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Explanation:

Cut the x coefficient (10) in half to get 10/2 = 5. Then square this to get 5^2 = 25.

We'll add 1 to both sides so that the "24" turns into "25", thereby completing the square

x^2 + 10x + 24 = 0

x^2 + 10x + 24+1 = 0+1

x^2 + 10x + 25 = 1

Notice on the left hand side we have something of the form A^2+2AB+B^2 where A = x and B = 5. We can factor this into (A+B)^2, which is the whole reason why we completed the square. You can use the FOIL rule to see how (A+B)^2 expands out into A^2+2AB+B^2. Factoring reverses this process.

This means x^2+10x+25 factors to (x+5)^2 and we now have these steps

(x+5)^2 = 1

x+5 = sqrt(1) or x+5 = -sqrt(1)

x+5 = 1 or x+5 = -1

x = 1-5 or x = -1-5

x = -4 or x = -6 are the two solutions

------------------

Let's check x = -4 to see if it works or not

x^2 + 10x + 24 = 0

(-4)^2 + 10(-4) + 24 = 0

16 - 40 + 24 = 0

-24 + 24 = 0

0 = 0

We get a true equation. That confirms x = -4 is a solution.

If we tried x = -6, then,

x^2 + 10x + 24 = 0

(-6)^2 + 10(-6) + 24 = 0

36 - 60 + 24 = 0

-24 + 24 = 0

0 = 0

That x value is confirmed as well.

Answer:

((x)h)g

Step-by-step explanation:

Hope this helps and if this is wrong then please comment the right answer and I will edit it thanks :)

Answer:

28 degrees

Step-by-step explanation:

there is a square in the corner which means it is a right angle, 90 degrees.

90-62=28

Answer:

28 deggrees

Step-by-step explanation

Answer:

guys its 8cm its the most logic answer because 8x 4 is 32, correct me if im wrong

Step-by-step explanation:

Answer: 7⁵

Step-by-step explanation:

7×7×7×7×7

Here 7 is mutiplied by 7 , 5 times

Therefore it will be 7 to the power 5 = 7⁵

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Answer: There will be 4977 bacteria present after 10 hours.

Step-by-step explanation:

The exponential function for continuous growth in t years is given by :-

[tex]P=Ae^{kt}[/tex]   (i)

, where A = initial population, k= rate of growth.

As per given, A= 2000,  

After t= 2 hours, P=2400

Put these values in  (i), we get

[tex]2400=2000e^{2k}\\\\\Rightarrow\ 1.2=e^{2k}[/tex]

Taking log on both sides

[tex]\ln 1.2=2k\\\\\Rightarrow\ k=\dfrac{\ln1.2}{2}=\dfrac{0.182321556794}{2}\\\\\Rightarrow\ k\approx0.09116[/tex]

put value of A=2000, k= 0.09116 and t= 10 , we get

[tex]P=2000e^{0.09116\times10}\\\\=2000e^{0.9116}\\\\=2000\times2.4883\\\\=4976.6\approx4977[/tex]

Hence, there will be 4977 bacteria present after 10 hours.

Answer:

Step-by-step explanation:

[tex]9-i+(-5-i)=9-i-5-i=4-2i[/tex]

Answer:

4

Step-by-step explanation:

Func 2 is -2

Func 3 is 1

Func 4 is 8

Func 1 is unknown

Answer:

The perimeter of a shape is the length around it.

Step-by-step explanation:

We will be using the x and y values and add them together to find the total perimeter.

To do this, let's find all the values of the 2 axis:

(2 to 4) = 2

(1 to 3) = 2

(4 to 10) = 6

(3 to 1) = 2

(10 to 12) = 2

(1 to 8) = 7

(12 to 2) = 10

(8 to 1) = 7

We now add these values together which gives us 38. Don't forget to add the units afterwards (cm, m and so forth).

Answer:

10.7

Step-by-step explanation:

Let x be the missing side.

The rectangles are similar. Wich means:

● 8/9 = x/12

Cross multiply

● 9x = 8×12

● 9x = 96

Divide both sides by 9

● 9x/9 = 96/9

● x = 10.666

Round it to the nearest unit

● x = 10.7

~Divide

6/1 ÷ 2/3

6/1 * 3/2

18/2 or 9

So, she can cut 9 two third sections of ribbon.

Best of Luck!

Answer:

3x3÷2= 4.5cm^2

The formula is 1/2×base×slanted height

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = ¹/₃•(¹/₂•10•9)•10 = ¹/₃•45•10 = 15•10 = 150 in²

Answer:36

Step-by-step explanation:

gcd(475-7,871-7)=gcd(468,864)=36

[tex]\begin{array}{c|c|c|c|c|c}&0&1&1&5&2\\468&864&468&396&72&\boxed{36}\\468&396&72&36&0\\\end{array}[/tex]

Answer:

17

Step-by-step explanation:

these positive integers are :

4, 64, 124, 184 ... , 964

964 = 4 + (n-1) (60)

964 = 4 + 60n -60

964 = 60n -56

60n = 1020

n = 1020/60

n = 17

so, the number of special integers smaller than 1000 are = 17

The digits n, n+1 and n+2 implies that the special numbers are consecutive i.e. they follow one another. The count of special numbers less than 1000 is 17.

