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3 years ago

If

= 6^{2m} " alt="36 ^{12 - m} = 6^{2m} " align="absmiddle" class="latex-formula">
, what is the value of m?
4
6
8
9

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

8 0

Answer:

Step-by-step explanation:

$6^{2(12-m)}=6^{2m}\\2(12-m)=2m\\24-2m=2m\\24=4m\\m = 6$

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Answer:

Line 1 Slope: - 4/3

Line 2 Slope: 3/4

Line 3 Slope: 3/4

---------------------------------------------------------------------------------------------------------------

Line 1 and Line 2: Perpendicular

Line 1 and Line 3: Perpendicular

Line 2 and Line 3: Parallel

Step-by-step explanation:

Line 1: Passes through (6, -4) and (0, 4).

We first find the slope by using this equation (y2 - y1) / (x2 - x1) -

(4 - (-4)) / (0 - 6)

(4 + 4) / (-6)

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-4 / 3

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Line 2: Passes through (-4, -2) and (8, 7).

We first find the slope by using this equation (y2 - y1) / (x2 - x1) -

(7 - (-2)) / (8 - (-4))

(7 + 2) / (12)

9 / 12

3 / 4

Slope = 3/4

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Line 3: Passes through (-4, -5) and (4, 1).

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(1 - (-5)) / (4 - (-4))

(1 + 5) / (4 + 4)

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3 years ago

How to solve equations with the substitution method

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Answer:

In a system, the substitution method is one of the 3 main ways to solve a system and can be very efficient at times.

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Step-by-step explanation:

1) Let's say we are given two equations below:

$y=4x \\ 4x-5y=-32$

We can use substitution here by substituting in for $y$ in the second equation. This means we put in $4x$ for $y$ in the 2nd equation so we only have $x$ variables in the equation, allowing us to solve for $x$ .

2) Solving it out:

$1) 4x-5(4x)=-32 \\ 2) 4x-20x=-32 \\3) -16x=-32 \\4)x=2\\5)y=4x = 4(2) = 8 \\ 6)y=8$

We essentially substitute in that value as seen in step 1. Steps 2 and 3 are just simplifying the left side and allowing for us to solve. Step 4 is where we divide by -16 on both sides to solve for x. Step 5 and 6 show us solving for y using the value for x. We get $x=2,y=8$

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The sum of four consecutive numbers is -26. what are the numbers?

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Answer: -8, -7, -6, -5

Remember: consecutive numbers are numbers that are back to back. For example, 1, 2, 3, and 4 are consecutive numbers while 1, 3, 5, and 6 are not.

Form your equation. Let x be your first number, x + 1 your second number, x + 2 your third, and x + 3 is your fourth. To further understand this, temporarily substitute 1 for x, and you will find that they are consecutive.
(x) + (x + 1) + (x + 2) + (x + 3) = -26

Solve for x.
(x) + (x + 1) + (x + 2) + (x + 3) = -26 Distributive Property
x + x + 1 + x + 2 + x + 3 = -26 Combine like terms
4x + 1 + 2 + 3 = -26 Combine like terms
4x + 6 = -26 Subtract 6 from both sides
4x = -32 Divide by 4 to both sides
x = -8 Isolated x

Substitute (-8) for x to find the numbers.
1st #: x = -8
2nd #: x + 1 = (-8) + 1 = -7
3rd #: x + 2 = (-8) + 2 = -6
4th #: x + 3 = (-8) + 3 = -5

The numbers are -8, -7, -6, and -5.

You can also check your work.
(-8) + (-7) + (-6) + (-5) = -26
-26 = -26

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