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Answer:

1200

Step-by-step explanation:

We can gather from what's given that y=20xy represents the total number of bottles produced in the given time in seconds, which is x. When x=1, y=20, This means that each second the machine can make 20 soda bottles. Each minute is 60 seconds, so when x=60, y=20*60 =1200 soda bottles.

Given:

The logarithmic equation is:

[tex]\log x+\log (x-3)=1[/tex]

To find:

The value of x.

Solution:

Properties of logarithm used:

[tex]\log a+\log b=\log (ab)[/tex]

[tex]\log 10=1[/tex]

[tex]\log x[/tex] is defined for [tex]x>0[/tex].

We have,

[tex]\log x+\log (x-3)=1[/tex]

Using properties of logarithm, we get

[tex]\log [x(x-3)]=\log 10[/tex]

[tex]x^2-3x=10[/tex]

Splitting the middle term, we get

[tex]x^2-5x+2x-10=0[/tex]

[tex]x(x-5)+2(x-5)=0[/tex]

[tex](x-5)(x+2)=0[/tex]

[tex]x=5,-2[/tex]

In the given equation, we have a term [tex]\log x[/tex]. It means the value of x must be greater than 0 or positive. So, the only possible value of x is:

[tex]x=5[/tex]

Therefore, the value of x is 5.

Answer:

y = 2(x + 3)² - 4

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Using the method of completing the square

y = 2x² + 12x + 14 ← factor out 2 from the first 2 terms

  = 2(x² + 6x) + 14

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

y = 2(x² + 2(3)x + 9 - 9 ) + 14

  = 2(x + 3)² - 18 + 14

  = 2(x + 3)² - 4 ← in vertex form

this one because x has to be bigger than 15.

The graph with inequality x>15 is (B)

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

x>15

As, x is greater than 15.

So, the graph with x value labelled from the numbers greater than 15 which is represented by graph on right top corner.

Learn more about inequality here:

https://brainly.com/question/20383699

#SPJ2

Answer:

W=5

Step-by-step explanation:

-4(w+1}=-24

-4w-4=-24

-4w=-20

w=5

Answer:

its 5

Step-by-step explanation:

i got i correct ;)

1 is the initial value because it started at 1 in the beginning, and it transfered up to 6,7.

Answer:

1

Step-by-step explanation:

The initial value is the y intercept or where the line crosses the y axis.

Answer: -1

Step-by-step explanation:

x is the slope and the value of x is negative one.

Answer:

B

Step-by-step explanation:

Answer: ( ∞ , -∞ )

Step-by-step explanation:

Answer:

J: 28 square root 3

K: 56

Step-by-step explanation:

not sure about J but def sure abt K

Answer:

16.6

Step-by-step explanation:

[tex]14^{2}+9^{2}= 277\\[/tex]

[tex]\sqrt{277}[/tex]=16.6(rounded)

i think its like 126

Answer:

the answer is c

Step-by-step explanation:

inscribed angles made by same base should be equal

Answer:

hi i need points and i dont know what to write i hope you have a great day or night :)

Step-by-step explanation:

yeoo, how are you? I hope you're doing well and having a great day g. Anyways I only need one more brainliest to pass this rank, so it would be real helpful but it's okay if not. I hope you are taking care of yourself, have a nice day/night !

Answer:

A pentagon has 5 lines of symmetry, not 10.

Step-by-step explanation:

There are only 5 lines connecting to form a pentagon and all five lines are the same length.

Answer:

The answer is 25

Step-by-step explanation:

Answer: 25 Is the correct answer.

Answer:

y = -5x + 4/3

Step-by-step explanation:

m is the slope and b is the y intercept. m= -5 so -5 is the slope and b= 4/3 so 4/3 is the y intercept.

......Answer: V = 1046.6

Answer:

Yes

Step-by-step explanation:

[tex]\frac{18}{9} =\frac{2}{1}[/tex]

The two ratios are,

→ 18 : 9 and 2 : 1

We have to find,

→ whether the ratios are equivalent?

Now simplify the first ratio,

→ 18(÷9) : 9(÷9) = 2 : 1

→ 2 : 1 = 2 : 1

Yeah, the two ratios are equivalent.

Answer:

Mary's reasoning is incorrect.

Step-by-step explanation:

1/8 < 1/4

Answer:

X=1, y=3

Step-by-step explanation:

-x+ 4=3x

4=4x

1=x

insert value of x into either equation to solve for y.

Y=3x

y=3(1)

y=3

Answer:

a set of cars can be bought in one way

1 different way

Answer:

The length of side x is 22.91

Step-by-step explanation:

As per law of cosine

[tex]X = \sqrt{a^2 + b^2- 2*a*bcos\gamma}[/tex]

Where

[tex]gamma = 56[/tex] degrees

a = 20

b = 27

Substituting the given values in above equation, we get -  

[tex]X = \sqrt{20^2 + 27^2 - 2*20*27*cos 56} \\X = 22.91[/tex]

Hence, the length of side x is 22.91

Answer:

I think neither

Step-by-step explanation:

Answer:

1/36

Step-by-step explanation:

Attached is a chart showing the 36 possible outcomes for rolling 2 number cubes.  The sum of the two cubes is 12 in only one of the outcomes (both sixes).  The probability is 1/36.

Answer:

43 + 24 = 67

38 + 29 = 67

This means that there equal making

D. 43 + 24 = 38 + 29

The correct answer.

Answer:

63

Step-by-step explanation:

the first one is 9x bigger then the second one

so 7x9 is 63

Answer:

C)

Step-by-step explanation:

I’m not sure

B.) μx =  3.48    σx = 1.21