A 10 1/2 -inch candle burns down in 6 hours. At what rate does the candle burn, in inches per hour?

Answer:

A) Domain: x∈R or in interval notation (- ∞, ∞)

Range: x∈R or in interval notation (- ∞, ∞)

Thus, they both the domain & the range of the first function are the same.

B) Domain: x∈R or in interval notation (- ∞, ∞)

Range: [-5,∞)

Using it's concepts, the domain and the range of the functions are given as follows:

a) Both all real numbers.

b) Domain all real numbers, range [tex]y \geq 5[/tex].

In this problem, neither function has any impediment, such as an even root or denominator, hence the domain is all real numbers. As for the range, a linear function assumes all real values, while a concave up quadratic function assumes values of the vertex, in this case y = 5, and greater, hence the range of the second function is [tex]y \geq 5[/tex].

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The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

From the given figure, the coordinate of the vertex A is represented as:

A = (-5, 2)

The coordinates of the vertex that A maps to after Daniel's reflections

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A' = (5 - 2, 2)

Evaluate the difference

A' = (3, 2)

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A'' = (3, -2 + 4)

Evaluate the difference

A'' = (3, 4)

Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)

The coordinates of the vertex that A maps to after Zachary's reflections

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A' = (-5, -2 + 4)

Evaluate the difference

A' = (-5, 2)

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A'' = (5 - 2, 2)

Evaluate the difference

A'' = (3, 2)

Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

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Answer:

it is False

Step-by-step explanation:

Using proportions, it is found that the fraction of each candy bar that each friend will get is:

[tex]\frac{2}{3}[/tex].

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the three friends that were there initially and the three that arrived later, 4 candy bars will be split between 6 friends, hence the fraction that each will get is:

[tex]\frac{4}{6} = \frac{2}{3}[/tex]

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Answer:

[tex]5\frac{6}{11}[/tex]

Step-by-step explanation:

Number of Values = 11.

Mean = Sum of values / Number of Values

= [tex]\frac{3+2+4+6+5+6+1+7+9+8+10}{11} \\=\frac{61}{11} \\= 5\frac{6}{11}[/tex]

line segment connecting the vertices of a hyperbola is called the transverse axis and the midpoint of the line segment is the center of the hyperbola.

What is transverse axis and center of hyperbola ?

The transverse axis is a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci lie on the line that contains the transverse axis. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints.

And The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect. Every hyperbola also has two asymptotes that pass through its center. As a hyperbola recedes from the center, its branches approach these asymptotes.

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Putting the other player's king in check is always a good move. true

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The equation which represent the interpretation of the scenario is 5 + 2x

Total laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)

= 5 + (2 × x)

= 5 + 2x

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The taxi fare for a journey of n miles in dollars is 1 + 2n

Linear equations are equations that have constant average rates of change, slope or gradient

The given parameters about the taxi fares are given as

First two miles = $5

Additional mile = Increment of $2

Let the number of miles be n

So, we have:

2 miles = $5

Additional miles = (n - 2) * 2

Add the above expressions

5 + (n - 2)* 2

Represent the value with f(n)

So, we have:

f(n) = 5 + (n - 2)* 2

Expand the bracket

f(n) = 5 + 2n - 4

Collect the like terms

f(n) = 5 - 4+ 2n

Evaluate the like terns

f(n) = 1 + 2n

Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n

So, the complete parameters are:

First two miles = $5

Additional mile = Increment of $2

n miles  1 + 2n

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Answer: -4, 0, 2

Step-by-step explanation:

The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].

The slope of the parallel line is 0 and the slope of the perpendicular line is undefined

The equation is given as:

y = 1

A linear equation is represented as:

y = mx + c

Where:

m represents the slope

By comparison, we have:

m = 0

The slope of the parallel line is:

Slope = m

This gives

Slope = 0

The slope of the perpendicular line is:

Slope =-1/m

This gives

Slope = -1/0

Slope = undefined

Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined

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The area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.

Given the coordinates of abcd are a (-6,0) b (0,0) c (o,6) and d (3,-3).

We are required to find the area of the triangle when bd is the altitude of the triangle.

When we draw the triangle we will find that that the base is ac and altitude is given bd.

ac=[tex]\sqrt{(6-0)^{2} +(0+6)^{2} }[/tex]

=[tex]\sqrt{36+36}[/tex]

=[tex]\sqrt{72}[/tex]

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

bd=[tex]\sqrt{(-3-0)^{2} +(3-0)^{2} }[/tex]

=[tex]\sqrt{9+9}[/tex]

=[tex]\sqrt{18}[/tex]

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

Area=(Base*Height)/2

=(6[tex]\sqrt{2}[/tex]*3[tex]\sqrt{2}[/tex])/2

=(18*2)/2

=18 square units.

Hence the area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.

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The height of the frame is 15 feet.

From the information given, the following can be depicted:

b - 10/a = 2/5

2a = 5b - 50

2a - 5b = -50

Also, slope of AC:

= (b - 10(/(a - 5) = 2/5

2a - 50 = -5b + 50

2a + 5b = 100

Both equations will be solved

The height of the frame will be:

= 5 + 10

= 15 feet

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Answer:

502.5

Step-by-step explanation:

C = 24(12) + 5.50(39)

C = 288 + 214.5

C = $502.5

Answer:

y = 9.84 mm

Step-by-step explanation:

Law of sine:

   [tex]\sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}[/tex]

    a = y

    A = 31°

   b  = 17 mm

    B = 117°

[tex]\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\[/tex]

          [tex]\sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\ y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm[/tex]

The permutations is computed below.

1. Evaluate 9P4

9P4 = 9!/(9 - 4)

= 9!/5!

