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kvasek [131]
3 years ago
10

5^7 + 5^6 = _* 6 AWARDING BRAINLIEST

Mathematics
2 answers:
enyata [817]3 years ago
6 0

Answer:

1.91666666666666666666...

Step-by-step explanation:

77julia77 [94]3 years ago
6 0

Answer:

5^{6} × 6

Step-by-step explanation:

Given

5^{7} + 5^{6} ← factor out 5^{6} from each term

= 5^{6} (5 + 1)

= 5^{6} × 6

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Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work. 20 Points!!
alexira [117]

|4x + 3| = 9 + 2x

Since the variable is on both sides of the equation, you would, at the end, check for extraneous solutions.

Extraneous solutions are solutions that do not work with the equation, therefore they are "extra" solutions and un-included in your final answer.

Start the problem by splitting the equation into two equations, a positive case and a negative case. Your two equations would look like:

  1. 4x + 3 = 9 + 2x {positive case}
  2. 4x + 3 = -(9 + 2x) {negative case}
<h2><u>---Solving the equations---</u></h2><h3>[POSITIVE CASE]</h3>

Let's solve for the positive case first. Start by subtracting 3 from both sides of the equation.

  • 4x + 3 = 9 + 2x becomes 4x = 6 + 2x

Now subtract 2x from both sides of the equation.

  • 4x = 6 + 2x becomes 2x = 6

Finish off the problem by dividing both sides by 2 to isolate the variable x.

  • 2x = 6 becomes x = 3.
<h2>---</h2><h3>[NEGATIVE CASE]</h3>

Now let's solve for x in the negative case. Start by distributing the negative sign (-) inside the parentheses.

  • 4x + 3 = -(9 + 2x) becomes 4x + 3 = -9 - 2x

Subtract 3 from both sides just like the positive case.

  • 4x + 3 = -9 - 2x becomes 4x = -12 - 2x

Now add 2x to both sides of the equation.

  • 4x = -12 - 2x becomes 6x = -12

Finish off the problem by dividing both sides by 6 to isolate the variable x.

  • 6x = -12 becomes x = -2.
<h2><u>---Checking for extraneous solutions---</u></h2><h3>[CHECKING X = 3]</h3>

To check for extraneous solutions, or solutions that do not work, substitute what you got for x back into the original absolute value equation: |4x + 3| = 9 + 2x. Substitute 3 and -2 into the equation. Let's start by substituting 3 for x.

  • |4x + 3| = 9 + 2x becomes |4(3) + 3| = 9 + 2(3)

Start by multiplying 4 and 3 together inside the absolute value symbols.

  • |4(3) + 3| = 9 + 2(3) becomes |(12) + 3| = 9 + 2(3)

Now multiply 2 and 3 together.

  • |(12) + 3| = 9 + 2(3) becomes |(12) + 3| = 9 + (6)

Add 12 and 3 together inside the absolute value symbols; also add 9 and 6 together.

  • |(12) + 3| = 9 + (6)  becomes |(15)| = (15), which is the same as 15 = 15.

15 = 15 is a true statement so this means that 3 is a solution to the absolute value equation, so it is not an extraneous solution.

<h2>---</h2><h3>[CHECKING X = -2]</h3>

Let's see if -2 is a solution or not - substitute -2 for x into the equation: |4x + 3| = 9 + 2x.

  • |4x + 3| = 9 + 2x becomes |4(-2) + 3| = 9 + 2(-2)

Multiply 4 and -2 inside the absolute value symbols.

  • |4(-2) + 3| = 9 + 2(-2) becomes |(-8) + 3| = 9 + 2(-2)

Multiply 2 and -2.

  • |(-8) + 3| = 9 + 2(-2) becomes |(-8) + 3| = 9 + (-4)

Add -8 and 3 inside the absolute value symbols; also add 9 and -4.

  • |(-8) + 3| = 9 + (-4) becomes |(-5)| = (5), which is the same as 5 = 5.

5 = 5 is a true statement so that means it is not an extraneous solution. After checking for extraneous solutions, we have come to the conclusion that the two answers for the equation --> I4x + 3I = 9 + 2x <-- are <u>x = 3 or x = 2</u>.

8 0
3 years ago
Please help. WIll give brainliest if you explain
Eddi Din [679]
The answer to 2 is <span>√30/5 or 1.09545

First, you multiply the numerator and denominator by </span>√5. 
√6x<span>√5=√30 
</span>√5x<span>√5=5 (when a square root of an expression is multiplied by itself, the result is that expression) Therefore, the answer is </span><span>√30/5 or 1.09545
</span>

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3 years ago
What is the measure of angle x? <br><br> please hurry
lawyer [7]
It should be 140 degrees.
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3 years ago
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Mrs. Mitchell decided to grade her projects by giving each student 50 points if they turned in a project and then an additional
photoshop1234 [79]
Let c be the amount of parts the student answered correctly.  Suppose that s(c) is a function between c and the score of a student's project.  As the student initially receives a fixed 50 points for turning the project in and 5 points for each correct part, the function is initially:

s(c) = 5c+50

When the students receive 7 points for each correct part, the coefficient of c changes, as the amount of points received per correct answer increases.  Thus:

s(c) = 7c+50.
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3 years ago
Find the sum or difference in -8+13=
balu736 [363]

Answer:

5

Step-by-step explanation:

8 0
2 years ago
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