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3 years ago

Given the function f(x) = 3|x - 2| + 6, for waht values of x is f(x) = 18?

Mathematics

1 answer:

bixtya [17]3 years ago

7 0

Answer:

x = 6, x =2

Step-by-step explanation:

To solve this problem, you need to plug in 18 where it says f(x)

For example: f(x) = 3 |x - 2| + 6

18 = 3|x - 2| + 6

Next, you need to get rid of the 6 in order to balance the equation which means to subtract 6 from both sides. For example : 18-6 = 3|x - 2| + 6 - 6

That leaves us with 12 = 3|x - 2|. You need to divide both sides by 3.

For example: 12÷3 = 3|x - 2| ÷ 3

Then, you get 4 = |x - 2|. In order to get rid of the absolute value signs, you need to make 2 equations out of it. On the first equation, the signs of the integers stay the same while the second equation, flip the signs. Keep the answer next to the equal sign, the same sign. For example:

4 = |x - 2|

1. 4 = x - 2 or x - 2 = 4

2. 4 = -x + 2 or -x + 2 = 4

number 1 answer: add 2 from both sides of the equation. For example:

x-2 + 2 = 4 + 2. Then get rid of the -2 + 2 of the equation. You are left with x = 6

Number 2 answer: To solve this equation for x, you need to subtract 2 from both sides of the equation. For example: -x + 2-2 = 4-2. Then get rid of the 2-2 of the equation. You are left with -x = 2. The x variable can't be negative so you have to divide by -1 on both sides. The variable x equals to 1. For example: -x÷ -1 = 2÷-1. You are left with x = -2 as your answer. That's how you find your answer.

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Calculate the force output by the larger piston of a hydraulic lift when a force of 800 N is exerted on the smaller piston. The

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answer:

step by step explanation

Note the second diameter was used as 50cm and not 500cm

given

F1=800N

D1=20cm

A1=πD1^2/4

=3.142*20^2/4

=314.2cm^2

D2= 50cm

A2=πD2^2/4

=3.142*50^2/4

=1963.75cm^2

The pressure applied on the smaller relative to the bigger end is expressed as

F1/A1=F2/A2

substitute we have

800/314.2=F2/1963.75

cross multiply we have

F2=800*1963.75/314.2

F2=1571000/314.2

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Step-by-step explanation:

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Find the length of the third side. If necessary, round to the nearest tenth. 5 10

snow_lady [41]

Answer:

$\boxed {\boxed {\sf 8.7}}$

Step-by-step explanation:

We are asked to find the length of the third side in a triangle, given the other 2 sides.

Since this is a right triangle (note the small square in the corner of the triangle representing a 90 degree /right angle), we can use the Pythagorean Theorem.

$a^2 + b^2 =c^2$

In this theorem, a and b are the legs of the triangle and c is the hypotenuse.

We know that the unknown side (we can say it is a) and the side measuring 5 are the legs because they form the right angle. The side measuring 10 is the hypotenuse because it is opposite the right angle.

b= 5
c= 10

Substitute the values into the formula.

$a^2 + (5)^2 = (10)^2$

Solve the exponents.

(5)²= 5*5 = 25
(10)²= 10*10= 100

$a^2 + 25=100$

We are solving for a, so we must isolate the variable. 25 is being added to a. The inverse operation of addition is subtraction, so we subtract 25 from both sides.

$a^2 +25-25=100-25$