What is the expression in radical form?
(5ab) =
○ √√25a²b²
O√√5a²b²
O √5a³b3
O √125a³b3

Thus cost per person c as a function of the number of people n is

c(n) = 43 + (n-1)(43-(n-1)2) and amount she makes is  $229

In the problem it is given that Elizabeth gives a walking tour of a popular tourist city to one person for 43 to increase her​ business, she would lower the price by​ $2 per person for each additional person. we have to find the cost per person c as a function of the number of people n on the tour. Also the amount she makes for a tour with 7 people.

So we can write it as

c(1) = 43

c(2) = 43 + 41

c(3) = 43 + 2(43-2*2)

c(4) = 43 + 3(43-3*2)

c(n) = 43 + (n-1)(43-(n-1)2)

To find the amount she makes we write c as a function of n where n=7

c(7) = 43 + 6(43-6^2) = 43 + 6*31 = 43 + 186 = $229

Thus cost per person c as a function of the number of people n is c(n) = 43 + (n-1)(43-(n-1)2) and amount she makes is  $229.

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The slope of the line is 2 , the correct option is (A).

Slope of the line is defined as the change in y coordinate with respect to the change in x coordinate of the line , the slope of the line is denoted by "m" .

The slope of the line passing through the two points (a,b) and (c,d) is given by m = (d-b)/(c-a) .

In the question ,

a line is given

let us name the points as M and N ,

the named graphed is shown below,

Assuming the cube in the graph be of 1 unit each.

So , the coordinates of M and N from the graph is

M = (1,1) and N= (-1,-3),

So the slope of the line passing through the points (1,1) and (-1,-3) is

slope = (-3-1)/(-1-1)

= -4/-2

= 2.

Therefore , the slope of the line is 2 , the correct option is (A).

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Answer:

it would be 150 more, so 1650

Step-by-step explanation:

divide 1500 by 10 to get 10%

The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3

The expressions related to the roots of each quadratic equation are listed below:

Case 1 - x² + 3 · x - 9 = 0

Roots: α = - 3 / 2 - 3√5 / 2, β = - 3 / 2 + 3√5 / 2

a) α + β = - 3

b) α² + β² = 27

c) α³ + β³ = - 108

Case 2 - x² + 4 · x - 2 = 0

Roots: α = - 2 - √6, β = - 2 + √6

a) α + β = - 4

b) α² + β² = 20

c) α³ + β³ = - 88

This question consists in two parts, find the roots by factoring the quadratic equations by algebra properties and determine the expressions based on the two roots of each expression. A root is a value of x such that the polynomial is equal to zero.

Case 1

x² + 3 · x - 9 = 0

x² + 3 · x = 9

x² + 3 · x + 9 / 4 = 9 + 9 / 4

(x + 3 / 2)² = 45 / 4

x + 3 / 2 = ± 3√5 / 2

x = - 3 / 2 ± 3√5 / 2

The roots are α = - 3 / 2 - 3√5 / 2 and β = - 3 / 2 + 3√5 / 2 and the following expressions are evaluated:

a) α + β = - 3

b) α² + β² = (- 3 / 2 - 3√5 / 2)² + (- 3 / 2 + 3√5 / 2)² = 27

c) α³ + β³ = (- 3 / 2 - 3√5 / 2)³ + (- 3 / 2 + 3√5 / 2)³ = - 108

Case 2

x² + 4 · x - 2 = 0

x² + 4 · x + 4 = 6

(x + 2)² = 6

x + 2 = ± √6

x = - 2 ± √6

The roots are α = - 2 - √6 and β = - 2 + √6 and the following expressions are evaluated:

a) α + β = - 4

b) α² + β² = (- 2 - √6)² + (- 2 + √6)² = 20

c) α³ + β³ = (- 2 - √6)³ + (- 2 + √6)³ = - 88

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The surface area of a cylinder is equal to 208π square units.How to calculate the surface area of right cylinder?The surface area is the sum of the areas of all faces of the solid. In the case of a right cylinder, the surface area is the sum of the two areas of the circular base and the lateral area (A), in square units, whose formula is described below:A = 2π · r² + 2π · r · h           (1)Where:r - Base radiush - HeightIf we know that r = 8 and h = 5, then the surface area of the right cylinder is:A = 2π · 8² + 2π · 8 · 5A = 208πThe surface area of a cylinder is equal to 208π square units.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{8 +4}\implies {\Large \begin{array}{llll} -\cfrac{1}{2} \end{array}}[/tex]

One package weighs 6.75 pounds.

In this question, we have been given Jack mails 10 packages that each weigh the same amount.

We need to find the weight of one packet.

Let each package weighs m pounds.

The combined weigh of all 10 package is 67 1/2 pounds.

So, we get an equation,

10m = 67.5

We solve above equation.

m = 67.5 / 10

m = 6.75 pounds

Therefore, one package weighs 6.75 pounds.

