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Delicious77 [7]
3 years ago
5

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
1 answer:
viktelen [127]3 years ago
3 0

Answer:

Degree:3

Y-intercept:-6

Step-by-step explanation:

The given function is:

f(x) =  -  {(x  + 1)}^{2}( {2x - 3)}(x +2 )

To find the degree, we multiply out the leading terms of each factor.

The leading term of the first factor is:

-  {x}^{2}

and that of the second factor is

2x

and the third one is:

x

If we multiply out the leading terms, we would get:

-  {x}^{2}  \times 2x \times x =  - 2 {x}^{3}

Therefore the degree of the function is:

3

To find the y-intercept, we put x=0 to get:

f(0) =  -  {(0  + 1)}^{2}( {2 \times 0 - 3)}(0 +2 )

\implies \: f(0) = ( 1)( - 3) \times (2) =  - 6

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Answer:

  • Let us rearrange
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  • y=-2/3x-4
  • So y intercept is -4
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In the cafeteria tables are arranged in groups of 4, with each table seating 8 students. How many students can sit at 10 groups
Arisa [49]
4 tables = 1 group. So in 10 groups of tables, there are 40 tables. Each table seats 8 students, so you multiply 8 by 40, and that leaves your answer as 320 students. :)
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Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) Without doing an
stepladder [879]

Answer:

Step-by-step explanation:

Given are 3 data sets with values as:

(i) 8 9 10 11 12   ... Mean =10

(ii) 7 9 10 11 13    ... Mean =10

(iii) 7 8 10 12 13   ... Mean =10

We see that  data set shows mean deviations as

(i) -2 -1 0 1 2  

(ii) -3 -1 0 1 3    

(iii) -3 -2 0 2 3  

Since variance is the square of std deviation, we find that std deviation is larger when variance is larger.

Variance is the sum of squares of (x-mean).  Whenever x-mean increases variance increases and also std deviation.

Hence we find that without calculations also (i) has least std dev followed by (ii) and then (iii)

(i) (ii) (iii) is the order.

b) Between (i) and (ii) we find that 3 entries are the same and 2 entries differ thus increasing square by 9-4 twice.  But between (ii) and (iii) we find that

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6 0
3 years ago
Find cos(2*ABC) 100POINTS
juin [17]

Answer:

-\dfrac{7}{25}

Step-by-step explanation:

<u>Trigonometric Identities</u>

\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

  • \cos(\angle ABC)=\dfrac{3}{5}
  • \sin(\angle ABC)=\dfrac{4}{5}

Therefore, using the trig identities and ratios:

\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}

7 0
2 years ago
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Lelu [443]
The function for the problem is p=5x +4y
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