How are exponents helpful?

6(2 + x) = 12 + 6x illustrates the distributive property.

What is distributive property ?

An algebraic property called the distributive property is utilized to multiply a single value by two or more values contained between parenthesis.

The distributive property of binary operations generalizes the distributive law, which declares that equality exists always accurate in elementary algebra.

Given

6(2+x )

= 12+6x

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Answer:

Distributive Property

Step-by-step explanation:

The remaining side length (L) of the rectangle is approximately 3.335 units.

To find the remaining side length (L) of a rectangle when given the perimeter and three sides of the rectangle, we can use the formula for the perimeter of a rectangle:

Perimeter = 2 * (Length + Width)

In this case, you have three sides, which means you have the sum of two lengths and one width:

3 * Side = 2 * Length + Width

Given that the perimeter is 30 and the three sides sum up to 70:

30 = 2 * Length + Width

We also know that 3 * Side = 70, so each side is equal to 70/3 = 23.33 (approximately).

Now, we can substitute this value for Width into the first equation:

30 = 2 * Length + 23.33

Subtract 23.33 from both sides:

30 - 23.33 = 2 * Length

6.67 = 2 * Length

Divide by 2 to isolate Length:

Length = 6.67 / 2 = 3.335

So, the remaining side length (L) of the rectangle is approximately 3.335 units.

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Opposite sides equals to 7 and so you add 7 + 7 which equals to 14. Next you subtract 30 by 14 to get the total of the opposite side of L and itself which gets you 16 which is then divided by 2 because you have L and its opposite side which would give you 8. So L equals to 8.

Check:

7 + 7 + 8 + 8

14 + 16

30

Solution:

Given: In the given figure, where there are pair of Quadrilateral, in which  AP=A Q, BP=B Q, C P=C Q .

To Prove : A, B and C are collinear.

Construction: Join AC , the point where it intersects P Q is M.

Proof:

AP=A Q,  C P=C Q,

So, the quadrilateral A P C Q is a kite.→→If in a quadrilateral One pair of adjacent sides are equal, then the quadrilateral is a kite.

As we know in a kite Diagonals bisect each other at right angles.

∠AMP=∠A M Q=∠CM P=∠C M Q=90°

Also, BP=B Q, C P=C Q.

So, the quadrilateral B P C Q is a kite.

∠B MP=∠B M Q=∠CM P=∠C M Q=90°

As you can see that , 1. ∠AMP +∠CM P=90°+90°=180°→→Shows Point A and C are in line.------------(1)

        2. ∠B MP +∠CM P=90°+90°=180°→→→Shows Point B and C are in line.------------------(2)

Combining (1) and (2),

Shows that point A, B,C lie in a line.

It means Points A, B,C are Collinear.

Answer:

-0.7

its easy hehe just - 1

Using the normal distribution, it is found that the z-scores are:

1) z = -0.8

2) z = 2.4

3) z = 0

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

• It measures how many standard deviations the measure is from the mean, either above the mean(positive z-score), or below(negative z-score).

Item 1:

0.8 standard deviations below the mean, hence z = -0.8.

Item 2:

2.4 standard deviations above the mean, hence z = 2.4.

Item 3:

The mean is 0 standard deviations from itself, hence z = 0.

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Final answer:

A standard score (z-score) signifies how many standard deviations a data point is away from the mean. A data value 0.8 standard deviations below the mean has a z-score of -0.8, meanwhile, if it is 2.4 standard deviations above the mean, its z-score is 2.4. The mean in a normal distribution has a z-score of 0.

Explanation:

In the field of statistics, a standard score (also known as a z-score) represents how many standard deviations an element is from the mean. In a normal distribution, a data value located 0.8 standard deviations below the mean has a Standard Score: z = -0.8. This is because the z-score is negative when the data value is below the mean. Conversely, a data value located 2.4 standard deviations above the mean has a Standard Score: z = 2.4. As the data value is above the mean, the z-score is positive. Finally, for the mean value itself in a normal distribution, the Standard Score: z = 0 because the mean value is the center of distribution, hence no deviation from itself.

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