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Answer:

-52

Step-by-step explanation:

I hope this helps!

Answer: -52

Step-by-step explanation: Using PEMDAS

(2x3)+4-62

6+4-62

10-62

= -52

Answer:

–37

Step-by-step explanation:

–42 – 19 – (–24)

–42 – 19 + 24

–61 + 24

= –37

The table of values indicates a proportional relationship between the number of gallons of gas and the number of miles driven, therefore;

A proportional relationship is one in which one variable, y, can be obtained from another variable, x, by multiplying x by a factor.

Please find attached a table showing the number of gallons of gas and the miles driven obtained from a similar question online

Let x represent the number of gallons of gas and let f(x) represent the number of miles driven

The difference between the consecutive terms of the first three values in the number of gallons and miles driven are each equal to 2 and 62 respectively

4 - 2 = 2 - 0 = 2

124 - 62 = 62 - 0 = 62

Therefore, given that the first difference is constant, the first three points have a linear relation, which gives;

Slope of the line = 62/2 = 31

Intercept = 0

Therefore;

f(x) = 31•x

Checking the fourth point, gives;

x = 10

f(10) = 31 × 10 = 310

The relationship between the miles driven, f(x), and the number of gallons is therefore a proportional relationship, which is presented as follows;

f(x) = 31•x

Therefore, if the number of gallons of gas, x, is known, the number of miles driven, f(x), can be found using the equation;

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5N² is expressed as a product of prime factors in index form as  [tex]5^{5} * 3^{2} * x^{10}[/tex] .

In the expression of a number as the product of its prime factors, known as prime factor index form, each prime factor is only mentioned once, either as itself or, if necessary, to a required power.

Given:

N is a number that is expressed as a product of its prime factors in index form.

N = [tex]3x * 5x^{2} * x^{3}[/tex]

We have to express 5N² as a product of prime factors in index form.

5N² = 5([tex]3x * 5x^{2} * x^{3}[/tex])²

       = [tex]5 * 9x^{2} *5^{4} x^{2} *x^{6}[/tex]

       = [tex]5 * (5^{2}x)^{2}* (3x )^{2} *x^{6}[/tex]

( using exponential properties  [tex]a^{m} *a^{n} = a^{m+n} and (a^{m} )^{n} = a^{mn}[/tex])

    = [tex]5^{5} * 3^{2} * x^{10}[/tex]

The prime factors of 5N² are 5,3 and x respectively.

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Step-by-step explanation:

[tex]sa = 2\pi \: r {}^{2} + 2\pi \: rh \\ = 2 \times 3.14 \times 3 { }^{2} + 2 \times 3.14 \times 11[/tex]

The Radical Form is [tex]185x^3y^4[/tex].

What is the Radical Form?

If n is a positive integer that is greater than 1 and 'a' is a real number then,

 [tex]n\sqrt{a} = a1n[/tex]   where n is called the index, a is called the radicand, and the symbol [tex]\sqrt{}[/tex] is called the radical. The left side of this equation is often called  The radical form and the right side is often called the exponent form.

Now, The question is :

The Expression is : (5x3y4)37

Convert to Radical form by using the formula :

[tex]a^\frac{x}{n} = \sqrt[n]{a^x}[/tex]

(5x3y4)37 = [tex]185x^3y^4[/tex]

Therefore, The Radical Form is [tex]185x^3y^4[/tex]

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The solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324

The equation is

2.54-x+12 = 21-42.5x+7

Rearrange the terms are do the suitable arithmetic operation in the equation

2.54-x+12= 21-42.5x+7

-x+12+2.54 = -42.5x+7+21

Add the like terms together

-x+14.54 = -42.5x+28

Here we have to rearrange the term and make the all the like terms in each sides

Move 14.54 to the right hand side and move -42.5x to the left hand side

Then the equation will become

-x+42.5x = 28-14.54

41.5x = 13.46

x = 13.46/41.5

x = 0.324

Hence, the solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324

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Answer:

(a - b)/(a + b).

Step-by-step explanation:

a²-ab-ac+bc / a² +ab-ac-bc

= a(a - b) - c(a - b) / a(a + b) - c(a + b)

= (a - c)(a - b) / (a - c)(a + b)

The (a - c) is common to top and bottom, so

= (a - b)/(a + b).

Answer:

Step-by-step explanation:

the angle C is the opposite angle to that of 85 degrees, therefore congruent, we subtract 85 x 2 ° from the sum of the angles (360 °, is a round angle) and find the sum of the other two angles, always opposite and increasing, divide by two and we have the value of the angle B

C = 85°

B = [360 - (85 * 2)] : 2

B = (360 - 170) : 2

B = 190 : 2

B = 95°

-----------------

check

85 + 85 + 95 + 95 = 360°

the answer is good

In my opinion, Report 1 is more persuasive than Report 2 due to the fact that the margin of error in Report 1 is narrower than in Report 2.

