Find x so the distance between the points (x,2) and (-1,-2) is [tex]2\sqrt{5}[/tex]

x =_____ , ______

Given :

A population of protozoa develops with a constant relative growth rate of 0.4142 per member per day.

On day zero the population consists of five members.

Differential equation : [tex]\dfrac{dP}{dt}=0.4142P[/tex]

To Find :

The population size after eight days.

Solution :

Rate of growth , R = 0.4142 .

Now ,

Differential equation is :

[tex]\dfrac{dP}{dt}=0.4142P\\\\P_n=Ce^{0.4142n}[/tex]

For n = 0 .

[tex]5=C(1)\\C=5[/tex]

So ,the relation is [tex]P_n=5e^{0.4142n}[/tex] .

Putting n = 8 .

[tex]P_8=5e^{0.4142\times 8}\\\\P_8=137.42[/tex]

Hence , this is the required solution .

The complete factorization of 21a² + 28ab​ is 7a(3a + 4b)

Factorization is an arithmetic operation used in resolving an expression into factors in which when the factors are being multiplied together, the original expression can be derived. They produce factors that can be divided into the original expression.

Given that:

= 21a² + 28ab

here, we will look for a factor that if divide in both 21 and 28, there won't be any remainder. The factor is 7;

So, we have:

= 7(3a² + 4ab)

= 7a(3a + 4b)

Therefore, the complete factorization of 21a² + 28ab​ is 7a(3a + 4b)

Learn more about factorization here:

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Answer:

Step-by-step explanation:

Hello,

You need to group the terms in x

[tex]-2 \times x + \times x = (-2+5) \times x = 3 x[/tex]

And then, you can divide by 3 to find the solution

[tex]-2x+5x=3x=9<=>x=9/3=3[/tex]

Hope this helps

Answer:

add the x's

You have to combine them

you have to subtract the -2x to the 5x

Answer:

E=108

Step-by-step explanation:

[tex]E=mc^2\\\\m=3\\\\c=6\\\\E=(3)(6)^2\\\\E=3*36\\\\E=108[/tex]

Steps to solve:

E = mc^2 when m = 3 and c = 6

~Substitute

E = (3)(6)^2

~Simplify

E = 3(36)

~Multiply

E = 108

Best of Luck!

The answer is 434 !!

You can also solve this by doing 317-117= ?

Answer:

434

Step-by-step explanation:

Answer:

8 and 7

Step-by-step explanation:

because the square root of something is something used in math

Answer:

-5 multiplied by positive five is your answer

Step-by-step explanation:

Answer:

14: 16 is the ratio of girls to boys

And the ratio 14:30 is the ratio of girls to the total of students

Step-by-step explanation:

Answer:

65 cents

Step-by-step explanation:

divide 10 by 2.25 to get the factor. Next divide 2.9 by that to get your answer. 10/2.25 = 4 4/9. 2.9/ 4 4/9 = 0.6525 --> 0.65

Answer:

Nell's mom's

Step-by-step explanation:

That's a lot even if you devide, you can see the difference easier

mom= 30/2 = 15

dad = 65/5 = 13

The lesser milk the mother had made her chocolate more chocolatery, and you can see that she has a 0.2 more than the father

Answer:

The correct answer is Nell's mom.

Step-by-step explanation:

Nell's mom makes chocolate syrup with 30 ml for every chocolate syrup for every 2 ounces of milk.

Nell's dad adds 65 ml of chocolate syrup for every 5 ounces of milk.

To compare who makes a more chocolaty drink we need to have same amount of milk.

Least common multiple of 2 and 5 is given by 10.

Thus in 10 ounces of milk, Nell's mom adds 30 × 5 = 150 ml of chocolate syrup.

In 10 ounces of milk, Nell's dad adds 65 × 2 = 130 ml of chocolate syrup.

Thus on comparison we can say Nell's mom adds more chocolate syrup and hence makes a more chocolaty milk.

Answer:

$130

Step-by-step explanation:

The person gets $13 and hour and works for 10 hours 15 minutes. You round down to 10 hours and 10x13=130.

