Solve the inequality -2x+10<=24

Find and simplify each of the following for

WINSTONCH [101]

Answer:

(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

(B) f(x + h) - f(x) = 8xh + 4h² - 6h

(C) $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

Step-by-step explanation:

* Lets explain how to solve the problem

- The function f(x) = 4x² - 6x + 6

- To find f(x + h) substitute x in the function by (x + h)

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) = 4(x + h)² - 6(x + h) + 6

- Lets simplify 4(x + h)²

∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²

∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²

- Lets simplify 6(x + h)

∵ 6(x + h) = 6(x) + 6(h)

∴ 6(x + h) = 6x + 6h

∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6

- Remember (-)(+) = (-)

∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

- Lets find f(x + h) - f(x)

∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)

- Remember (-)(-) = (+)

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6

- Simplify by adding the like terms

∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)

∴ f(x + h) - f(x) = 8xh + 4h² - 6h

* (B) f(x + h) - f(x) = 8xh + 4h² - 6h

- Lets find $\frac{f(x+h)-f(x)}{h}$

∵ f(x + h) - f(x) = 8xh + 4h² - 6h

∴ $\frac{f(x+h)-f(x)}{h}=\frac{8xh + 4h^{2}-6h}{h}$

- Simplify by separate the three terms

∴ $\frac{f(x+h)-f(x)}{h}=\frac{8xh}{h}+\frac{4h^{2} }{h}-\frac{6h}{h}$

∴ $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

* (C) $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

4 0

2 years ago

An object is moving at a speed of 3 kilometers per hour. Express this speed in feet per

Anvisha [2.4K]

Answer:

590,551.2

1km ⇦.0003048ft

1hr⇦60min

3÷0.0003048×60=590,551.18110236

590551.2

6 0

3 years ago

An exponential function is graphed for all real numbers. This includes which of the following sets of numbers?

anygoal [31]

In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.

An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.

Before you start, f(0) = 20 = 1

After 1 hour f(1) = 21 = 2

In 2 hours f(2) = 22 = 4

In 3 hours f(3) = 23 = 8

and so on.

With the definition f(x) = bx and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.

8 0

3 years ago

The area of the Pacific Ocean is about 6.0061 x 107 square miles. The area of the Southern Ocean is about 7.8483 x 106 square mi

Scilla [17]

Answer:

A. 8

Step-by-step explanation:

6.0061 x 10^7

/ = 6/8 x 10^7/10^6

7.8483 x 10^6

0.75 x 10^7-6

0.75 x 10^1

A: 0.75 = 7.5 = 8.

5 0

2 years ago

Ciara is naking a new outfit she needs 2 1/2 yards of the fabric for the shawl and 1 3/4 yards of fabric for the dress. If she h

valentina_108 [34]

Answer:

1 1/4 yards

$20

Step-by-step explanation:

The amount of fabric more that she needs can be determined by subtracting the sum of the yards needed for the shawl and the dress from the fabric she has

sum of the yards needed for the shawl and the dress =

$2\frac{1}{2} + 1\frac{3}{4}$