Simplify each expression. Rationalize all denominators. 4√7xz+2 √7xz

The range of the function f(x) = | x + 2| - 2 for all x belongs to real is [-2,∞].

Closed interval includes the points and we denote it by third brackets and open interval do not include the points and denoted by first brackets.

According to the given question we have to determine the range of the function y = |x + 2| - 2 where domain of x ∈ R.

We know, |x + 2| ≥ = 0.

∴  | x + 2 | - 2 ≥ -2  and f(x) = | x + 2 | - 2 so, f (x) ≥ - 2, ∀ x ∈ R.

There fore the range of the function f(x) is [ -2, ∞ ].

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The bag that has the lowest unit price per pound is the 5 pound bag.

Unit price is the value of a single unit of measure.

A 3-pound bag of apples costs $3.94, and a 5-pound bag costs $5.92.

Let's find the unit price per pounds of each products to know the lowest.

Therefore,

unit price per pound  for the 3 pound bag = 3.94 / 3

unit price per pound  for the 3 pound bag = 1.31333333333

unit price per pound  for the 3 pound bag = $1.313 per pound

unit price per pound  for the 5 pound bag = 5.92 / 5

unit price per pound  for the 5 pound bag = 1.184

unit price per pound  for the 5 pound bag = $1.184 per pound

Therefore, the apple bag of 5 pound has the lowest unit price.

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Answer:

12_(1.5,2)

13_(3,2)

14_8.5

15_6

16_-1.5

17_-4.5

18_2.5

19_3

28_(-7,-5)

38_1.8

40_1.5

42_1.6

Step-by-step explanation:

12_ midpoint formula x1+x2/2 , Y1+Y2/2

-7+4/2 , 2+2/2

-3/2 , 4/2

(1.5,2)

13_3+3/2, 9+(-5)

6/2, 4/2

(3,2)

14-19 just find the middle between the 2 numbers

for 20-27 just repeat what i did in question 12 and 13

28_ to get from 1 to -3 you have to -4 so to find the x of the other endpoint you have to -4 from -3 same goes for the Y coordinate to get from 7 to 1 you have  to -6 to find the Y for the other endpoint you have to -6 again from one

same goes for questions 29-33 its easier to draw a number line and do it their

38_the distance between -4 and 5 which is 9 then you have to find 1/5 of 9 which is 1/5 x 9 = 1.8

40_the distance between -7 and 2 which is 9 then you have to find 1/6 of 9 which is 1/6 x 9 = 1.5

42_distance formula √(x1- x2)²+(Y1-Y2)²

√(2-(-5)²+(9-5)²

√7²+4²

√49+16

√65

=8.0

1/5 x 8.0 =1.6

The rest of the answers and solutions are in the pdf

The equation of the line shown in the reference graph, attached hereby, that passes through the points (-6, 0) and (0, 4) is  [3y = (2x + 12)].

As per the question statement, we are provided with a straight line, drawn on the cartesian quadrants that pass through two points, (-6, 0) and (0, 4).

We are required to determine the equation of the line.

To solve this question, we need to know the formula to determine the linear equation of a line passing through two points, (x₁, y₁) and (x₂, y₂), which goes as [tex][(y-y_{1})=(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}) (x-x_{1})][/tex].

Here, let us consider, (-6, 0) to be (x₁, y₁), and (0, 4) to be (x₂, y₂). Therefore, using these values in the above mentioned equation, we get

[tex](y-0)=[\frac{4-0}{0-(-6)}][x-(-6)]\\ or, y=(\frac{4}{6})(x+6)\\ or, y=(\frac{2}{3})(x+6)\\or, 3y=2x+12[/tex]

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Answer:

18=49

Step-by-step explanation:

answer:

63

step-by-step explanation:

1. (6+3)=9

parentheses always comes first

2. 7 x 9 = 63

The single transformation which takes shape A to shape B is given by the vector [tex](^{-5}_{-5})[/tex]

Transformation is the movement of a point from its initial location to a new location. Types of transformations are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

The single transformation which takes shape A to shape B is given by the vector [tex](^{-5}_{-5})[/tex]

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Answer:

We would predict 177 girls

Step-by-step explanation:

We can set up a proportion

[tex]\frac{Girls}{Boys}[/tex] = [tex]\frac{Girls}{Boys}[/tex]  Put in the number that I know and solve for the number that I do not know.

[tex]\frac{3}{4}[/tex] = [tex]\frac{g}{236}[/tex]  I can cross multiply to solve for x

4g = 3(236)

4g = 708  Divide both sides by 4

g = 177

The division of f (x) and g (x) is x - 1 and the domain is  [ 1 , ∞ ].