Hope this helps.

The required wage or pay for the day of the weekly time card is $113.75.

Given that,
A table has been shown,
Describing the working hours,
pay per hour =  $13/hr.

Daily wage to be determined

In mathematics, it deals with numbers of operations according to the statements.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Here are the total working hour,
= 4:00 + 4:45
= 8:45 hours or (8 + 3/4) hours

Wage per hour = $13/hour
                          = 13 *  35/4
                          = $113.75

thus, the required wage or pay for the day of the weekly time card is $113.75.

Learn more about arithmetic here:

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The value of ( 3 x 1,000 ) - ( 2 x 100 ) is 2,800.

Here,

Given that,  ( 3 x 1,000 ) - ( 2 x 100 )

What is subtraction of two number?

Subtraction is the operation of taking the difference of two numbers.

Now,

Firstly the value of 3 x 1000 = 3000

And, 2 x 100 = 200

⇒ 3000 - 200 = 2800

Hence, The value of ( 3 x 1,000 ) - ( 2 x 100 ) is 2,800.

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Answer:

-7.83333333333

Explanation:

To turn a fraction into a decimal divide the numerator by the denominator

-47 ÷ 6

= -7.83333333333

Answer:

His rate would be 2.5 books per month

Answer:

the answer is .5 i think

Answer:

$7075 or 7718

Step-by-step explanation:

91100-6200=84900

84900/11= 7718.18181818 or rounded= 7718

(This is if the december month doesnt count.)

84900/12=7075

(If december is included.)

Answer:

her monthly salary = 84900/12= 7075 dollars

Step-by-step explanation:

total earns= 91100 dollars

actual salary does not include bonus

her actually salary : 91100-6200= 84900

her monthly salary = 84900/12= 7075 dollars

Answer:

The equation is (i guess):

300*y = 23*t  -41,180

This is a linear equation, where y represents the population, and t represents time (in years)

Now, to find the gradient, we must derive the function y with respect to the time.

then we can write:

y = (23/300)*t - (41,180)/300.

now, remember that when we have:

y = a*x^n

we also have:

dy/dx = n*a*x^(n-1)

then in this case, we have:

dy/dt = (23/300) + 0

now we pass aain the 300 to the right:

300*dy/dt = 23.

d(300*y)/dt = 23

what does this mean?

Thie mean that for each unit of that t increases, we have an increase of 23 units in 300*y.

Answer:

i believe the answer is 114g of protein. i hope this helps

Step-by-step explanation:

Answer:

(3+2)²*4-10=x

Step-by-step explanation:

If it was a typo and is actually times 4, not divided by 4, then here is the answer:

(3+2)²*4-10=x

5²*4-10=x

25*4-10=x

100-10=x

90=x

If it actually was divided by 4, I don’t see any way it can be done.

Answer:

B

Step-by-step explanation:

(3+2)²*4-10=x

Answer:

x =-3.5

Step-by-step explanation:

0.4x+3=0.2(3x+1)−x

Distribute

.4x +3 = .6x+.2 -x

Combine like tersm

.4x+3 = -.4x+.2

Add .4x to each side

.4x+3 +.4x = -.4x +.2 +.4x

.8x +3 =.2

Subtract 3 from each side

.8x+3-3 = .2-3

.8x = -2.8

Divide each side by .8

.8x/.8 = -2.8 /.8

x =-3.5

Answer:

x=-3.5

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

1. Circle the two boats you picked for your trip.

the yacht and the tall ship (aka the pirate ship)

2. Make sense of the problem.

what do you know?

The tall ship makes the trip in 10 hours. The yacht makes the trip in 2.5 hours. The tall ship is 30 knots slower than the yacht.

what do you want to find out?

How fast is each boat traveling in knots (nautical miles per hour)?

what kind of answer do you expect?

probably just some numbers like 10 miles per hour or 40 miles per hour

Writing some expressions

3. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time. (2 points)

the expression would be D = 10(x-30), d is the distance. it could also be simplified to 10x - 300

4. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island. (2 points)

so the yacht's speed would be S = x knots, s is for speed.

5. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time. (2 points)

the distance returning from the island would be D = 2.5x.

6. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island. (1 point)

10x - 300 = 2.5x

7. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)

  10x - 300 = 2.5x  

10x - 300 + 300 = 2.5x + 300

  10x -2.5x = 300

   7.5x = 300

        x = 40

x is the speed of the yacht. (40 nautical miles per hour)

8. How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)

the yacht travels at 40 nautical miles per hour and the tall ship travels at 100 (10x - 300) nautical miles per hour.

9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.

Find the speed for the kayak. Use one of these facts to help.

The steamboat's speed is 4 less than 8 times the speed of the kayak.

The tall ship's speed is 1 more than 3 times the speed of the kayak.

The yacht's speed is 5 less than 15 times the speed of the kayak.

Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)

the equation for the speed of the kayak is 40 = 15x - 5, which in this case, x is the speed of the kayak

 40 = 15x - 5

  40 + 5 = 15x -5 + 5

 45 = 15x

   x = 3

therefore, the speed of the kayak is 3 nautical miles per hour.

10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.

It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then?

If so, how long will you have to spend at the reef?

If not, how late will you be for the return trip?

Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)

the distance to the island is 100 nautical miles, so the expression would be 100 = 20x -40, with x being the distance to the reef.

we can solve for x by doing:

100 = 20x -40

100 + 40 = 20x - 40 + 40

140 = 20x

140 / 20 = x

    x = 7

so the distance from my starting point to the reef will be 7 nautical miles, and the distance from the island to the reef would be 93 nautical miles.in that case, I would be like a day and a half late, but if you are trying to say that the ship is waiting for me at the starting point of my "adventure", then I would not be late if I kayak from my starting point to the reef, in fact, I could stay at the reef for like 50 min, because:

7 / 3 = 2 1/3 hours.

2 1/3 x 2 = 4 2/3 hours or 280 min. (to the reef and back)

7:30 p.m. - 2:00 p.m. = 5 1/2 hours or 330 min. (how much time I have till the ship leaves)

330 - 280 = 50 min. (how many min I can spend at the reef)

This is for the people that want to find out how to find the distance to the island.

jamescodwell answered all the questions  correctly btw.

Step-by-step explanation:

Distance travelled divided by trip time = speed

trip time multiplied by speed = distance travelled

So the steamboat makes the trip in 5 hours travelling at a speed of 20 knots.

5 * 20 = 100 The trip to the island is 100 nautical miles.

By Gauss's Law the approach of solving sum of a sequence of n terms in arithmetic progression is :

[tex]S_n=\dfrac{n}{2}(a_1+a_n)[/tex]        ......1 )

Here, [tex]a_n = 302[/tex] , [tex]a_1=2[/tex] .

We know :

[tex]a_n=a_1+(n-1)d\\\\302=2+3(n-1)\\\\n = 101[/tex]

Putting, all values in equation 1) we get :

[tex]S_n=\dfrac{101}{2}\times (2+302)\\\\S_n=101\times 152\\\\S_n=15352[/tex]

Therefore, the sum of sequence using Gauss's Law is 15352.

Hence, this is the required solution.

Answer:

[tex]Rate = \$1.76/kg[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{16}kg[/tex] of nails costs [tex]\$ \frac{11}{100}[/tex]

Required

Determine the rate

The rate, in this case, will be calculated as:

[tex]Rate = \frac{amount}{weight}[/tex]

[tex]Rate = \frac{\frac{11}{100}}{\frac{1}{16}}[/tex]

This gives

[tex]Rate = \frac{11}{100}/\frac{1}{16}[/tex]

[tex]Rate = \frac{11}{100} * 16[/tex]

[tex]Rate = \frac{176}{100}[/tex]

[tex]Rate = \$1.76/kg[/tex]

Answer:

Answer:

Step-by-step explanation:

Given

of nails costs

Required

Determine the rate

The rate, in this case, will be calculated as:

This gives

Step-by-step explanation:

Answer:

4!! hope this helps <3