2m - 6 = 8m then 3m =

B refers to the base of the triangle,
and a signifies the length of the two identical sides.

The measurement labeled as 'a' is larger than 'b' since those equal sides are longer than the base. Given "one of the longer sides measures 6.3 cm," we assign a = 6.3.

Substitute 6.3 for each 'a' in the equation and solve for b:
2a + b = 15.7
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6 (applying subtraction property of equality)
b = 3.1

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

The equation is:
f(x) = 2x² - 44x + 185
f(x) = 2(x² - 22x + 121 - 121) + 185 =
= 2(x² - 22x + 121) - 242 + 185 =
= 2(x - 11)² - 57
Conclusion:
The vertex is located at (11, -57) and the vertex form is: f(x) = 2(x - 11)² - 57

<span>P(black socks): 24/42 or 12/21
P(black socks without replacement): 23/41. Consequently, the chance of randomly selecting 2 black socks, without replacement, from the basket is 12/21×23/41=276/861, equivalent to 32%. Hope this helps!</span>

Dimensions of the rectangle are defined as Length=2x
Width=x
The formula for perimeter is given by 2(Length) + 2(Width).

First, we need to determine the dimensions of the rectangle, specifically its length and width.

We can derive this equation:
24=2(2x)+2(x)
4x+2x=24
6x=24
x=24/6
x=4

Consequently, Length becomes 2x, leading to 2(4)=8.

Therefore, the length is 8 inches and the width is 4 inches.

Next, we will calculate the area of the rectangle.
The area can be computed as Length multiplied by Width.

Area=(8 in)(4 in)=32 in²

Conclusion: The area of Marshall's rectangular poster is 32 in².