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AlekseyPX
2 years ago
7

Can someone solve and explain how to do these absolute equations for 40 points? I'll give brainliest to the best correct answer.

Mathematics
1 answer:
irga5000 [103]2 years ago
4 0

Answer:

Explanation Below

Step-by-step explanation:

1.    -4 + | x - 1 | = 3

= -4 + | x - 1 | + 4 = 3 + 4

= | x - 1 | = 7

= x - 1 = -7     or    x - 1 = 7

= x = -6 or x = 8

2.   6 + 4 | 2x + 6| = 14

 = 6 + 4 | 2x + 6 | - 6 = 14 - 6

 = 4 | 2x + 6 | = 8

 = 4 | 2x + 6 | / 4 = 8/4

 = 2x + 6 = -2          or         2x + 6 = 2

 = x = -4    or     x = -2

3.  -10 + | -6 - x | = 1

  = -10 + | -6 + x | + 10 = 1 + 10

  = | -6 - x | = 11

  =  -6 - x = -11     or   -6 - x = 11

  = x = -17        or       x = 5

4.    | 7 - 2x | + 4 = 5

   = | 7 - 2x | + 4 - 4 = 5 - 4

   = | 7 - 2x | = 1

   = 7 - 2x = -1            or             7 - 2x = 1

   = x = 3       or   x = 4

Here are the Steps:

SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Step 1: Isolate the absolute value expression.

Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

Step 3: Solve for the unknown in both equations.

Step 4: Check your answer analytically or graphically.

Hopes this Helps :D

Mark me Brainliest : )

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The demand equation illustrates the price of an item and how it relates to the demand of the item.

  • The slope of the demand function is -1/2
  • The equation of the demand function is: R(x) = (300 - 10x) \times (20 + 5x)
  • The price that maximizes her revenue is: Ghc 85

From the question, we have:

Plates = 300

Price = 20

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}

The slope (m) is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

So, we have:

m = \frac{25-20}{290-300}

m = \frac{5}{-10}

m = -\frac{1}{2}

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

R(x) = (300 - 10x) \times (20 + 5x)

Open the brackets to calculate the maximum revenue

R(x) =6000 + 1500x - 200x - 50x^2

R(x) =6000 + 1300x - 50x^2

Equate to 0

6000 + 1300x - 50x^2 =0

Differentiate with respect to x

1300 - 100x =0

Collect like terms

100x =1300

Divide by 100

x =13

So, the price at maximum revenue is:

Price= 20 + 5x

Price= 20 + 5 * 13

Price= 85

In conclusion:

  • The slope of the demand function is -1/2
  • The equation of the demand function is: R(x) = (300 - 10x) \times (20 + 5x)
  • The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

brainly.com/question/21586143

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20. If a certain linear function f(x) is evaluated at 0, the answer is 4.
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Answer:

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Use the slope-intercept equation:  y = mx + b.

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4 = (1/3)(0) + b, so that b = 4.  The desired equation is y = (1/3)x + 4.

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