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Alinara [238K]
4 years ago
8

The speed of a toy car over time can be represented by a parabola with minimum speed 2 m/s after 3 seconds. After 5 seconds, the

car's speed is 3 m/s. What is the equation in vertex form of a parabola that represents the car's speed, y, over time, x?
Mathematics
2 answers:
Eduardwww [97]4 years ago
7 0
You have to solve x multiplying y
uranmaximum [27]4 years ago
6 0

Answer:

Step-by-step explanation:

y=ax²+bx+c

x=0,y=0,c=0

y=ax²+bx

2=9a+3b (×-5)

3=25a+5b(×3)

add

9-10=75a-45a+15b-15b

30a=-1

a=-1/(30)

2=9×(-1/30)+3b

3b=2+3/10=23/10

b=23/30

y=-1/30 x²+23/30=-1/30(x²+23x+(23/2)²)+1/30 ×(529/4)

y=-1/30(x+23/2)²+529/120

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A bag contains 6 red balls and 5 black balls . Two balls are picked , one after the other . Find the probability that :
Kaylis [27]

Answer:

<u>There are:</u>

  • 6 red balls - R
  • 5 black balls - B
  • Total number = 11 balls
<h3>A. Without replacement</h3>

i. <u>Two blacks </u>

  • P(BB) = 5/11*4/10 = 2/11

ii. <u>The first is black</u>

  • P(B) = 5/11

or, alternatively

  • P(BR or BB) = 5/11*6/10 + 2/11 = 3/11 + 2/11 = 5/11

iii. <u>Both are of same colour</u>

  • P(BB or RR) = 2/11 + 6/11*5/10 = 2/11 + 3/11 = 5/11
<h3>B. With replacement</h3>

i. <u>Two blacks </u>

  • P(BB) = 5/11*5/11 = 25/121

ii. <u>The first is black</u>

  • P(B) = 5/11

or alternatively

  • P(BR or BB) = 5/11*6/11 + 25/121 = 30/121 + 25/121 = 55/121 = 5/11

iii. <u>Both are of same colour</u>

  • P(BB or RR) = 5/11*5/11 + 6/11*6/11 = 25/121 + 36/121 = 61/121
7 0
3 years ago
Emath has a stockpile of 1850 algebra textbooks. They are being purchased at a steady rate of 120 books per week. Write a linear
labwork [276]

Answer: b = 1850 - 120w

Step-by-step explanation:

Let w represent the number of weeks for which the books are purchased.

They are being purchased at a steady rate of 120 books per week. This means that the number of books purchased after w weeks would be 120w.

The total number of algebra textbooks that she had initially is 1850

If b represents the number of books left after w-weeks of sales, then the linear function that models the number of books left after w weeks would be

b = 1850 - 120w

8 0
3 years ago
Consider the polynomials p(x) = 3x + 27x^2 and q(x)= 2 . Find the x -coordinate(s) of the point(s) of intersection of these two
Tom [10]

Answer:

The x -coordinate(s) of the point(s) of intersection of these two polynomials are x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333

The sum of these x -coordinates is \frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}

Step-by-step explanation:

The intersections of the two polynomials, p(x) and q(x), are the roots of the equation p(x) = q(x).

Thus, 3x + 27x^2=2 and we solve for x

3x+27x^2-2=2-2\\27x^2+3x-2=0\\\left(27x^2-6x\right)+\left(9x-2\right)\\3x\left(9x-2\right)+\left(9x-2\right)\\\left(9x-2\right)\left(3x+1\right)=0

Using Zero Factor Theorem: = 0 if and only if = 0 or = 0

9x-2=0\\9x=2\\x=\frac{2}{9}

3x+1=0\\3x=-1\\x=-\frac{1}{3}

The solutions are:

x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333

The sum of these x -coordinates is

\frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}

We can check our work with the graph of the two polynomials.

4 0
4 years ago
Cuantas clases de progresiones conoces
kozerog [31]

Answer:ninguna

Step-by-step explanation:

8 0
3 years ago
Solve 2(y – 3) = 1.2 – y.
Ne4ueva [31]
First write down your equation. 2(y-3)=1.2-y. the distribute your 2. 2 times y is 2y and 2 times -3 is -6. now you have 2y-6=1.2-y. bring your y to the other side of the equation with the opposite sign and do the same with your 6. you have 2y+y=1.2+6. combine the like terms and constants. now you have 3y=7.2. divide bother sides of the equal by 3 to get y alone. 3y/3= 7.2/3. your answer is y=2.4.
6 0
3 years ago
Read 2 more answers
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