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sweet
1 month ago
5

The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°

Mathematics
2 answers:
Svet_ta [12.7K]1 month ago
7 0
Initially, it's important to recognize that m6 and m7 are vertical angles. Since vertical angles are congruent, we conclude that m6 is equal to m7.

m6 = m7

Next, we can substitute the values given in the problem, replacing m6 with "11x + 10" and m7 with "12x - 4." This allows us to solve for x to determine the degree measurements of both angles.

m6 = m7

Substituting the values gives us:

11x + 8 = 12x - 4

Now, we will eliminate 11x from both sides.

11x + 8 - 11x = 12x - 4 - 11x

So we have 8 = x - 4

Adding 4 on both sides leads to:

8 + 4 = x - 4 + 4

This results in x = 12.

With the value of x found, we can calculate m6 and m7.

m6 = 11x + 8

m6 = 11(12) + 8

Thus, m6 = 132 + 8

Consequently, m6 = 140.

Now for m7:

m7 = 12x - 4

Substituting gives m7 = 12(12) - 4

So m7 = 144 - 4

Therefore, m7 also equals 140.

Next, we determine m8, knowing that m6 and m8 form a straight angle which equals 180 degrees.

m6 + m8 = 180

Replace m6 with 140:

140 + m8 = 180

Subtracting 140 from both sides gives us:

m8 = 40.

With m8 determined, we can now find m4.

Using the rules regarding parallel lines and transversals, we find:

m1 = m5

m2 = m6

m3 = m7

m4 = m8

Since m4 is equivalent to m8, we can substitute the known value of 40, leading to m4 = 40.
PIT_PIT [12.4K]1 month ago
7 0
M< 6 is equal to m< 7 since they are vertical angles.
11x + 8 = 12x – 4
12x - 11x gives 8 + 4
x = 12
therefore
m< 6 = 11x + 8
m< 6 = 11(12) + 8
m< 6 = 132 + 8
m< 6 = 140

For m< 4, we find it by subtracting m< 6 from 180
m< 4 = 180 - 140
m< 4 = 40

result

<span>m< 4 = 40</span>
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762,508 expressed in expanded form with exponents is:

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We need to write 762,508 using expanded notation with exponents.

Expanded form indicates how to represent numbers to highlight the individual digit values.

Displaying 762508 in Expanded format

Let's determine the positional values of each digit:

The concept of place value signifies the worth assigned to each digit based on its location.

For 7, the place value is 700,000

In 762508, the digit 7 is located in the hundred-thousands position.

For 6, the place value is 60,000

In 762508, the digit 6 occupies the ten-thousands position.

For 2, the place value is 2,000

In 762508, 2 is in the thousands position.

For 5, the place value is 500

In 762508, 5 is placed in the hundreds position.

For 0, the place value is 0 x 10 = 0

In 762508, 0 is found in the tens position.

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In 762508, 8 is positioned in the units place.

Thus, the expanded form is:

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