All categories

3 years ago

Five times a number added to twelve is nine times the number

Mathematics

1 answer:

8_murik_8 [283]3 years ago

8 0

Instructions? "Find the number."

12 + 5n = 9n

12 = 4n and so n = 3 (answer)

You might be interested in

If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

4 0

3 years ago

Solve 4(2x-3)=6x+2 I don't understand the steps pls

Marysya12 [62]

Answer: x = 7

Step-by-step explanation:

4(2x-3) = 6x+2 <--distribute the 4

8x - 12 = 6x + 2 <---add 12 to both sides

8x = 6x + 14 <--- subrtract 6x from both sides

2x = 14 <--- divide by two

x = 7

6 0

3 years ago

HURRY PLEASE 6TH GRADE MATH HERE. A football field is 100 yards in length. How many inches long is a football field? 300 inches

Rufina [12.5K]

Answer:

3,600

Step-by-step explanation:

1 yard= 36 inches

36 inches*100= 3,600

__________________________________________________________

Brainliest? I am trying to get to a new rank so I can help more people and I would totally appreciate it if you did!

Merry Christmas!

3 0

3 years ago

Read 2 more answers

Write a unit rate for the situation. 1080 miles on 15 gallons

Masja [62]

72 miles=1 gallon

Step by step Explanation:
Divide 1080 by 15 and divide 15 by 15. You get 72 and one.
Hope me helped!

4 0

2 years ago

Read 2 more answers

Find the value of x that will make A||B

Jlenok [28]

Answer:

x=20

Step-by-step explanation:

For A to be parallel to B, the angles of 5x+20 and 3x+60 must be equal.

5x+20=3x+60

2x=40

x=20

3 0

3 years ago

Read 2 more answers