Zoning activityIf you wanted to build a new house, or add an addition to the house you own, where would you go to get permission? What codes would you have to follow?

Answers:

The first blank is 180

The second blank is 60

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The triangle sum theorem basically says that adding up all three angles of any triangle always leads to 180 degrees. So that's why

(angle1)+(angle2)+(angle3) = 180

x+x+x = 180

3x = 180

Divide both sides of that last equation by 3. This is to undo the multiplication of 3 done to x.

3x = 180

3x/3 = 180/3 ... divide both sides by 3

x = 60

Each angle of this equilateral triangle is 60 degrees. In an equilateral triangle, all three sides are the same length. Also in an equilateral triangle, all three angles are the same measure and always 60 degrees.

Final answer:

The Triangle Sum Theorem says that all angles in a triangle add up to 180 degrees. In an equilateral triangle, all angles are equal. Hence, each angle is 60 degrees.

Explanation:

The Triangle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees. Now, in an equilateral triangle, all angles are equal. Let's denote the measure of each angle with x. According to the theorem, the sum of these measures is x + x + x = 180. Simplifying this gives 3x = 180. Hence, solving for x, which refers to the measure of each angle in the equilateral triangle, we get x = 180 / 3 = 60 degrees. Thus, each angle in an equilateral triangle measures 60 degrees.

Learn more about Triangle Sum Theorem here:

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Final answer:

The student correctly solved the equations given for x. Note that an equation with an unknown variable squared might have two solutions. The way to solve for x alters according to what the equation requires, whether it is adding, subtracting, or dividing.

Explanation:

It seems like the student is trying to solve equations for x. The equations given were all solved correctly. Keep in mind that when an equation contains an unknown variable squared, there could be two solutions, and one or both could be reasonable depending on the problem. For example, consider the equation x² +0.0211x -0.0211 = 0. This could be rearranged to solve for x. Other variables are known unless additional calculations needed if they are not.

Remember that the principle of altering the equation to solve for x is employed, whether we add, subtract or divide by certain values. Like mentioned in the information provided, when dividing by powers of 10, you would move the decimal to the left, corresponding to the number of zeros in the power of ten.

Learn more about Solving for x here:

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Answer:

for perimeter you add all sides. so Lenth x2 + width x2 is 24+30 which would equal 54

for area it's Lenth times width so 12 times 15 equals 156

Answer:

The percentage is 68.26%

Step-by-step explanation:

Before we use the empirical rule , we need to find the value of the z-score

Mathematically;

z-score = (x - mean)/SD

Thus;

z-score = (7.85 - 7.45)/0.4 = 0.4/0.4 = 1

So the percentage we want to calculate now is the percentage of values within 1 standard deviation of the mean

According to the empirical rule, 68.26% of values are within 1 standard deviation of the mean