Given,

f (x) = x - 2

g (x) = x ² - 3 x + 2

The question states to find the division of the function f, that is, f (x) = x - 2, and function g, that is, g (x) = x ² - 3 x + 2

Performing the division operation on these functions is just like simple division.

This implies, dividing the two functions f (x) and g (x), we get

g (x) / f (x) = x² - 3x + 2 / x - 2

            x - 1

        ___________

x - 2 |   x² - 3x + 2

           x² - 2x

         ____________

                   -x + 2

                   -x + 2

         ____________

                           0

=> g (x) / f (x) = x - 1

This implies that the division of the two functions f (x) and g (x) gives x - 1

To find the domain :

y =  x - 1

=> x ≥ 1

=> Domain = [ 1 , ∞ ]  

Therefore, we get the division of f (x) and g (x) as x - 1 and the domain as  [ 1 , ∞ ].

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let's first of all, convert all the mixed fractions to improper fractions and then proceed.

[tex]\stackrel{mixed}{3\frac{4}{15}}\implies \cfrac{3\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{49}{15}} ~\hfill \stackrel{mixed}{6\frac{3}{10}}\implies \cfrac{6\cdot 10+3}{10}\implies \stackrel{improper}{\cfrac{63}{10}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{3\frac{4}{15}}{ ~~ 8\cdot 6\frac{3}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ 8\cdot \frac{63}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ \frac{252}{5} ~~ }\implies \cfrac{49}{15}\cdot \cfrac{5}{252}\implies \cfrac{49}{252}\cdot \cfrac{5}{15} \\\\\\ \cfrac{7}{36}\cdot \cfrac{1}{3}\implies \cfrac{7}{108}[/tex]

Answer:

Hope this helps!

Answer: Positive ÷ positive = positive.

Negative ÷ negative = positive.

Negative ÷ positive = negative.

Step-by-step explanation: The division of two positive integers results positive integer.

Positive (+) ÷ Positive (+) = Positive (+)

The division of two negative integers results positive integer.

Negative (+) ÷ Negative (+) = Positive (+)

The division of two different sign integers results negative integer.

The domain of given points are :

IR x ≠ ± [tex]\sqrt{-3}[/tex]

Points of discontinuity - x = ± [tex]\sqrt{-3}[/tex]  ( non removable / asymptote )

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

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=x²-1/x²+3

y=(x+1)(x-1)/[tex]x^{2}[/tex]+3

The domain of given points are :

IR x ≠ ± [tex]\sqrt{-3}[/tex]

Points of discontinuity - x = ± [tex]\sqrt{-3}[/tex]  ( non removable / asymptote)

x-intercept :

0 = (x + 1)(x-1)

x = ± 1

y - intercept :

(0+1)(0-1) / (0+3) = -1/3

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Based on the introduction given, the element that is missing from excerpt is the Topic.

The element that is missing in this introduction to the use of Dalmatians by Firefighters is a topic. The topic is the element that would give clues about what the text is about.

The hook is the statement that grabs the reader which in this case is, "What's black, white, and famous for sitting atop firetrucks for centuries?" and there was general information provided on the Dalmatian use by firefighters.

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Answer: Thesis (C)

Step-by-step explanation: Due to the other answer being wrong, topic is out, it has general info, thats out, it has a hook, thats out, meaning the answer must be "Thesis".

The solution for the given equation (log 3 x=1) is and  the nearest ten-thousandth = 3.3333333.

Begin by identifying the base, which is "b" within equation, the exponent, which would be "y," and the exponential expression, which is "x." Then, shift the exponential expression with one side of the equation and apply the exponential to the base by multiplying it by itself a number of times.

Given  log 3 x=1

this can be written as log₁₀(3x) = 1

so,

log₁₀(3x) = 1

Applying the log rule we get:

3x = 10

x = 10 /3

x = 3.3333333

The solution for the given equation (log 3 x=1) is and  the nearest ten-thousandth = 3.3333333.

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The only one that is not  part of the process for copying ∠CAB is; Option D: Label the intersection of the arc and the new line C'.

The steps for constructing a copy of an angle using only a compass and a straightedge are as follows;

Step 1: Mark the point that will be the vertex of the new angle, and label it P.

Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.

Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.

Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.

Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.

Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.

Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.

Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.

Looking at the given options, the only one that is not  part of the process for copying ∠CAB is; Option D: Label the intersection of the arc and the new line C'.

