Determine the value of x

1)70
2)140
3)40
4)280

Answer:

$540

Step-by-step explanation:

Define x as:

x = the Original Price, in dollars ($)

Then,

x - (80%)x = 108, where we note that (80%)x is the reduction amount, so that

20%x = 108,

0.2x = 108,

x = 108/0.2 = $540

Final answer:

The original price of the sofa was $540.

Explanation:

Question:

After an 80% reduction, you purchase a new sofa on sale for $108. What was the original price?

Detailed Answer:

To find the original price, we need to determine what the 80% reduction represents in terms of the original price. If the sale price is 80% of the original price, then we can set up the equation: sale price = 0.2 * original price. We know the sale price is $108, so we can solve for the original price by dividing both sides of the equation by 0.2: original price = $108 / 0.2 = $540. Therefore, the original price of the sofa was $540.

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Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.

What is equation?

An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.

Here,

Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.

Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).

Since we know that A = B, we can substitute B for A in the last equation to get:

B² - B² = (2x - 9) - (B²)

Simplifying this equation, we get:

0 = 2x - 9 - B²

Now we can substitute the equation B² = 3x - 5 into the above equation to get:

0 = 2x - 9 - (3x - 5)

Simplifying this equation, we get:

0 = -x - 4

Solving for x, we get:

x = -4

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9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

When the graph of the left side of the equation does not intersect the graph of the right side of the equation, there are no solutions.

__

Additional comment

Even if you extend the domain to complex numbers, there are no solutions. The f(x) = |x| function always returns a positive real value, even for complex numbers.

Answer: z= 1.51

Step-by-step explanation:

Test statistic for proportion is given by :-

Where n is sample size ,p is the sample proportion , P Is the population proportion and Q =1 - P.

Given : P=57% = 0.57

Q= 1- P = 1-0.57=0.43

n = 25

Test statistic for proportion will be :-

We should report the value of test statistic z= 1.51

Answer:

245÷9 =0 witt remainder 9

Answer:

Parallel: y = 3x +b, where b ≠ 4

Perpendicular: y = -1/3x + b

Step-by-step explanation:

Parallel Lines have the same slope but different y-intercepts.

Perpendicular Lines have a negative reciprocal in slope.