A pitcher of water at 40 degrees Fahrenheit is placed into a 70 degree room. One hour later, the temperature has risen to 45 deg

Answer:

The function decreases across all real numbers x where x < 1.5.

Step-by-step explanation:

We have

This represents an upward-opening vertical parabola

The vertex denotes a minimum point

The vertex is located at (1.5,-6.25)

We know that

The function is decreasing within the interval ----> (-∞, 1.5) x < 1.5

This means----> the function is continuously decreasing for all real x values under 1.5

Conversely, the function is increasing within the interval ----> (1.5, ∞) x> 1.5

Thus, for all real x values greater than 1.5, the function is increasing

Check the attached figure for further clarification

Therefore

The true statement is

The function decreases across all real numbers x where x < 1.5.

Answer:

It is a) 40°

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Answer:

3) A line has one dimension, length. (True)

5) A plane is made up of an infinite collection of lines. (True)

Explanation:

Geometry has three undefined terms:

a) point

b) line

c) plane

Examining the given statements:

1) A point described as (x, y) has two dimensions — this is incorrect because a point has no dimensions.

2) A plane has clear start and end points — this is false as a plane extends infinitely without boundaries.

3) A line has exactly one dimension, which is its length. (True)

4) A point consists of countless lines — this is false; actually, a line consists of infinite points.

5) A plane consists of an unending set of lines. (True)

To simplify the expression:
-(6 x^3 - 2 x + 3) - 3 x^3 + 5 x^2 + 4 x - 7

Start with - (6 x^3 - 2 x + 3) = -6 x^3 + 2 x - 3:
-6 x^3 + 2 x - 3 - 3 x^3 + 5 x^2 + 4 x - 7

Next, combine similar terms: -3 x^3 - 6 x^3 + 5 x^2 + 4 x + 2 x - 7 - 3 = (-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3):
(-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3)

-3 x^3 - 6 x^3 results in -9 x^3:
-9 x^3 + 5 x^2 + (4 x + 2 x) + (-7 - 3)

Combine 4 x and 2 x to get 6 x:
-9 x^3 + 5 x^2 + 6 x + (-7 - 3)

The operation -7 - 3 yields -10:
-9 x^3 + 5 x^2 + 6 x - 10

Factoring out -1 from -9 x^3 + 5 x^2 + 6 x - 10 leads to:
Final Answer: - (9 x^3 - 5 x^2 - 6 x + 10)