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Answer:

d

Step-by-step explanation:

Using a linear function, it is found that 1466 gallons of water were in the tank when jabria began adding water.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

A linear function is modeled by: y = mx + b

where,

In this problem, we have given that in 12 minutes, the amount of water increased by 3456 gallons, hence the slope is given by :

m = 3456/12 = 288.

In 7 minutes, the tank contained 3,482 gallons of water, hence the initial amount was given by :

3482 - 7 x 288 = 1466

1466 gallons of water were in the tank when jabria began adding water.

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The fraction that's left to read in the book is 3/8.

From the information given, it should be noted that Tim has 5/10 of a book left to read for school. Tim read 1/8 of a book on Monday.

Therefore, the fraction that will be left to read will be:

= 5/10 - (1/8)

= 20/40 - 5/40

= 15/40

= 3/8.

The fraction that is left will be 3/8.

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The equations which represents the minimum and maximum scores of the students is  x = 87 ± 1.8.

It is given that average score on a lab report is 87 points with all the students scoring within 1.8 points

According to the question if  x represents a student score then , it is given by  [tex]x=87\pm1.8[/tex]

The equation which represent maximum score is given by

          [tex]x=87+1.8\\x=88.8[/tex]

The equation which represent minimum score is given by

         [tex]x=87-1.8\\x=85.2[/tex]

Hence, maximum and minimum scores are 88.8 and 85.2 respectively.

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Answer:

The lesser integer is 3.

Step-by-step explanation:

Let the integer be x.

2(x+1) - x =5

or, 2x + 2 - x = 5

or , x = 5 - 2

so, x = 3

Answer:

-7>x

Step-by-step explanation:

-2x-7>5x+14

-7>3x+14

-21>3x

-7>x

Answer:

Step-by-step explanation: if there is 75 trout and the caught 120 trout they would have counted the trout wrong

Answer:

b = [tex]\frac{a}{c}[/tex]

Step-by-step explanation:

[tex]\frac{a}{b}[/tex] = c ( multiply both sides by b )

a = bc ( isolate b by dividing both sides by c )

[tex]\frac{a}{c}[/tex] = b

For each conditional statement, the hypothesis and conclusion are given as follows:

5.

6.

7.

A conditional statement is written in this following format:

If Clause 1 then Clause 2.

In which:

That is, the term coming after the if is the hypothesis, while the term coming after the then being the conclusion, hence the answers for items 5 to 7 are given at the end of the answer.

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Step-by-step explanation:

(0.5-2)-1 = -1.5 - 1

= -2

(3+4) -2 = 7 - 2

= 5

(-8+5)+3 = -3+3

= 0

-(0.5-2)+1 = -(-1.5)+1

= +1.5 + 1

= 2.5

-(3+4)+2 = -(7) +2

= -5

-(-8-5) -3 = -(-13) -3

= +13 -3

= 10

The functions are f(x) = 5x-1 and g(x) = [tex]\frac{x+1}{5}[/tex].

We have to find two functions such that their composition gives the identity function.

That is, we need to find functions f and g such that f(g(x)) = x.

Also f(g(x)) = (f o g)(x)

A function g is said to be the inverse of a function f if, (f o g)(x) = f(g(x)) = x, for all real numbers x.

So  in short if we take f(x) any function then we should find its inverse function.

Let f(x) = 5x - 1.

Then take y = 5x - 1.

⇒ x =  [tex]\frac{y+1}{5}[/tex]

That is if we take g(x) = [tex]\frac{x+1}{5}[/tex], then,

f(g(x)) = f([tex]\frac{x+1}{5}[/tex]) = 5([tex]\frac{x+1}{5}[/tex]) - 1 = x

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Answer:

answers is 26.3%.

Step-by-step explanation:

you will say ( NEW price-OLD price)

95.99-75.99=20

20/75.99*100%

=26.3%

Data of different sizes can be easily arranged with histograms, but not with stem-and-leaf diagrams. This is a drawback.

Stem-and-leaf charts often include the original data values while histograms do not. This is a crucial advantage the former has over the latter.

The primary benefit of stem-and-leaf charts over histograms is that they display the original data values.

In contrast to stem-and-leaf charts, which lack this capability, histograms make it straightforward to organize data of various sizes. This is a serious disadvantage.

In conclusion, a stem-and-leaf display, sometimes referred to as a stem-and-leaf plot, is a tool that shows quantitative data graphically to assist visualize the form of a distribution.

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Answer:

A.

Step-by-step explanation:

D: there is no square root

for both C and B there is no decimal.

A should end up being y=-8x+5 which is in y=mx+b form