at least 2 bags of almonds. Cecil does not want the cost of the cashews to exceed the cost of the almonds. What is the maximum number of bags of cashews that Cecil can buy?

Answers

The maximum number of bags of cashews are one

Find the y-intercept for the graph of the quadratic function. y + 4 = (x + 2)2 A. (0, 4) B. (0, 0) C. (4, 0) D. (0, -4

Answers

For y-intercept, x = 0.
y + 4 = (0 + 2)^2
y + 4 = 2^2
y + 4 = 4
y = 4 - 4 = 0

y-intercept is (0, 0)

If 2x-3(x+4)=-5 then x=

Answers

2x - 3(x + 4) = -5
2x - 3x - 12 = -5
-x - 12 = -5
-x = -5 + 12
-x = 7
x = -7

The answer is: x = -7.

Factor this trinomial completely.15x²+11x-12
OA. (3x+3)(5x-4)
OB. (3x+4)(5x-3)
C. (x+3)(15x-4)
OD. (x+4)(15x-3)

Answers

Answer:

B

Step-by-step explanation:

given the trinomial

15x² + 11x - 12

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 15 × - 12 = - 180 and sum = + 11

the factors are + 20 and - 9 , since

+ 20 × - 9 = - 180 and + 20 - 9 = + 11

use these factors to split the x- term

15x² + 20x - 9x - 12 ( factor the first/second and third/fourth terms )

= 5x(3x + 4) - 3(3x + 4) ← factor out (3x + 4) from each term

= (3x + 4)(5x - 3)

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