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diamong [38]
3 years ago
13

Question 10 Express 40 as a product of prime factors​

Mathematics
1 answer:
Step2247 [10]3 years ago
5 0

Answer:

2 x 2 x 2 x 5

Step-by-step explanation:

The first few prime numbers:  {2, 3, 5, 7, 11, 13, 17, 19}

One way to start is to divide by the first prime until you can't do that any more, then try the next prime and so on until all the numbers in your list are prime.

40 = 2(20)  divide 20 by 2 again

40 = 2(2)(10)  divide 10 by 2 again

40 = 2(2)(2)(5) stop--all factors are prime.

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Sam is walking across a bridge and accidentally drops an orange into the river basin below
irina1246 [14]

Answer:

We assume that the orange is dropped at t = 0s.

Once the orange is on the air, the only force acting on it is the gravitational force, then the acceleration of the orange is the gravitational acceleration.

A(t) = -32.17 ft/s^2

Where the negative sign is because this acceleration points downwards.

For the velocity equation, we need to integrate over time, we will get:

V(t) = (-32.17 ft/s^2)*t + V0

Where V0 is the initial vertical velocity of the orange, because the orange is accidentally dropped, this initial velocity is equal to zero.

V(t) =   (-32.17 ft/s^2)*t

For the position equation we need to integrate again, this time we get:

P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + P0

Where P0 is the initial height of the orange, we know that it is 40ft, then the position equation is:

P(t) =  (1/2)*(-32.17 ft/s^2)*t^2 + 40 ft

Now that we know the equation, we can graph it. (you can see the graph below)

Now we also want to find at what time does the orange hit the water.

This happens when:

P(t) = 0 ft =   (1/2)*(-32.17 ft/s^2)*t^2 + 40 ft

We just need to solve that equation for t.

0 ft =   (1/2)*(-32.17 ft/s^2)*t^2 + 40 ft

(1/2)*(32.17 ft/s^2)*t^2 =  40 ft

t^2 = (40ft)/( (1/2)*(32.17 ft/s^2))

t = √(  (40ft)/( (1/2)*(32.17 ft/s^2)) ) = 1.58 s

The orange hits the water 1.58 seconds after it is dropped.

3 0
2 years ago
If (5x− 4)(3x+ 7) = 15x²-ax-b,then find the value of a and b
Mkey [24]

Answer:

a=-23\\\\b=28

Step-by-step explanation:

Let's start by using distributive multiplication:

(a\pm b)(c\pm d)=ac\pm ad \pm bc \pm bd

So:

(5x-4)(3x+7)=15x^2+35x-12x-28\\\\

Grouping like terms:

15x^2 +(35x-12x)-28\\\\15x^2+23x-28

Now, 15x^2+23x-28 is equal to:

15x^2-ax-b

In this sense:

15x^2+23x-28=15x^2-ax-b

In order to satisfied the equality:

23x=-ax\hspace{10}(1)\\\\and\\\\-28=-b\hspace{10}(2)

Hence, from (1), let's solve for a:

23x=-ax\\\\-a=\frac{23x}{x} \\\\-a=23\\\\a=-23

And from (2), let's solve for b:

-28=-b\\\\b=28

Let's verify the result evaluating the values of a and b into the original equation:

(5x-4)(3x+7)=15x^2+23x-28=15x^2 -ax -b\\\\(5x-4)(3x+7)=15x^2+23x-28=15x^2 -(-23)x -(28)\\\\(5x-4)(3x+7)=15x^2+23x-28=15x^2 +23x -28

As you can see, the values satisfy the equation, therefore, we can conclude they are correct.

3 0
3 years ago
Petra is going to do a science experiment she will plant seeds in nine different pots and places the pots in different locations
Rufina [12.5K]

Answer:

126

Step-by-step explanation:

word your question a little better next time this was almost illegible.

8 0
2 years ago
The lunch special at Karen’s restaurant is a sandwich, a drink and a dessert. THERE ARE 2 sandwiches, 4 drinks, and 1 dessert to
hichkok12 [17]

Answer:

There are 8 possible combinations.

Look at this example:

2 sandwiches: PB&J, turkey sandwich

4 drinks: soda, water, lemonade, tea

1 dessert: cake

all 8 combos:

  • PB&J, soda, cake
  • PB&J, water, cake
  • PB&J, lemonade, cake
  • PB&J, tea, cake
  • turkey sandwich, soda, cake
  • turkey sandwich, water, cake
  • turkey sandwich, lemonade, cake
  • turkey sandwich, tea, cake

hope this helps

7 0
3 years ago
3.) - 6+ 5x = 6x - 3<br> Come someone please help me solve this
Thepotemich [5.8K]

- 6+ 5x = 6x - 3

move -6 to the other side

sign changes from -6 to +6

-6+6+5x= 6x-3+6

5x= 6x-3+6

5x= 6x+3

move -6x to the other side

sign changes from +6x to -6x

5x-6x= 6x-6x+3

5x-6x= 3

-x= 3

mutiply both sides by -1 to get +x

(-1)(-x)= x , (-1)(3)= -3

Answer: x= -3

8 0
3 years ago
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