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3 years ago

When solving for x, what is x squared plus 15 equals -8x

Mathematics

1 answer:

VLD [36.1K]3 years ago

5 0

Answer:

x = - 5, x = - 3

Step-by-step explanation:

Given

x² + 15 = - 8x ( add 8x to both sides )

x² + 8x + 15 = 0 ← in standard form

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are 5 and 3, since

5 × 3 = 15 and 5 + 3= 8, thus

(x + 5)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x + 3 = 0 ⇒ x = - 3

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The dot plot displays the number of marshmallows added to hot cocoa by several kids. What is the MAD of the data represented in

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Mean absolute deviation (MAD) of the data set indicates the average distance of all elements from mean of the data set.

MAD of the data represented by dot plot in the picture will be Option A.

Elements in the given dot plot are,

3, 4, 5, 5, 5, 5, 5, 5, 6, 7

Steps to be followed for the mean absolute deviation of this data set.

Find the mean of the data set
Find the absolute distance of each element from the mean
Find the average distance of all the elements which will be MAD of the data set.

Step - 1 :

Mean of the data set = $\frac{\text{Total of the data}}{\text{Total number of elements}}$

= $\frac{3+4+5+5+5+5+5+5+6+7}{10}$

= $\frac{50}{10}$

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Step - 2 :

Absolute distance of each element from the mean of the data set,

3 - 5 = |-2| = 2

4 - 5 = |-1| = 1

5 - 5 = 0

6 - 5 = 1

7 - 5 = 2

Step - 3 :

Average of the absolute distance = $\frac{2+1+0+0+0+0+0+0+1+2}{10}$

= $\frac{6}{10}$

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Therefore, Option A will be the correct option.

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