HAND-WRITTEN ANSWER ONLY!
The state of Colorado is shaped like a rectangle, with approximate
dimensions of 385 miles long and 275 miles wide. Draw Colorado, label the
dimensions and find the approximate area.

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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The amount deducted from Joseph's account for each ticket is $8

The amount deducted from Joseph's account for each ticket = Total amount deducted from the value of the subway pass ÷ Number of times he rode the subway

= $40 / 5

= $8 per ticket

Total amount remaining in the subway pass = Total cost of subway pass Joseph bought - Total amount deducted from the value of the subway pass

y = $55 - $40

= $15

The mathematical equation to represent this situation is y = $55 - $40

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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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Answer:  X = 4

Step-by-step explanation:

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]

Answer:

2 ≤ x ≤ 3 where x represents the number of hours walking

Step-by-step explanation:

The distance to walk in miles can be modeled as the following inequality

Let x represent the number of hours Blake will be walking.

To cover 10 mi at 5 mph, Blake will take 10/5 = 2 hours
To cover 15 mi at 5 mph, Blake will take 15 /5 = 3 hours

The actual number of hours walked must lie within these limits

So

2 ≤ x ≤ 3 where x represents the number of hours walking

to get the equation of any straight line, we simply need two points off of it, let's use those two from the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{0 +4} \implies \cfrac{ -6 }{ 4 }\implies -\cfrac{3}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{3}{2}}(x-\stackrel{x_1}{(-4)}) \implies y -3=-\cfrac{3}{2} (x +4) \\\\\\ y-3=-\cfrac{3}{2}x-6\implies {\LARGE \begin{array}{llll} y=-\cfrac{3}{2}x-3 \end{array}}[/tex]

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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If a scientist has 315 cells in a container and she expects the number of cells to triple in one day then the number of cells the scientist will have after one day is equal to 945.

The number of cells the scientist will have after one day can be figured out using multiplication. Multiplication is one of the four parts of arithmetic. It can be considered as the opposite of division and can be defined as the repeated addition of the same number or groups of equal sizes.

The number of cells the scientist will have after one day can be calculated as follows;

Number of cells = 315

As it is expected to triple, which means that it is expected to increase three times in amount.

Therefore;

3 × number of cells in the container

3 × 315 = 945

Hence, the number of cells the scientist will have after one day is calculated to be 945.

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answer:

63

step-by-step explanation:

1. (6+3)=9

parentheses always comes first

2. 7 x 9 = 63

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:

  (3/2, 9/2)

Step-by-step explanation:

You want the midpoint of the line segment with end points R(4, 3) and S(-1, 6).

The coordinates of the midpoint will be the average of the end point coordinates:

  M = (R +S)/2

  M = ((4, 3) +(-1, 6))/2 = (4 -1, 3 +6)/2 = (3, 9)/2

  M = (3/2, 9/2) . . . . coordinates of the midpoint

The amount spent on calculators is $310 which is option (b) .

It is given that half people ordered $29.95 calculator which means that 5 people have ordered $29.95 per calculator then , amount is given by

    (number of people ) × cost per calculator = total amount spent

       [tex]5\times29.95=\$149.75[/tex]

It is given that least expensive calculator was $19.95 and the most expensive calculator was $39.95.

Mean will be [tex]=\frac{least\ + \ most}{2}[/tex]

                      [tex]=\frac{19.95+39.95}{2} \\\\=\frac{59.9}{2} \\\\=29.95[/tex]

so the other 5 people have spent an average of amount [tex]=5\times29.95[/tex]

                                                                                 [tex]=\$149.75[/tex]

Total amount spent on calculators will be [tex]=149.75+149.75=\$299.5[/tex]

which is approximately equal to $310 which is option (b) .

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Answer:

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

Answer:

He received $45 for the bike

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

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:

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 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:

1. 600000+90000+ 6000

2. 6000+ 300

3. 6x+ 33x

4.

5.

6.

7. 75

8. 21

9. -5x

10. 3x

11. 10 km

12. 4.6

13.

14.

15. $3.5

16.$1.5

17. 4x-1=3x-5

+1 +1

4x= 3x-4

-3x -3x

x=-4

18. 3x-3=27-2x

+3 +3

3x= 30-2x

+2x +2z

5x= 30

/5 /5

x= 6

19. 0.5

20. 1

The steps to express a fraction as a decimal is the reverse of the steps required to write a decimal as a fraction, with the resulting fraction being simplified further as follows;

To write a decimal as a fraction gives a fraction having all the digits of the decimal up to the last nonzero digit in the numerator, and 10 raised to the power, the number of places to the decimal point is moved up to the right of the last non zero digit, and vice versa.

Starting from question 2, we have;

2. 0.3 is ten times as great as 0.03, given that we have;

10 × 0.03 = 0.3

0.003 is 1/10 of 0.03, given that we have;

1/10 × 0.03 = 0.003

Expressing the decimals as fractions gives;

3. 0.001 = 1/1000

4. 0.05 = 5/100 = 1/20

5. 0.512 = 512/1000 = 64/125

6. 0.309 = 309/1000

Writing the fractions as decimals gives;

7. 2/1,000 = 0.002

8. 34/100 = 0.34

9. 508/1000 = 0.508

10. 99/1,000 = 0.099

Independent practice

Writing the decimals as fractions

11. 0.007 = 7/1,000

12. 0.08 = 8/100 = 2/25

13. 0.065 = 65/1,000 = 13/200

14. 0.9 = 9/10

15. 0.832 = 832/1,000 = 104/125

16. 0.203 = 203/1,000

17. 0.78 = 78/100 = 39/50

18. 0.999 = 999/1,000

19. 434/1,000 = 0.434

20. 3/10 = 0.3

21. 873/1,000 = 0.873

22. 17/1,000 = 0.17

23. 309/1,000 = 0.309

24. 5/1,000 = 0.005

25. 6/100 = 0.06

26. 999/1,000 = 0.999

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Answer:

might be C

Step-by-step explanation:

Using the Pythagorean Theorem, we have that the distance from home plate to second base is about 127 feet.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared of the triangle, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

The distance between each consecutive base is of 90 feet, hence the distance from home plate to 2nd base is the hypotenuse of a right triangle in which the legs are of 90 feet, being the distances from home plate to 1st base and 1st base to 2nd base.

Then:

h² = 90² + 90²

h = sqrt(90² + 90²)

h = 127 feet.

The distance from home plate to second base is about 127 feet.

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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".

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 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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Answer:

-45.5

Step-by-step explanation:

8x+4 -10x +5 = 100

x = - 91/2

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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