A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.

Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)

Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)

Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)

The quotient is -27m/ 55.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

(9mn²)(−3m*6n)÷33m*10n³

=9mn² *(-18mn) / 330mn³

= -162m²n³/ 330mn³

= -27m/ 55

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The required equation of the line passing the coordinates will be y = 3/4x - 1/4

The standard equation of a line is expressed as y= mx + b

where

m is the slope

b is the y-intercept

Given the coordinate points on a line (3, 2) and (-1, -1)

Slope = -1-2/-1-3

Slope = 3/4

Determine the y-intercept

2 = 3/4(3) + b
2 = 9/4 + b

b = 2 - 9/4

b = -1/4

The required equation of the line passing the coordinates will be y = 3/4x - 1/4

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Whatever... I'll try to solve the first two problems.

[tex]2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}[/tex]

1.

[tex]x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4[/tex]

One solution is [tex]x=4[/tex], and [tex]4\in D[/tex], therefore[tex]\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4[/tex].

We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.

Answer:

4/11 of an inch (about .4 of an inch)

Step-by-step explanation:

[tex]l \times 33 \times 5.75 = 69[/tex]

[tex]189.75l = 69[/tex]

[tex]l = \frac{69}{189.75} = \frac{4}{11} = .3636[/tex]

So the length of the popcorn box is 4/11 of an inch, or about .4 of an inch.

The ratio of the median weekly earnings is 3 : 5

From the graph, we have the median weekly earnings to be:

So, the ratio is:

Ratio = $750 : $1250

Simplify

Ratio = 3 : 5

Hence, the ratio of the median weekly earnings is 3 : 5

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

Both rectangles have a width of 1 unit.

So, we have:

Ratio = 3 * 1: 5 * 1

Simplify

Ratio = 3 : 5

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width

So, we have:

Ratio = 3 * 3 : 5 * 5

Simplify

Ratio = 9 : 25

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width.

Since the base are squares, we have:

Ratio = 3 * 3  * 3 : 5 * 5 * 5

Simplify

Ratio = 27 : 125

Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125

The most misleading graph is graph B.

This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

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Based on the stated annual interest rate and the face value of the bond, the semiannual payments will be $1,000,000.

The formula to find the semiannual payment is:

= (Face value x Stated annual interest rate) / 2 semi-annual periods per year

Solving gives:

= (50,000,000 x 4%) / 2

= 2,000,000 / 2

= $1,000,000

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Answer:

x f(x)

0 0

-2 -4

4 -2

You need to draw y = 2 f (x-1)

So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values

New function

x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0

x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8

x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4

So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)

Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.

y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)

So basically here you are doing both things.

So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)

Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)

Using the Empirical Rule, it is found that standard deviation of the sample proportions is of 0.058.

It states that, for a normally distributed random variable:

0.684 and 0.916 is within 2 standard deviations of the mean(below and above), hence there are 4 standard deviations between these measures, so:

4s = (0.916 - 0.684)

s = (0.916 - 0.684)/4

s = 0.058.

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Answer: 8x+70

Step-by-step explanation:

[tex]\sum^{5}_{n=2} (2x+5n)=(2x+10)+(2x+15)+(2x+20)+(2x+25)=\boxed{8x+70}[/tex]

Answer:

Step-by-step explanation:

-3 +2 +-1 +-2 +-3 +1 = -6 yards total

-6 / 6 =  -1 yard per play average

Answer:

(-5, -6)

Step-by-step explanation:

The smaller integer is x.

The larger integer is x + 1.

x + 1 = 7 + 2x

-x = 6

x = -6

x + 1 = -6 + 1 = -5

Answer: (-5, -6)

The length is 6.8 meters and the width is 8.2 meters.

Represent the length and the width with x and y

So, we have:

y = 1.2x

P = 2(x + y)

The perimeter is 30.

So, we have:

2(x + y) = 30

Divide by 2

x + y = 15

Substitute y = 1.2x

x + 1.2x = 15

This gives

2.2x = 15

Divide by 2.2

x = 6.8

Substitute x = 6.8 in y = 1.2x

y = 1.2 * 6.8

Evaluate

y = 8.2

Hence, the length is 6.8 meters and the width is 8.2 meters.

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The rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The rate of gas will be calculated as:-

Suppose the hours are represented by x and the gallons are represented by y.