Given that:

[tex]\{n,n+1,n+2\} = \{4,5,6\}[/tex]

[tex]Range = 1000[/tex]

First, calculate the LCM of 4, 5 and 6.

[tex]4 = 2 \times 2[/tex]

[tex]5 = 5[/tex]

[tex]6 = 2 \times 3[/tex]

So, the LCM is:

[tex]LCM = 2 \times 2 \times 5 \times 3[/tex]

[tex]LCM = 60[/tex]

This means that the special digit occurs after every other 60 digits (i.e. the difference between a special digit and another is 60)

To calculate the count of special digits, we make use of arithmetic progression formula

[tex]L = a + (n - 1) \times d[/tex]

Where

[tex]L = 1000[/tex] --- the last term

[tex]a = 4[/tex] --- the first special digit

[tex]d = 60[/tex] --- the common difference as explained above

So, we have:

[tex]L = a + (n - 1) \times d[/tex]

[tex]1000 = 4 + (n - 1) \times 60[/tex]

Collect like terms

[tex]1000 - 4 =(n - 1) \times 60[/tex]

[tex]996 =(n - 1) \times 60[/tex]

Divide both sides by 60

[tex]16.6 =n - 1[/tex]

Add 1 to both sides

[tex]1 + 16.6 =n[/tex]

[tex]17.6 =n[/tex]

Rewrite as:

[tex]n =17.6[/tex]

Remove the decimal part (do not approximate)

[tex]n =17[/tex]

Hence, the special numbers are 17 in total (that are less than 1000).

Read more about arithmetic progression at:

https://brainly.com/question/21093837

Answer:

40

Step-by-step explanation:

The first box is 2--> 16*3 divided by 24= 2

Second box is 40--> 5*24 divided by 3= 40

Hope it helps.

Answer:

Assuming you mean "American History V World History"

American History tends to focus on the history of the United States, beginning largely with the colonial era and tracking forwards towards the present. It's largely a national history. World History, on the other hand, is far more encompassing, both geographically as well as temporally.

Assuming you mean "Global History V World History"

World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of inter-connectivity. World History examines the individual histories of different locations around the world, whereas Global History examines how those locations are connected.

Answer:

World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of interconnectivity. ... Furthermore, the fluid nature of what world and global histories mean ensures a number of disagreements with these definitions.

Answer:

1/4

Step-by-step explanation:

25 people took a vitamin and still got the flu and the total number is 100 so the fraction is 25/100 which can be reduce to 1/4

The P(took a vitamin | got the flu) will be 1/4.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Here, the table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day.

We need to find the P(took a vitamin | got the flu).

Now, 25 people took a vitamin and still got the flu.

The total number is 100.

So, the fraction is 25/100 which can be reduce to 1/4.

P(took a vitamin | got the flu) = 25/100

P(took a vitamin | got the flu) = 1/4

Therefore, the P(took a vitamin | got the flu) will be 1/4.

Learn more about the unitary method;

https://brainly.com/question/23423168

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Answer:

its 80 meters longs

Step-by-step explanation:

if it is wrong just go look it up

Answer:

C

Step-by-step explanation:

5a + 18 < -27

5a < -45

a < -9

Graph C matches the solution set of this inequality.

Answer: x = 8.77

Step-by-step explanation:

Using Pythagoreus Theorem

In the smaller rectangle

4²+5² = h²

41 = h²

h = √41

Therefore two sides of the rectangle will √41

No using pythagoreus theorem in the bigger triangle

6² + (√41)² = x²

x² = 36+41

x² = 77

x = √77

x = 8.7749643874

When rounded off to nearest tenth the hundreth digit is in 0-5 range

x = 8.77

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Answer:

x=8.6 c.x=5.7 d.x=26.3. d.x=26.3 is the answer

Answer:

-385y

Step-by-step explanation:

This expression cannot be factored with rational numbers, so -385y is your answer.

Answer:

7y - 2y² - 4

Step-by-step explanation:

5y - 5y² - 5 + 2 + 2y + 3y² - 1

5y + 2y - 5y² + 3y² - 5 + 2 - 1   (combine like terms)

7y - 2y² - 4

Answer:

Step-by-step explanation:

No. of miles driven in 1 gallon = 30 miles.

since we have to distance traveled in miles.multiply LHS and RHS by x

No. of miles driven in 1*x gallon = 30*x miles.

No. of miles driven x gallons = 30*x = 30x miles

As given that

the number of miles Bill travels is represented by y

gas used is x

then

y = 30x

=> x = y/30

Thus, Bill's car uses y/30 gallon gas to travel Y miles.

Answer:

Part a: Bill’s car travels 30 miles per gallon of gas. If y represents the number of miles the car travels on x gallons of gas, the equation that represents this situation is y = 30x.

Part b:       gallons of gas (x) miles (y)

                                    1         30

                                    2        60

                                    3        90

Part c: There is no x-value that would lead to multiple y-values.

Part d: Yes, y = 30x is a function, because for every input, or x-value, there is only one output, or y-value.

