5x 3x + 20 Solve for x

Simplify by combining like terms: -10 + 7x +24 -2x

spin [16.1K]

-10 + 7x +24 -2x

Step 1: (7X-2X) + (24-10)
Step 2: 5X + 14

7 0

3 years ago

Write the linearization of the function at the points indicated. (Enter your answer as an equation. Let x be the independent var

Natalija [7]

Answer:

$\displaystyle y=5+\frac{x}{10}$

$\displaystyle y=10+\frac{(x-75)}{20}$

Step-by-step explanation:

Linearization

It consists of finding an approximately linear function that behaves as close as possible to the original function near a specific point.

Let y=f(x) a real function and (a,f(a)) the point near which we want to find a linear approximation of f. If f'(x) exists in x=a, then the equation for the linearization of f is

$y=f(x)=f(a)+f'(a)(x-a)$

Let's find the linearization for the function

$y=\sqrt{25+x}$

at (0,5) and (75,10)

Computing f'(x)

$\displaystyle f'(x)=\frac{1}{2\sqrt{25+x}}$

At x=0:

$\displaystyle f'(0)=\frac{1}{2\sqrt{25+0}}=\frac{1}{10}$

We find f(0)

$f(0)=\sqrt{25+0}=5$

Thus the linearization is

$\displaystyle y=f(0)+f'(0)(x-0)=5+\frac{1}{10}x$

$\displaystyle y=5+\frac{x}{10}$

Now at x=75:

$\displaystyle f'(75)=\frac{1}{2\sqrt{25+75}}=\frac{1}{20}$

We find f(75)

$f(75)=\sqrt{25+75}=10$

Thus the linearization is

$\displaystyle y=f(75)+f'(75)(x-75)=10+\frac{1}{20}(x-75)$

$\displaystyle y=10+\frac{(x-75)}{20}$

5 0

3 years ago

Jan 18 Spiral Review Find the surface area of the following complex shapes.

zepelin [54]

Answer:

320 in.²

Step-by-step explanation:

Let's think of the shape as a normal rectangle with a height of 16 inches. Now all we need is the length. If you look at the right corner, it looks like a piece has been cut out. Since that piece has the same length and height of 8 inches, it is a square. This tells us the missing length of the entire length of the rectangle. Now the length of the rectangle is 16 inches + 8 inches, which is 24 inches.

The total area of the rectangle is 16 × 24, which is 384.

Then from the total area, we just need to subtract the area of the cut-out part. The area of the cut-out square is 8 × 8, which is 64.

384 - 64 = 320

The total surface area of the following complex shape is 320 in.²

4 0

3 years ago

How to express my answer an an equation

lys-0071 [83]

N = g/p, because you divide p by each side

5 0

3 years ago

In a recent year, companies spent a total of $88.8 billion on newspaper, television, and radio ads. The total amount spent on

g100num [7]

Answer:

The amount spent on radio is $8.5 billion

The amount spent on television is $37.5 billion

The amount spent on newspaper is $42.8 billion

Step-by-step explanation:

Let;

x represent the amount spent on radio ads

y represent the amount spent on television ads

z represent the amount spent on newspaper ads.

The total amount spent on ads

x + y + z = 88.8 ......1

The total amount spent on television and radio ads was only $3.2 billion more than the amount spent on newspaper ads alone.

x + y = 3.2 + z

x + y - z = 3.2 .....2

The amount spent on newspaper ads was $5.3 billion more than what was spent on television ads.

z = 5.3 + y

z - y = 5.3 ......3

Subtracting equation 2 from equation 1;

(x + y + z) - (x + y - z) = 88.8 -3.2

z + z = 85.6

2z = 85.6

z = 85.6/2

z = 42.8

We can now substitute the value of z into equation 3

42.8 - y = 5.3

y = 42.8 - 5.3

y = 37.5

Substituting y and z to equation 1, we have;

x + 37.5 + 42.8 = 88.8

x =88.8 - (37.5 + 42.8)

x = 8.5

Therefore;

The amount spent on radio is $8.5 billion

The amount spent on television is $37.5 billion

The amount spent on newspaper is $42.8 billion

7 0

4 years ago