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What number x makes the equation 8 to the power of x = 2 correct?

Daniel [21]

A linear equation in one variable has a single unknown quantity called a variable represented by a letter. Eg: ‘x’, where ‘x’ is always to the power of 1. This means there is no ‘ x² ’ or ‘ x³ ’ in the equation.The process of finding out the variable value that makes the equation true is called ‘solving’ the equation.An equation is a statement that two quantities are equivalent.For example, this linear equation: x + 1 = 4 means that when we add 1 to the unknown value, ‘x’, the answer is equal to 4.To solve linear equations, you add, subtract, multiply and divide both sides of the equation by numbers and variables, so that you end up with a single variable on one side and a single number on the other side. As long as you always do the same thing to BOTH sides of the equation, and do the operations in the correct order, you will get to the solution.For this example, we only need to subtract 1 from both sides of the equation in order to isolate 'x' and solve the equation:x + 1 - 1 = 4 - 1Now simplifying both sides we have:x + 0 = 3So:x = 3With some practice you will easily recognise what operations are required to solve an equation.Here are possible ways of solving a variety of linear equation types.Example 1, Solve for ‘x’ :x + 1 = -31. Subtract 1 from both sides:x + 1 - 1 = -3 - 12. Simplify both sides:x = -4Example 2, Solve for ‘x’ :-2x = 121. Divide both sides by -2:2. Simplify both sides:x = -6Example 3, Solve for ‘x’ :1. Multiply both sides by 3:2. Simplify both sides:x = -6Example 4, Solve for ‘x’ :2x + 1 = -171. Subtract 1 from both sides:2x + 1 - 1 = -17 - 12. Simplify both sides:2x = -183. Divide both sides by 2:4. Simplify both sides:x = -9Example 5, Solve for ‘x’ :1. Multiply both sides by 9:2. Simplify both sides:3x = 363. Divide both sides by 3:4. Simplify both sides:x = 12Example 6, Solve for ‘x’ : 1. Multiply both sides by 3: 2. Simplify both sides: x + 1 = 21 3. Subtract 1 from both sides: x + 1 - 1 = 21 - 1 4. Simplify both sides:x = 20Example 7, Solve for ‘x’ :7(x - 1) = 211. Divide both sides by 7:2. Simplify both sides:x - 1 = 33. Add 1 to both sides:x - 1 + 1 = 3 + 14. Simplify both sides:x = 4Example 8, Solve for ‘x’ :1. Multiply both sides by 5:2. Simplify both sides:3(x - 1) = 303. Divide both sides by 3:4. Simplify both sides:x - 1 = 105. Add 1 to both sides:x - 1 + 1 = 10 + 16. Simplify both sides:x = 11Example 9, Solve for ‘x’ :5x + 2 = 2x + 171. Subtract 2x from both sides:5x + 2 - 2x = 2x + 17 - 2x2. Simplify both sides:3x + 2 = 173. Subtract 2 from both sides:3x + 2 - 2 = 17 - 24. Simplify both sides:3x = 155. Divide both sides by 3:6. Simplify both sides:x = 5Example 10, Solve for ‘x’ :5(x - 4) = 3x + 21. Expand brackets:5x - 20 = 3x + 22. Subtract 3x from both sides:5x - 20 - 3x = 3x + 2 - 3x3. Simplify both sides:2x - 20 = 24. Add 20 to both sides:2x - 20 + 20 = 2 + 205. Simplify both sides:2x = 226. Divide both sides by 2:7. Simplify both sides:x = 11

6 0

3 years ago

Read 2 more answers

Find the domain and range!!! 10 points!! Help needed

larisa86 [58]

ANSWER

B. Domain is (-∞,∞) and Range is (-∞,∞).

The given function is

$f(x) = \sqrt[3]{x - 6} + 5$

This is function is obtained by shifting the base cubic root function 6 units to the right and 5 units up.

This function is defined for all real values of x.

Therefore the domain is all real numbers.

The range is all real numbers.

The domain for this function becomes the range for the inverse function and the range becomes the domain.

Hence the domain is (-∞,∞) and the range is (-∞,∞).

4 0

4 years ago

Please help me on this!

trapecia [35]

Answer:

1) Jina is not a member of the Music Club.

2) Three students are a member of the Music Club but not the Math Club.

3 Mary and Dan are in all three clubs.

Step-by-step explanation:

Look at the diagram and notice how each club has its own circle. If a student is in that circle, then they are a member of that club. When circles overlap, that overlap space means that a student is a member of two or all three clubs, depending on how many and which circles overlap.

1) Looking at Jina's location on the diagram, she is in the overlap between the math and chess club circles. However, her position does NOT overlap with the Music Club circle, therefore she is not a member of the Music Club.

2) Let's look at the students of the Music Club circle and its overlaps with the Chess Club circle, but NOT the overlaps with the Math Club circle. We can see that Lucy, Josh, and Juan are in these locations, therefore there are three students who are members of the Music Club but not the Math Club.

3) To find which students are in all three clubs, you would look at the middle of the diagram where all three circles overlap. The students listed in this location are Mary and Dan, therefore they are in all three clubs.

8 0

3 years ago

Solve (x + 3 < 5) U (x - 7 > 1).

ale4655 [162]

Answer:

{ x | x < 2 or x > 8}

Step-by-step explanation:

Given the expression

(x + 3 < 5) U (x - 7 > 1).

Solve x+3 < 5

Subtract 3 from both sides

x+3 - 3 < 5-3

x < 2

For x - 7 > 1

Add 7 to both sides

x-7+7 > 1 + 7

x > 8

Hence the union of both is { x | x < 2 or x > 8}

4 0

3 years ago

Insert two geometric means between 729 and 64

Liula [17]

Answer:

324 and 144

Step-by-step explanation:

We require

a₁, a₂, a₃, a₄

where a₂ and a₃ are the required geometric means

The n th term of a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 729 and a₄ = 64, thus

729(r³) = 64 ( divide both sides by 729 )

r³ = $\frac{64}{729}$ ( take the cube root of both sides )

r = $\sqrt[3]{\frac{64}{729} }$ = $\frac{4}{9}$ , then

a₂ = 729 × $\frac{4}{9}$ = 81 × 4 = 324

a₃ = 324 × $\frac{4}{9}$ = 36 × 4 = 144

Thus

729, 324, 144, 64

8 0

3 years ago

I NEED HELP ASAP! PLEASEEEE​I will give you 5 stars rate

I NEED HELP ASAP! PLEASEEEEI will give you 5 stars rate