Step-by-step explanation:

edmentum answers 100% correct

Answer:

2x^2 - 18x + 45

Step-by-step explanation:

Standard form is ax^2 + bx + c

Expand the (x-5)^2 = (x-5)(x-5) --

x^2 - 5x - 5x + 25

x^2 - 10x + 25

So we now have

2(x^2 - 10x + 25) + 2(x-5) + 5

From here, distribute the 2 to each term in x^2 - 10x + 25, and distribute the 2 to each term in x - 5.

2x^2 - 20x + 50 + 2x - 10 + 5

Combine like terms

2x^2 - 20x + 2x + 50 - 10 + 5

2x^2 - 18x + 40 + 5

2x^2 - 18x + 45

Answer:

8 salt water

7 fresh water

Step-by-step explanation:

Let's represent salt water fish with the variable "s" and fresh water fish with the variable "f".

We can make a system of equations - one equation for the number of fish and the other for the price of the fish.

We know that the total number of fish Laura has is 15, and the total price of the fish was $23.

Solve the system of equations by subtracting the bottom equation from the top equation.

Laura bought 8 salt water fish. Since the total number of fish is 15, the number of fresh water fish must be 7.

Answer:

8  

7

Step-by-step explanation:

Let the number of fresh water be: - x

Number of salt fishes be 15 - x

x + 2 (15 - x) = 23

x + 30 - 2x = 23

x = 7

Number of fresh water fish bought: -7

Number of salt water fish bought by: -15 -7 = 8

Answer:

Part A

16y = 7x + 101

Part B

3y = 5x + 30

Part C

y = -5x/3

Part D

x = -3

Answer:

volume = x(x+2)(2x+1) = 2x^3+5x^2+2x

a = 2

b = 3

c = 5

d = 2

e = 2

f = 1

Answer: 290

Step-by-step explanation:

[tex]First\ integer\ on\ line\ n\ is:\ \dfrac{n^2}{2}-\dfrac{n}{2}+1 \\\\For \ line\ 17\ : \dfrac{17^2}{2}-\dfrac{17}{2}+1 =137\\\\\\Last \ integer\ on\ line\ n\ is:\ \dfrac{n*(n+1)}{2} \\\\For\ line\ 17:\ \dfrac{17*(17+1)}{2} =153\\\\Sum=137+153=290[/tex]

I have not say the equation in u(n+3) for the recurrence,

the resolution of the equation caracteristic and the resolution of a system of 3 equations with 3 variables.

Answer:

see explanation

Step-by-step explanation:

sum the parts of the ratio, 2 + 1 = 3 parts , thus

81 cm² ÷ 3 = 27 cm² ← value of 1 part of the ratio

2 parts = 2 × 27 = 54 cm²

Area of A = 54 cm² and area of B = 27 cm²

The side of the original square = [tex]\sqrt{81}[/tex] = 9 cm

The width of both rectangles is 9 cm ( width remains unchanged after cut )

Thus

Rectangle A

9 × length = 54 ( divide both sides by 9 )

length = 6 cm

Rectangle B

9 × length = 27 ( divide both sides by 9 )

length = 3 cm

Rectangle A → length = 6 cm, width = 9 cm

Rectangle B → length = 3 cm , width = 9 cm

Answer:

Rectangle A                 Rectangle B

length = 9 cm                length = 9 cm

width = 6 cm                  width = 3 cm

Step-by-step explanation:

Area of square At = 81 cm²

Square is cut into two pieces = A + B

The ration of area A to B = 2:1

Find

Rect A        Rect B

length         length

width           width

---------------------------------

first, get the side of the square = A = s²

81 = s²,      

s = √81      

s = 9 cm

since the ratio is 2:1, therefore the side can be divided into 3

9 ÷ 3 = 3 cm ----- take note of this to get the Width

Rectangle A

L = 9 cm (which is the s = 9 cm)

W = 3 cm (2 ratio) = 6 cm

Rectangle B

L = 9 cm  (which is the s = 9 cm)

W = 3 cm (1 ratio) = 3 cm

Proof:

At = A + B

81 = (9x6) + (9x3)

81 = 54 + 27

81 = 81  ----- OK

Answer:

Enterprises usually adopt some quality practices to control the product quality during the manufacturing process in order to assure the delivery of qualitative good products to customers. The quality practices or quality management systems adopted by industries will further evolve due to the changes of quality concepts as time goes by. This chapter discusses the change of quality concepts and the related revolution of quality management systems in the past century. The quality concepts were gradually changed from the achievement of quality standards, satisfaction of customer needs, and expectations to customer delight. Since merely satisfying customers is not enough to ensure customer loyalty, the enterprises gradually focus on customers’ emotional responses and their delight in order to pursue their loyalty. The emotion of “delight” is composed of “joy” and “surprise,” which can be achieved as the customers’ latent requirements are satisfied. Thus, the concept of “customer delight” and the means to provide the innovative quality so as to meet the unsatisfied customers’ latent needs are elaborated on. Finally, a framework of innovation creation is developed that is based on the mining of customer's latent requirements. This outline will manifest the essential elements of the related operation steps.