Every 9 out of 12 were chosen

Anna71 [15]

$4-(2a+3b)^2$

$(2a+3b)^2 :$

$4a^2+12ab+9b^2$

$= 4-(4a^3+12ab+9b^2)$

$=-(4a^2)-(12ab)-(9b^2)$

apply minus - plus rules :

$+(-a)=-a$

Refine:

$=-4-4a^2-12ab-9b^2$

hope this helps!

7 0

3 years ago

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

The circumference of a circular field is 200.96 meters. What is the diameter of the field? Use 3.14.

artcher [175]

Answer:

1262.0288

Step-by-step explanation:

2×3.14×200.96

3 0

3 years ago

A rectangular pyramid measures three feet by four feet at the base, and has a height of seven feet. Find its volume. A. 21 ft3 B

sweet-ann [11.9K]

Answer:

C. 28 ft³

Step-by-step explanation:

The general formula for the volume of a pyramid:

V = $\frac{1}{3}Bh$ , where B = the area of the base and h = height of the pyramid

Since the base is a rectangle, we can find area using the formula:

A = l x w or A = 3 x 4 = 12 ft²

Using B = 12 and h = 7:

V = $\frac{(12)(7)}{3}$

V = 28 ft³

3 0

3 years ago

I need help plzzz this is algebra

SpyIntel [72]

Set like terms on each side by adding six to the first side and subtracting 1/2x from the first side. this gives you 9<1.5x. divide both sides by 1.5 to get 66. the answer is 4) x>6

3 0

3 years ago