Nayeli went to the grocery store and bought bottles of soda and bottles of juice. each bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar. nayeli purchased 5 more bottles of soda than bottles of juice and they all collectively contain 205 grams of sugar. write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. define the variables that you use to write the system.

log 2x + log x = 11 => x = 223600, by properties of logarithm.

Now,

log (2x) + log (x) = 11

=> log [(2x)(x)] = 11 (as log (a) + log (b) = log (ab))

=> log (2x²) = 11

Since, generally the base of log is 10, raising them to 10

=> [tex]10^{log_{10}(2x^{2})} = 10^{11}[/tex]

=> 2x² = 10¹¹

=> x² = [tex]\frac{10^{11}}{2}[/tex]

=> x = [tex]10^{5}\sqrt{\frac{10}{2}} = 10^{5}\sqrt5[/tex]

=> x = 10⁵ (2.2360)

=> x = 223600

Hence, log 2x + log x = 11 => x = 223600, by properties of logarithm.

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Answer:

Step-by-step explanation:

the independent variable is money.

sodas are the dependent.

the amount of sodas you buy are dependent on the amount of money you have.

The value of each number is 52 and 39.

The ratio given is = 4 :3

Given, the sum of x + y = 91

(4n) + (3n) = 91

7n = 91

n = 13

So,

x = a*n = 4*13 = 52

y = b*n = 3 *13= 39

The ratio of 52:39 is 4:3.

The sum 52+39 = 91

Hence, the numbers are 39 and 52.

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Each person will owe $7.7

Three friends eat lunch together

The bill accumulates to $10 plus a 10% tax fee

If they split the bill and and tax evenly

The amount each person will pay can be calculated as follows

21 × (1+10/100) /3

= 21 × (1+0.1)/3

= 21 × 1.1/3

= 23.1/3

= 7.7

Hence each person will pay $7.7

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The graph of g(x) is gotten by translating the function f(x) = |x| down by 3 units to get to function g(x)

The equation of the function is given as; g(x) = |x| - 3

The above function is an absolute value function.

The parent function of an absolute value function is; f(x) = |x|

This means that the function f(x) is translated to get to function g(x)

In this case, the function is f(x) is translated down by 3 units to get to function g(x)

So, the graph of g(x) is gotten by translating the function f(x) = |x| down by 3 units to get to function g(x)

See attachment for the graph of g(x)

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Answer: its c

Step-by-step explanation:

plug in 0 to the equation and you get (0,3)

Answer:

Yes.

Step-by-step explanation:

A good test to do is the vertical line test. You draw the equation you're trying to determine is or isn't a function, and then draw a vertical line through it, if it goes through once it is a function. If twice then it is not a function. Hope this helps. :)

Answer:

P1 - (4,2) P2 - (-2,1)

Step-by-step explanation:

You write the point as (x,y) so just put the numbers from the graph into their correct positions

Answer:

[tex]p_{1}(4,2)[/tex] and [tex]p_{2} (-2,1)[/tex]

Step-by-step explanation:

Latitude and longitude are broken into degrees, minutes, seconds and directions, starting with latitude. For instance, an area with coordinates marked 41° 56' 54.3732” N, 87° 39' 19.2024” W would be read as 41 degrees, 56 minutes, 54.3732 seconds north; 87 degrees, 39 minutes, 19.2024 seconds west.

The simplify of the expression is  [tex]20 \sqrt{3}[/tex].

Fixing an equation manner that we ought to discover the fee of the variable, with the aid of the use of homes of actual numbers and combining like terms, which make the equation true. Simplifying an algebraic expression manner that we most effectively need to lessen the expression by means of the use of properties of actual numbers and mixing like phrases.

The square root of 2 hundred in its simplest radical form is 10√2. If we know the high factorization of quite a number, we can write the radical shape of the rectangular root of that variety. As a result, the high factorization of 2 hundred is two × 2 × 2 × five × five. As a result, the square root of 200 within the handiest radical shape has to be 10√2.

Simplify genuinely manner to make it easy. In arithmetic, genuinely or simplification is reducing the expression/fraction/trouble in an easier shape. It makes the hassle easy with calculations and fixing.

[tex]\sqrt{48} +2 \sqrt{27} + 5\sqrt{12}[/tex]

[tex]\sqrt{48} = 4\sqrt{3}[/tex]

[tex]2 \sqrt{27} = 6\sqrt{3}[/tex]

[tex]5\sqrt{12} = 10 \sqrt{3}[/tex]

[tex]4\sqrt{3} +6 \sqrt{3} + 10 \sqrt{3}[/tex]

[tex]= 20 \sqrt{3}[/tex]

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The ratio of malts to the total ice creams is 3:10 .

Ratio is defined as the fraction which defines the relationship between two quantities .

Ratio is denoted by a:b such that it can also be written as a/b where a and b are co-prime. Ratio can also be denoted as a decimal but mostly it is represented as fraction in its lowest terms

Now the given ice cream shop has 14 shakes that are sold for every 6 malts.

Hence when 14 shakes are sold total number of ice cream sold is

14+6 = 20 .

