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olga2289 [7]
2 years ago
12

Michael reads 12 pages of a book in 18 minutes, 8 pages in 12 minutes,and 20 pages in 30 minutes. Is this a proportional relatio

nship? If so, what is the constant of proportionality? What does it represent? Write an equation to represent this situation.
Mathematics
1 answer:
maria [59]2 years ago
7 0

Answer:

  • y = 2/3x

Step-by-step explanation:

<u>Reading rate is y pages per x minutes and proportional relationship formula is:</u>

  • y = kx

<u>The coefficient is:</u>

  • k = y/x

<u>Let's verify if the given numbers fit into the same relationship:</u>

  • 12/18 = 2/3
  • 8/12 = 2/3
  • 20/30 = 2/3

We confirm all same and it means k = 2/3

<u>Required equation is:</u>

  • y = 2/3x

This represents that Michael reads 2 pages per 3 minutes and for x minutes he reads 2/3x pages

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If f(x)=2x^3-6x^2-16x-20f(x)=2x *3 −6x *2−16x−20 and f(5)=0, then find all of the zeros of f(x)f(x) algebraically.
mihalych1998 [28]

The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:

x = 5, x = -1 + i, x = -1 - i.

<h3>How to obtain the solutions to the equation?</h3>

The equation is defined by the rule presented as follows:

f(x) = 2x³ - 6x² - 16x - 20.

One solution for the equation is given as follows:

x = 5.

Because f(5) = 0.

Then (x - 5) is a linear factor of the function f(x), which can be written as follows:

2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).

This is because the product of a linear function and a quadratic function results in a cubic function.

Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:

2x³ - 6x² - 16x - 20 =  = ax³ + (b - 5a)x² + (c - 5b)x - 5c.

Then these coefficients are obtained comparing the left and the right side of the equality as follows:

  • a = 2.
  • -5c = -20 -> c = 4.
  • b = -6 + 5a = 4.

Hence the equation is:

2x² + 4x + 4.

Using a quadratic equation calculator, the remaining zeros are given as follows:

  • x = -1 + i.
  • x = -1 - i.

More can be learned about the solutions of an equation at brainly.com/question/25896797

#SPJ1

8 0
9 months ago
5 : 2 : 11 =.... : 6 : ....
lubasha [3.4K]
5:2:11=15:6:33
Multiply by 6/2=3
7 0
2 years ago
What is the area and perimeter of the triangle ABH? How do I solve it? The process and answers? I am trying to help my 7th grade
n200080 [17]

Step-by-step explanation:

I dont remember perimeter but area is A= 1/2 bh

7 0
3 years ago
64 times -7/8 minus 1/2
Vesna [10]
64 \times (- \dfrac{7}{8}) -  \dfrac{1}{2}

=-56 -  \dfrac{1}{2}

=-56\dfrac{1}{2}
3 0
3 years ago
How many different twotwo​-letter passwords can be formed from the letters
Anna [14]

Answer:

70

Step-by-step explanation:

GIVEN: two two​-letter passwords can be formed from the letters  A, B, C, D, E, F, G and H.

TO FIND: How many different two two​-letter passwords can be formed if no repetition of letters is​ allowed.

SOLUTION:

Total number of different letters =8

for two two​-letter passwords 4 different are required.

Number of ways of selecting 4 different letters from 8 letters=^8C_4

                                                                                                   =\frac{8!}{4!4!}

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Hence there are 70 different two-letter passwords can be formed using 8 letters.

5 0
3 years ago
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