The rate of the gas will be the slope so the slope will be calculated as:-

[tex]m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \dfrac{2-20}{3-0}[/tex]

[tex]m =\dfrac{-18}{3}[/tex]

m = -6

The equation will be given as:-

y = mx + c

y  = -6x + 20

Therefore the rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

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Answer:

-26

Step-by-step explanation:

2 is 14 away from -12. The other number that is 14 away from -12 is -26.

-12 + x = 2

x  = 14

-12 - 14 = -26

Answer:

The answer will be 30.625 m

Based on the definition of a circumcircle, the center of the circle as shown in the image below is located: B. inside the triangle.

A circumcircle, as shown in the diagram attached below, is a circle that is drawn so that all the vertices of a triangle touches the circumference of the circle.

Thus, as shown in the image attached below, the center of the circle is located: B. inside the triangle.

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Answer: OUTSIDE THE TRIANGLE

Step-by-step explanation: ANSWER ON EDMENTUM/PUTO

Answer:

  18π ≈ 56.5 meters

Step-by-step explanation:

The length of the arc of a circle is given by the formula ...

  s = rθ . . . . where r is the radius, and θ is the central angle in radians

You are given the values of r and θ, so you only need to put them into the formula and simplify.

  s = (27 m)(2π/3) = 18π m

The length of the arc is 18π meters, about 56.5 meters.

Answer:

let the no. of students who failed the examination be X

therefore, no. of students passed = 5x

total no. of students = 582

5x + X = 582

6x = 582

x = 97

no. of students failed the examination = 97

no. of students passed = 97*5 = 485

The blank space in the task content should be filled with; false negatives.

Baye's theorem can be used to correct measurement errors provided the real probabilities, the chance of a false positive and the chance of a false negative is known.

Hence, it follows from the methodology above that the Baye's rule combines accuracy, false positives and false negatives in a bid to determine the probability of a result.

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Answer:

A cylinder

Step-by-step explanation:

Hope this helps :)

Answer:

370 + 80x ≤ 1090

Step-by-step explanation:

By using letter variables for the unknown numbers, we can break down the question into mathematical terms:

If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.

If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.

The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:

$370 (1 day) + $80 (x hours) ≤ $1090 per day

The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.

To simplify this, we can rewrite it as:

370 + 80x ≤ 1090

Answer:

Try retyping ,which expressions ..?? Maybe it didn't come out

Answer:

15

Step-by-step explanation:

Actual Question:

These expressions represent four numbers. The value of the median of the expressions is 12.

x  ,   2x,   6x,  11x

Work out the value of the mean of the expressions.

_____________________________________________

See the attachment for steps.

Answer:

4,051,500

Step-by-step explanation:

You have 7.3 % that are one native one foreign

Multiply that by the number of households

.073 * 55,500,000

4,051,500

Answer:

Let first check the coordinates of the points

A = (1 , -6)

B = (2 , -4)

C = (2, -2)

D = (4, -2)

E = ( 6, 0)

Option 4 is correct..

Explanation -

to find the coordinates we have to find the distance of that point from x Axis and then y axis. from origin.

The solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

The graphed parabola is f(w), and we have the inequality:

f(w) ≤ 0.

So we need to identify the intervals such that the parabola is below the horizontal axis. By looking at the graph, we can see that the two intervals are:

Left side:

(-∞, -1]

Right side:

[3, ∞)

Where the brackets are used because points x = -1 and x = 3 are solutions.

Then the solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

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Answer:

x²-16x+64

Answer:

  (x -8)² = x² -16x +64

Step-by-step explanation:

A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.

All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.

__

One of the patterns that is used with quadratics is the square of a binomial.

  (a - b)² = a² -2ab +b²

This is the result of applying the distributive property several times.

First of all, the exponent indicates repeated multiplication:

  (a -b)² = (a -b)×(a -b)

The distributive property tells you each term outside parentheses multiplies each term inside:

  = a×(a -b) -b×(a -b)

  = a·a -a·b -b·a +b·b . . . . . and again

Now, we collect terms, recognizing that ab=ba.

  = a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication

So, the pattern for the square of a binomial is ...

  (a -b)² = a² -2ab +b²

__

For your specific case, ...

  (x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern

  (x -8)² = x² -16x +64

_____

Additional comment

If you want to do this without using the pattern, just make use of the distributive property:

  [tex](x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}[/tex]

__

While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:

Then the product is ...

  (x -8)² = x² -8x -8x +64 = x² -16x +64

__

Of course, the distributive property is involved in what we call "collecting terms."

  -8x -8x = (-8-8)x = -16x

The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.

Answer:

Seitokachou-sama uhuuuyy7 is