Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below. 4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

Since the point lies on the circle, its coordinates must be,

The distance "d" from the point to (30,40) can be calculated as,

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when is at its lowest value.

Let’s set up the equation,

We find the critical points,

Then,

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

This leads us to conclude that the closest point is (78,104)

Answer: OPTION C.

Step-by-step explanation:

It is essential to consider the following:

Dilation:

• A transformation where the image retains the same shape as the original but differs in size.

• Dilation maintains the order of points.

•  Measurements of angles remain unchanged.

Translation:

• A transformation that keeps the image identical in size and shape to the original.

• Translation preserves the ordering of points.

• The angle measurements do not change.

Consequently, since Square T underwent translation followed by dilation to form Square T'', we conclude that the rationale explaining why they are similar is:

Translations and dilations maintain the order of points; thereby, the corresponding sides of squares T and T″ are proportional.

Try this method:
When a graph shifts right, replace 'x' with 'x' minus the number.
When it shifts down, subtract the number from 'y'.
So the final equation becomes: y = 4(x - 5)² - 18.
The answer is A.

Answer:

160/1001, 175/1001

Step-by-step explanation:

i) We calculate:

₈C₁ methods to select 1 new camera from a selection of 8

₆C₃ methods to select 3 refurbished cameras from a selection of 8

₁₄C₄ methods to select 4 cameras from the total of 14 cameras

The probability formula is:

P = ₈C₁ ₆C₃ / ₁₄C₄

P = 8×20 / 1001

P = 160 / 1001

P ≈ 0.160

ii) For at most one new camera, it means we want either one new camera or none at all. We've calculated the probability of selecting one new camera already. The probability of not selecting any new camera is equivalent to selecting 4 refurbished cameras:

P = ₆C₄ / ₁₄C₄

P = 15 / 1001

Therefore, the combined probability is:

P = 160/1001 + 15/1001

P = 175/1001

P ≈ 0.175

Answer:

The formula representing the penny's height as a function of time is:

After 7 seconds, the height of the penny will reach 667 feet.

Step-by-step explanation:

The penny experiences free fall.

With an initial velocity of zero and an initial height of h(0)=1,451.

Gravity acts as the acceleration, measured as g=32 ft/s^2.

The model can be initiated by analyzing speed:

Then, the height is expressed as:

The height of the penny at approximately 7 seconds can be calculated as:

After 7 seconds, the penny will stand at a height of 667 feet.