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2 years ago

If-1 is a root of f), which of the following must be true?

Mathematics

1 answer:

ANEK [815]2 years ago

6 0

Answer:

A factor of f(x) is (x + 1).

Step-by-step explanation:

When we put x+1= 0 then we get the value x= -1

This value is then put into the function to find out whether it is a root or not. For a root to exist it must not have a remainder or the remainder must be zero.

Suppose the function is

F(x)= 2x³ - 42x - 40

f(-1)= 2(-1)³ - 42(-1) - 40

f(-1)= -2 + 42- 40

f(-1)= 0

This gives -1 as the root of the function.

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What is the inverse of the function f(x) = 2x + 1?

Gekata [30.6K]

5 0

3 years ago

The output y and input x of a device are related by y = x + 1.4x3 . (a) Find the values of the output for steady-state operation

erma4kov [3.2K]

Answer:

a) $y(1) = 2.4$ , $y(2) = 13.2$ , b) $y(x) = 2.4 + 5.2\cdot (x-1)$ , $y(1) = 2.4$ , $y(2) = 7.6$

Step-by-step explanation:

a) The values of the output for steady-state operation are:

$y(1) = 1 + 1.4\cdot (1)^{3}$

$y(1) = 2.4$

$y(2) = 2 + 1.4\cdot (2)^{3}$

$y(2) = 13.2$

b) The formula for linearization is:

$y(x) = y(1) +\frac{dy}{dx}|_{x = 1} \cdot (x-1)$

The first derivative of the formula evaluated at x = 1 is:

$\frac{dy}{dx}|_{x=1} = 1 + 4.2\cdot (1)^{2}$

$\frac{dy}{dx}|_{x=1} = 5.2$

The linearized model is:

$y(x) = 2.4 + 5.2\cdot (x-1)$

The output at x = 2 is presented below:

$y(2) = 2.4 + 5.2\cdot (2-1)$

$y(2) = 7.6$

Linearized model offers reasonable approximations for small intervals.

5 0

2 years ago

The distance between 19 and -15 on a number line is 4?

Murrr4er [49]

Answer:

See explanation below.

Step-by-step explanation:

No.

The distance between 19 and 15 is 4. Both numbers are positive, 4 units apart.

The distance between -19 and -15 is also 4. Both numbers are negative, 4 units apart.

When you find the distance from 19 to -15, keep in mind that one number is positive, 19, and one number is negative, -15. The two numbers are on different side of zero on the number line.

Start at -15. -15 is 15 units to the left of zero. To get to 0, you need to go 15 units right. Now you need to go from 0 to 19. That is another 19 units right. Add 15 + 19 to get 34.

The distance from 19 to -15 on a number line is not 4. It is 34.

8 0

2 years ago

The length of a football field should be measured in

tiny-mole [99]

The length of a football field should be measured in yards

3 0

2 years ago

Read 2 more answers

The area of a storage shed floor is 20 ft2. The length is 3 more than twice the width. Find the dimensions of the storage shed f

vladimir1956 [14]

Answer:

2.5 ft wide
8 ft long

Step-by-step explanation:

The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.

<h3>Given relation</h3>

Let x represent the width of the shed. Then the length is (2x+3), and the area is ...

A = LW

20 = (2x+3)(x) . . . . . area of the shed

<h3>Solution</h3>

Completing the square gives ...

2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides

2(x +0.75)² = 21.125 . . . . . . . write as a square

x +0.75 = √10.5625 . . . . . divide by 2, take the square root

x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution

The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.

8 0

1 year ago