Now we have to find the ratio of the malts to the total number of ice creams

∴ malts : ice creams = 6 : 20

Reducing to lowest terms we get :

ratio = 3:10

Hence the ratio of malts to total ice cream is 3:10

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answer is  y=x+216 and -6.

In the question, the expression is given 221--x-5=y;(9-11)3

An equation is said to be linear equation in two variables if it is in the form of ax + by + c=0, where a, b & c are real numbers and  a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

Unique Solution:

For the given linear equations in two variables, the solution will be unique , if and only if they intersect at a point.

No Solution:

For the given linear equations in two variables, the given system of equations has no solution if lines of two linear equations are parallel.

Infinitely many solution:

For the given linear equations in two variables, the given system of equations has infinitely many solution if lines of two linear equations coincident.

Two consecutive minus signs have the same mathematical meaning as a single plus sign .

221+x-5=y,(9-11).3

x+216=y

Subtract 216 from both sides of the equation,

x+216-216=y-216

x=y-216

replace x with y-216 in the expression

(9-11).3

subtract 11 from 9

-2.3

Multiply -2 by 3

-6

Hence, Final answer is y=x+216 and -6.

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Domain of inverse of f(x)=√x -1 is [-1,∞),{x|x≥-1}

Range of inverse of f(x)=√x -1 is [0,∞),{y|y≥0}

Finding the Inverse Function but not the Inverse Function's Domain and Range

First, we must determine the domain and range of the original function f in order to determine the domain and range of an inverse function (x).

1.Find the function's domain and range.

Assume that the domain of the function f(x) is [0,∞),{x|x≥0}

Assume that the range of the function f(x) is [-1,∞),{y|y≥-1}

2. Substitute Domain for Range and Range for Domain

The domain of the calulated function f^-1(x) is [-1,∞),{x|x≥-1}

f^-1(x) calculated function (x) the interval for range is [0,∞),{y|y≥0}

∴Domain of inverse of f(x)=√x -1 is [-1,∞),{x|x≥-1}

Range of inverse of f(x)=√x -1 is [0,∞),{y|y≥0}

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Answer:

B) 600000

Step-by-step explanation:

First we need to answer A

13822×623/14 = 615,079

B) 615,079 = 600000

Answer: Or you could make six groups of 2 so that way no one is on the same team.

Step-by-step explanation: I hope I'm explaining this right because I don't fully get your question ;)

The perimeter P  is  mathematically given as

P=[Number of sides of regular polygon] * [Length of each side]

This is further explained below.

Generally, The formula for calculating the perimeter of a regular polygon is ns.

Having said that; The formula for the number of sides of a regular polygon is n.

The length of each side is equal to one unit.

Find:The formula for calculating the perimeter of a regular polygon

Hence

The formula for calculating the perimeter of a regular polygon is as follows:

Perimeter = [Number of sides of regular polygon] * [Length of each side]

In conclusion, The formula for calculating the perimeter of a regular polygon is

P= [Number of sides of regular polygon] * [Length of each side]

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Answer:

-2x²+8x-18

not sure if the x's are multiplication or x but this what I got.

Answer:

Step-by-step explanation:

3ײ + 8 × - 8 - 5× ² - 10 please solve and give a solution tthankyou!! asap!!​

3x² + 8x - 8 - 5x²- 10 =

-2x² + 8x - 18

The correct option is (d).

d) (2,-6) & (4,-16)

Now, To find the correct option that is equivalent to this equation, we can begin by narrowing down the given options.

Since, The slope contains a negative number, that's mean the second point must have a lower y value than the first x value.

Hence, By using this criteria, we can eliminate the first and the third option.

Now, we can check the second and fourth option as;

We can test using by putting in values.

Let's plug in the point values to check whether they work:

Hence, For option 2:

y = -5x + 4

-24 = -5(4) + 4

-24 = -20 + 4

-24 ≠ -16

And, For option 4:

y = -5x + 4

-16 = -5(4) + 4

-16 = -20 + 4

-16 = -16

Therefore, The correct  option is option (d).

The complete question is this;

Which line has an equation of y= -5x+4 in slope intercept form?

A line passing through the points -

a) (1,9) & (3,19)

b) (2,-14) & (4,-24)

c) (1,1) & (3,11)

d) (2,-6) & (4,-16)

Answer: divide 22/2

Step-by-step explanation:

Answer:

Divide 22/2

Step-by-step explanation:

22/2 is 11, a whole number.

Simplifying:

(22/2)*(3/9)*4

11*(3/9)*4

11*(1/3)*4

Solving:

11*(1/3)*4

11*4=44 44/3=14 2/3

(22/2)*(3/9)*4=44/3 or 14 2/3

The image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin is (5, 5)

The point is given as

Point = (10, 10)

The scale factor is given as

k = 1/2 centered at the origin

The image after a dilation by the scale factor is calculated as

Image = Point * k

This gives

Image = (10, 10) * 1/2

Evaluate

Image = (5, 5)

Hence, the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin is (5, 5)

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426135 is the number in which the value of 2 is 10 times the value of 2 in 42780.