= (9 × 8 × 7 × 6)

= 3024

2. How many ways can 5 students sit on a row of 15 chairs for a photograph?

= 15!(15 - 5)

= 15!/10!

= (15 × 14 × 13 × 12 × 11)

= 360360

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Answer:

37

Step-by-step explanation:

6m+5n

plug in your given values

6(2) + 5(5)

12+25

=37

Answer:

37

Step-by-step explanation:

6m + 5n

6*2  +  5*5 = 12 + 25

= 37

Answer:

The ¨mandatory dues¨ asked by the unions are not much (practically none), since it´s a voluntary system implemented, normally all the members pay a ¨agency fee¨ but not more than that, this changes depending on the personal involvement with the union.

a natural person can refuse the membership at any moment, without issues, and this way avoid any kind of activity with the union, including contributing with money (dues) or duties.

However, when this happens, the person it´s restricted to certain activities like participate in union elections, general or important meetings, and the contribution in the bargain for the collective elections is banned as well, these as main aspects to highlight.

If one doesn't pay they union dues, they will not be able to participate in collective bargaining with owners.

Only the real representatives of the union could participate in collective bargaining with owner (in which they could negotiate the new term of the salary with the owner). Without paying their dues, they're still haven't been acknowledged as the member of union.



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The measure of each angle formed by the place where the median meets the vertex is 30 degrees

The median of an equilateral triangle divides the side and the angle into equal parts.

If the angle at the vertex is, the new angle would be

Angle = x/2

The angle at the vertex of an equilateral triangle is 60.

So, we have:

Angle = 60/2

Evaluate

Angle = 30

Hence, the measure of each angle formed by the place where the median meets the vertex is 30 degrees

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Answer:

c) 700

Step-by-step explanation:

Add 800 and 600, and then divide by the number of number, or in this case, two. This should give you 700.

The country is 3250 miles in distance from east to west, and 3400 miles from north to south.

Given Information

It is given that,

The distance of the country on map from east to west, l = 65 inches

The distance of the country on map from north to south, b = 68 inches

As per the given scaling of map, 1 inch = 50 miles

How large is the actual country?

Thus, the actual distance from east to west, L = l × 50 miles

L = 65 × 50 miles

L = 3250 miles

The actual distance from north to south, B = b × 50 miles

B = 68 × 50 miles

B = 3400 miles

Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.

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Answer:

X=10

Step-by-step explanation:

You can subtract 180 by 110 to get 70. Then you can do 8x+30+70=180
Add 30+70 to get 100
Subtract 100 to 180 to get 80.
8x=80
You divide 8 from both sides which leaves you with x=10.

Answer:

x=10

Step-by-step explanation:

See attached image

Answer:

5

Step-by-step explanation:

5×(-4)=20

5×3=15

5×0.5=2.5

5×5=25

5×0=0

5×(-2)=-10

Answer:

A and B

Step-by-step explanation:

x < 100 means x is less than 100. Therefore, pick any x-values that are less than 100 which are x = 54 and x = 89.

Hence, A and B are the answer.

The system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store are;

y = 50x + 100    ------(eq 1)

y = 75x + 50    ------(eq 2)

A) Let the total cost of the cat tree be y

Let each additional piece added be x.

Since basic tree is $100 and each additional platform costs $50, then we can say that;

y = 50x + 100    ------(eq 1)

Now, their basic cat tree starts at $50 and each additional piece costs $75. Thus;

y = 75x + 50    ------(eq 2)

B) Subtract eq 1 from eq 2 to gte;

25x - 50 = 0

25x = 50

x = 50/25

x = 2

y = 75(2) - 50

y = $100

C) The Store that would be cheaper depending on the add - ons is Puuur Place because as x increases, it's y-value increases at a lesser rate than that of Meow.

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Answer:

137

Step-by-step explanation:

VYXW is a parallelogram.

The opposite angles of a parallelogram are congruent, meaning their angle measurements are equal.

Following this information we can write an equation to find the value of x:

10x - 27 = 2x + 29 transfer like terms to the same side of the equation

10x - 2x = 29 + 27 add/subtract

8x = 56 divide both sides by 8

x = 7 replace x with 7 to find the given angle measures

now, the consecutive angles in a parallelogram are supplementary meaning their sum is equal to 180

m<V + m<W = 180

m<V + 2*7 + 29 = 180

m<V + 43 = 180 subtract 43 from both sides

m<V = 137

Based on the percentage of people who actually voted and the margin of error, the data implies that people lied when responding to the survey.

The evidence that people lied about voting would bet be shown by the confidence interval. If the confidence interval of the survey does not have the actual percentage of people who voted in it, then people lied.

The confidence interval is:

= Average ± Margin of error

Solving:

= 70% + 3%

= 73%

= 70% - 3%

= 67%

Confidence interval is:

67% - 73%

The actual percentage of 61% who voted is not in this interval which means that some people lied about voting in the survey.

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Answer:

See below.

Step-by-step explanation:

a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.

C = $250 + ($40/hr)*h

b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.

$1000 = $250 + ($40/hr)*h

($40/hr)*h = $750

h = 18.75 hours

(18.75 hours)(60 min/hr) = 1125 minutes

c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?

(18.75 hr)*(1000 cards/hr) = 18,750 cards

d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?

Photocopy Cost for the first 1000 single-sided cards is:

(1000 cards)*($0.15) = $150

Photocopy Cost for the final 17,750 single-sided cards is:

(17,750)*($0.10) = $1,775

Totoal photocopy cost for 18,750 single-sided cards is $1,925.  [1775+150]

The cheapest option for 18,750 cards is printing:  $1,000

Printing is (1,925 - 1000) $925 cheaper than photocopying.