This is further explained below.

Generally,  we consider report one and report two

For Report

at 98% confidence interval = $64.35 to $83.59

Therefore, the Margin of error

M.E= $83.59 - $64.35

M.E = $19.24

For Report 2:

95% confidence interval = $58.37 to $71.93

Margin of error

M.E= $71.93 - $58.37

M.E= $13.56

Since Report 1 has a smaller margin of error than Report 2, I find Report 1 to be more convincing.

In conclusion, A report with a lower margin of error, in my opinion, is often more credible than one with a bigger one.

This is because more exact data indicates a report with a reduced margin of error.

To put it another way, information in a report with a lower margin of error is more likely to be correct than information in a report with a higher margin of error.

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[tex]__________________________[/tex]

Refer to the attachment for the answer

Answer: a) $171          b) $729

Step-by-step explanation:

a) 0.19 * $900 = $171

b) net pay = the money one earns after all deductions

$900 (what she earned) - $171 (taxes she had to pay) = $729

The graph of the function after transformation is attached below.

The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system.

The graph of the transformed function is attached below. The red graph indicates the parent function f(x) = x² and the blue graph indicated the graph of transformation g(x) = x² - 2

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The side of the triangle is 15 inches.

The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square.

Hence,

let

perimeter of the square = x inches

perimeter of an equilateral triangle = x + 17

Let

side of the square = y

side of the triangle = 8 + y

Therefore,

Perimeter of the square

x = y + y + y + y

x = 4y

Perimeter of the triangle

x + 17 = 8 + y + 8 + y + 8 + y

x + 17 = 24 + 3y

x - 3y = 7

Combine the equation,

x = 4y

x - 3y = 7

Therefore,

4y - 3y = 7

y = 7

x = 4(7)

x = 28

Therefore,

side of the triangle = 8 + y = 8 + 7 = 15 inches

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Step-by-step explanation:

22. 7 + x

24. 5x

26. f/10

28. 3x + 16

30. k² - 11

32. x + 10

34. 18q

23. x - 35

25. x/3

27. 45/r

29. 18 - 3d

31. 20/t⁵

(although, if being superficial, it could mean (20/t)⁵)

33. (k + 2) - 15

35. 2m + 6

Answer:

9. 160/2

10. 270/9

Step-by-step explanation:

To find unit rates, divide the top number (numerator) by the bottom number (denominator).

9.

160/2 = 80 mph

210/3 = 70 mph

10.

270/9 = 30 ft/min

180/9 = 20 ft/min

Answer:6+2w=h

The height of the tree will be 32 inches on week 13

Step-by-step explanation:

ok

The number of sodas that can fit in inside each cooler is 8

From the question, the given parameters are:

Number of packs = 6

Kinds of soda = 4

Number of cooler = 3

The number of sodas in each cooler is calculated as

Sodas = Number of packs x Kinds of soda/Number of cooler

Substitute the known values in the above equation

So, we have

Sodas = 6 x 4/3

Evaluate

Sodas = 8

Hence, there are 8 sodas in each cooler

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The result of the Nested absolute inequality  when resolved gives:
x = -10, 0. See the solution below.

It is to be noted that when one absolute-value expression is inside another one, this is called a "nested" expression. Absolute expressions are expressions that values that can NEVER be negative.

The solution hence is given as follows:

Given: ||x-5|4|≤1

One absolute-value expression is stacked inside another in this equation. I'll work from the outside in, sorting items into their respective cases. Assume the argument of the outer bars is negative (do the "minus" case):

Step 1 - first splitting:

|x-5| -4 ≤ -1
|x-5|  ≤ 3

I have to stop here since the last statement above states that an absolute value equals a negative number. Absolute values, on the other hand, are never negative! As a result, this step is invalid; it yields no viable solutions to the original problem.

Now I'll look at the scenario where the argument of the outside bars is positive (the "plus" case):

|x-5| -4 ≤ 1

|x-5|  ≤ 1 + 4

Recall that absolute values are never negative. This equation is correct, and I've isolated the leftover absolute value, so I'll go over the two situations again.

Step 2 - First, consider the "minus" case:

x+5  ≤ -5

x ≤ -5-5
x≤ -10

The variable can have a "minus" value; the sole constraint is that an absolute-value expression cannot have a "minus" value. Now consider the "plus" case:

⇒ x + 5 ≤ 5 again recall that this is an absolute expression hence the laws of polarity while cross the inequality sign is suspended.

x ≤ 5-5

x≤0

Hence the answer which is complete is:

x = -10, 0

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Answer: A is not equivalent to the other 2

Step-by-step explanation:

A. 15j+30

B. 5(3j-6) = 15j-30

C 3(5j-10) = 15j-30

multiply the stuff inside paranthesis for the last 2

So a is the outsider