Find the real and imaginary solutions of each equation.
25 x⁴-40 x²+16=0

The constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

In the question it is given that

"x" represent the number of yellow rosebushes.

"y" represent the number of red rosebushes.

The word "at least' means "≥".

So "at least 4 times as many yellow rosebushes as red rosebushes" means x≥4y .  (constraint 1)

The number of red or yellow rosebushes cannot be negative .

So , x>0 (constraint 2)

y>0   (constraint 3)

Also ,

the cost of each yellow rosebushes = $7.50

number of yellow rosebushes = x

total cost of yellow rosebushes =7.50x

the cost of each red rosebushes = $4.75

number of yellow rosebushes = y

total cost of yellow rosebushes =4.75y

According to the question ,

she can spend no more than $125  , that means

7.50x+4.75y≤125  ( constraint 4)

Therefore , the constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

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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".

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

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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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

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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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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Ludlow's z-score is z = 13.5

Given that the heights of American men are approximately normal.

Mean of the population, μ = 69.3 inches

Standard Deviation of the population, σ = 2.8 inches

Height of Robert Ludlow is 8 feet 11.1 inches = 107.1 inches [since 1 feet = 12 inches and 8 feet = 96 inches. 96 + 11.1 = 107.1 inches]

So [tex]\bar x[/tex] = 107.1 inches.

Since the population is assumed to be normal, we can find the z-score,

z = [tex]\frac{\bar x-\mu}{\sigma}[/tex]

  = (107.1-69.3)/2.8  

  = 37.8 / 2.8

  = 13.5

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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:

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

answer:

63

step-by-step explanation:

1. (6+3)=9

parentheses always comes first

2. 7 x 9 = 63

Answer:

He received $45 for the bike

Answer:

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

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:

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

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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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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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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[tex] \bf \implies{184980}[/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 1745[ \frac{1050}{10}}] [/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 1745 \times \frac{105 \cancel{0}}{1 \cancel{0}}}[/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 1745 \times 105}[/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 183225}[/tex]

[tex] \large\bf\Longrightarrow{1755 + 183225}[/tex]

[tex] \large \bf\Longrightarrow{184980}[/tex]

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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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 value of h from the given formula u = hg is u/g.

i.e h = u/g

A variable is any characteristic, number, or quantity that can be measured or counted.

Example:

x + 2 = y + 2

x and y are variables.

We are given a formula:

u = hg

We need to solve for h.

u = hg

Divide both sides by g.

u/g = h

h = u/g

Thus the value of h from the given formula u = hg is u/g.

i.e h = u/g

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Answer:

-7>x

Step-by-step explanation:

-2x-7>5x+14

-7>3x+14

-21>3x

-7>x

The measure of the value of x from the figure is 62

Vertical angles are angles that are equal and meet at a point of intersection X. Given the following measure of angles;

<M1 =. 2x - 8

<M3 = 116 degrees

Since the measure of both angles are the same hence;

2x - 8 = 116

Add 8 to both sides

2x - 8 + 8 = 116 + 8

2x = 116 + 8

2x = 124

Divide both sides by 2

2x/2 = 124/2

x = 124/2

x = 62

Hence the measure of the value of x from the figure is 62

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The answer is  [tex]=\frac{4x^{14/3} }{9}[/tex]

The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.

The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.

Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.

Apply exponent rule [tex](\frac{a}{b} )^{c} =\frac{a^{c} }{b^{c} }[/tex]

[tex](8x9^{2} y^{12} )^{2/3} : 4x^{6}y^{8}[/tex]

[tex](27x^{2} y^{12}) ^{2/3} : 9x^{4/3} y^{8}[/tex]

[tex]\frac{4x^{6} y^{8} }{9x^{4/3} y^{8} }[/tex]

apply exponent rule : [tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]

[tex]\frac{4y^{8} x^{-4//+6} }{9 y^{8} }[/tex]

subtract the number: [tex]6-\frac{4}{3} = \frac{14}{3}[/tex]

[tex]\frac{4y^{8} x^{14/3} }{9y^{8} }[/tex]

cancel the common factor : [tex]y^{8}[/tex]

= [tex]\frac{4x^{14/3} }{9}[/tex]

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Answer:

Hope this helps!

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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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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