How many quarts in a gallon

What does 3x2 + 9x − 30

Harlamova29_29 [7]

Answer:38

Step-by-step explanation:

7 0

3 years ago

A knife is three times the cost of a spoon. 9 spoons and 12 knifes cost ?82.80 workout the cost of 1 knife.

tankabanditka [31]

Let S = spoon

Let K = knife

1 knife is thee times the cost of a spoon, so it would be 3S

Now you have 9S + 12K = 82.80

We can replace the K with 3S:

9S +12(3S) = 82.80

Simplify the left side:

9S + 36S = 82.80

Add:

45S = 82.80

Divide both sides by 45"

S = 82.80 / 45

S = 1.84

One spoon cost $1.84

We know one knife cost 3 times as much, so multiply the cost of a spoon by 3:

Knife = 1.84 x 3 = $5.52

7 0

3 years ago

Read 2 more answers

If the local linear approximation of f(x) = 2cos x + e^2x at x = 2 is used to find the approximation for f(2.1), then the % erro

yKpoI14uk [10]

Answer-

The % error of this approximation is 1.64%

Solution-

Here,

$\Rightarrow f(x) = 2\cos x + e^{2x}$

$\Rightarrow f'(x) = -2\sin x + 2e^{2x}$

And,

$\Rightarrow f(2) = 2\cos 2 + e^{4}$

$\Rightarrow f'(2) = -2\sin 2 + 2e^{4}$

Taking (2, f(2)) as a point and slope as, f'(2), the function would be,

$\Rightarrow y-y_1=m(x-x_1)$

$\Rightarrow y-(2\cos 2 + e^{4})=(-2\sin 2 + 2e^{4})(x-2)$

$\Rightarrow y=(-2\sin 2 + 2e^{4})(x-2)+(2\cos 2 + e^{4})$

The value of f(2.1) will be

$\Rightarrow y=(-2\sin 2 + 2e^{4})(2.1-2)+(2\cos 2 + e^{4})$

$\Rightarrow y=(-2\sin 2 + 2e^{4})(0.1)+(2\cos 2 + e^{4})$

$\Rightarrow y=64.5946$

According to given function, f(2.1) will be,

$\Rightarrow f(2.1) = 2\cos 2.1 + e^{2(2.1)}$

$\Rightarrow f(2.1) = 65.6766$

$\therefore \%\ error=\dfrac{65.6766-64.5946}{65.6766}=0.0164=1.64\%$

5 0

3 years ago

= Homework: Section 9.6

MA_775_DIABLO [31]

Answer:

here is an an example

Step-by-step explanation:

Let x = the width of the rectangle

P = 2l + 2w

2(40) + 2x ≤ 150

80 + 2x ≤ 150

2x ≤ 70

x ≤ 35 cm

7 0

3 years ago

Solve (x + 5)^(3/2)= (x - 1)^3

IRINA_888 [86]

Answer:

x = 4

Step-by-step explanation:

For an equation of this sort, my first step is to rewrite it so the solutions are the x-intercepts of the graph:

(x +5)^(3/2) -(x +1)^3 = 0

The graph is attached. The one real solution is x=4.

__

The solution method for something like this is necessarily ad hoc. Here, it appears that progress can be made by raising both sides of the equation to the 2/3 power:

((x +5)^(3/2))^(2/3) = ((x -1)^3)^(2/3)

x +5 = (x -1)^2

Now, you have an ordinary quadratic that can be solved using any of the usual methods.

x^2 -2x +1 = x +5 . . . . swap sides, expand the square

x^2 -3x -4 = 0 . . . . . . put in standard form

(x -4)(x +1) = 0 . . . . . . factor

The solutions to this are ...

x = 4, x = -1 . . . . . . . values of x that make the factors zero

__

To see if either of these solutions is extraneous, we can check them:

(4 +5)^(3/2) = (4 -1)^3 . . . . . substitute 4 for x

9^(3/2) = 3^3 . . . . . . . . . true

(-1 +5)^(3/2) = (-1 -1)^3 . . . . . substitute -1 for x

4^(3/2) = (-2)^3

8 = -8 . . . . . . . . . . . false; x = -1 is extraneous

The solution is x = 4.

_____

Additional comment

You can eliminate the x=-1 "solution" by considering the domains of the left- and right-side expressions. The 3/2 power is equivalent to the square root of the cube. That will generally only be defined for non-negative values (x ≥ -5). The cube on the right will only be positive for x > 1, so the practical domain of this equation is x ≥ 1.

5 0

3 years ago