Given:

The number = 42,780

Here, the place value of 2 is 2000 or 2  thousand.

Let's check all the options for the right answer.

There is only one option with 2 in it.

That is option c 426135

We have given that, the value of 2 should be 10 times the value of 2 in 42780.

That is, 2000 x 10 = 20000.

The value of 2 in 426135 is 20000 or 2 ten thousand.

Thus, 426135 is the number in which the value of 2 is 10 times the value of 2 in  42,780.

Rest of the options are incorrect.

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The question is incorrect and the corrected question is given below.

The value of the digit 2 in the number 42,780 is 10 times the value of the digit 2 in which number?

The options are 34,651 or 146,703 or 426,135 or 510,400

The example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5

The associative property of multiplication states that

(a * b) * c = a * (b * c)

Using the above equation as a guide, we have the following equation

7 • (3 • 5) = (7 • 3) • 5

The above equation is the option (3) of the associative property of multiplication

Hence, the example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5

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population at 1992 = 3590

Population after Seven years (1999) = 4500

Given two points (t1, P1) and (t2, P2), the slope of the line m can be found.

p1 = (1992, 3590) and p2 = (1999, 4500)

m= ΔP/Δt

m= ((4500-3590))/((1999-1992))

m = 910/7

m=130 is the slope

The linear population function P(t) is

P(t)=130t + P0

Find the Y-Intercept P0

The population function P(t) is measured since the year 1990, year zero. The first moose population was measured in 1992, one year later. This provides an initial condition P (1) = 4500.

P (1) =130 (1) + P0 = 4500

P0 = 4370

P(t)=20t+4630

The moose population P(t) changes linearly year after year. The population function P(t) is measured in terms of t years since 1990.

t= 1990, P (0) =4370

t =1992, P (1) =130 (1) + 4370 = 4500 matches data

t=1999, P (2) = 130(2) + 4370 = 4630

t=2006, P (3) = 130(3) + 4370 = 4760

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Answer:

[tex]5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5[/tex]

Answer: (-2,3) (1,4) (-1,-4) (2,-3) the answer would be -16,1

Step-by-step explanation: graphing it

Answer: 6 would be left

Step-by-step explanation: divide 3494 by 8

There will be 6 comics left over after putting them in groups of 8

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Bertie has 3494 comic books he wants them in groups of 8.

∴ The no. of groups can be obtained if we divide the total number of books by no. of books in each group which is,

= (3494/8).

= 438×8 + 6.

So, There will be 6 comics left over after putting them in groups of 8.

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Answer:

yes

Step-by-step explanation:

Answer:

The correct answer is the last choice

Step-by-step explanation:

You see that the pattern is increasing by 4 each step.  If start at -5 and back up 4 three more times to get to the starting number, you will be at -17

Answer:

C

Step-by-step explanation:

because the 21:9 is break to the smallest form which is C

The domain of given points are :

IR x ≠ 2, 3

Points of discontinuity -  x = 2 ( removable/hole )

                                        x = 3 ( non removable / asymptote )

x - intercept =  2/3 , y -  intercept = 1

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).

y = 6-3x/[tex]x^{2}[/tex]-5x+6

  = -3(x-2)/[tex]x^{2}[/tex]-3x-2x+6

  = -3(x-2)/x(x-3)-2(x-3)

  = -3(x-2)/(x-2)(x-3)

The domain of given points are :

IR x ≠ 2, 3

Points of discontinuity -  x = 2 ( removable/hole )

                                        x = 3 ( non removable / asymptote )

x-intercept :

 0=-3(x-2)

-3x+2=0

 2=3x

 x=2/3

 y - intercept :

-3( 0-2)/(0-2)(0-3)

y = 1

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Putting together the solutions from each of the equations, the 4 letter code is GFBA

From the question, we are to solve each of the linear equations to determine the 4 LETTER CODE

1. -2x + 1 = 3x + 16

Add 2x to both sides

-2x + 2x + 1 = 3x + 2x + 16

1 = 5x + 16

Subtract 16 from both sides

1 - 16 = 5x + 16 - 16

-15 = 5x

x = -15/5

x = -3

The letter that corresponds to this is G

2. 7 - 8x = 4x - 17

Add 8x to both sides

7 - 8x + 8x = 4x + 8x -17

7 = 12x - 17

Add 17 to both sides

7 + 17 = 12x - 17 + 17

24 = 12x

x = 24/12

x = 2

The letter that corresponds to this is F

3. 20 -2(x - 2) = 2x

Clear the parentheses

20 -2x + 4 = 2x

Simplify

24 -2x = 2x

Add 2x to both sides

24 - 2x + 2x = 2x + 2x

24 = 4x

x = 24/4

x = 6

The letter that corresponds to this is B

4. 5(x + 4) = 6x - 5

Clear the parentheses

5x + 20 = 6x - 5

Subtract 5x from both sides

5x - 5x + 20 = 6x - 5x - 5

20 = x - 5

Add 5 to both sides

20 + 5 = x - 5 + 5

25 = x

x = 25

The letter that corresponds to this is A

Hence,

The code is GFBA

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Answer:

I don't understand you hear me