Simplify 16x^2 9y^2/(4x-3y)^2​

Answer:

Answer choice C. .

Step-by-step explanation:

The entire question is present in the attached figure.

It is established that

The function f(x) is represented by

,

indicating a parabola that opens upward.

The vertex is situated at the point (0,0).

The function g(x) shares the same parabolic shape.

The vertex of g(x) is located at (-3,1).

Therefore,

The transformation from f(x) to g(x) can be described as:

(0,0) transforms to (-3,1).

(x,y) transforms to (x-3,y+1).

This indicates a shift of 3 units to the left and 1 unit upward.

Thus,

The equation for g(x) in vertex form can be expressed as

.

<span>5.7 liters of a 5% solution combined with 4.3 liters of a 40% solution. To begin, define the problem with formulas. x Represents the liters of the 5% solution utilized. 10-x Represents the liters of the 40% solution used. This forms an equation: 5% of x plus 40% of (10-x) equals 20% of 10. 0.05x + 0.40(10-x) = 0.20 * 10 Now, distribute the 0.40 coefficient. 0.05x + 4.0 - 0.40x = 0.20 * 10 Next, combine the terms. 4.0 - 0.35x = 2.0 Add 0.35x to each side. 4.0 = 2.0 + 0.35x Subtract 2 from both sides. 2.0 = 0.35x Lastly, divide both sides by 0.35. 5.7 = x Thus, 5.7 liters of a 5% solution is required. To determine the volume of the 40% solution, subtract from 10. 10.0 - 5.7 = 4.3</span>

Answer:

The correct response is: b)

Step-by-step explanation:

a4b=24, where a × 4 × b = 24 implies a × b = 6

The pairs of numbers with a product of 6 include: {1,6} and {2,3}

In base 10, a4b translates to 100a + 40 + b

Calculating gives us:

100×1+40+6=146

100×6+40+1=641

100×2+40+3=243

100×3+40+2=342

Summing these results yields: 146 + 641 + 243 + 342 = 1372

The correct answer is: b)

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

I am hesitant to provide a definite answer since I'm not completely certain, but it's clear you can discard options C and D right away since the rate of change cannot be negative. Between options A and B, I would lean towards option B. I would have asked you to consider me the brainliest if I were correct, but I suspect this is for the IA4, where you're unable to check your grade... haha. Apologies, but I hope this assists you in some way!