Te solutions to the **linear equation **given as y = 12x + 24 are (0, 24), (1, 36) and (2, 48)

From the question, the **linear equation **is given as

y = 12x + 24

To determine the **solutions**, we assume values for the variable x and then calculate the **y values**

Having said that, we have

y = 12x + 24

Set x = 0

So, we have

y = 12 x 0 + 24 = 24

Set x = 1

So, we have

y = 12 x 1 + 24 = 36

Set x = 2

So, we have

y = 12 x 2 + 24 = 48

So, the ordered pairs of the **solutions **are (0, 24), (1, 36) and (2, 48)

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The following table shows a proportional relationship between wand z.318z 2. 545819Write an equation to describe the relationship between w and z.

when w = 18 then z =2

take ratio,

k = 18/2

k = 9

when w =45 then z = 5

take ratio

k = 45/5

k = 9

now it is clear that the constant of proportionality is k = 2

so, the relation between w and z is

w = k z

put k = 9

**w = 9z**

**so, the relation between w and z is w = 9z**

Jared sells jewelry online. He can make 25 necklaces from 375 beads. Yesterday he made 21 necklaces. How many beads did Jared use to make necklaces yesterday

The number of** beads** he used to make 21 necklaces is 315 beads.

He **sells** jewellery online. He can make 25 necklaces from 375** beads**.

This means Jared uses 375 **beads** to make 25 necklaces.

Yesterday he made 21 necklaces.

Therefore, the number of **beads** he used to make the 21 jewellery can be calculated as follows:

Hence,

25 necklaces = 375 **beads**

21 necklaces = ?

cross multiply

number of** beads** used to make the necklaces = 21 × 375 / 25

number of **beads** used to make the necklaces = 7875 / 25

Therefore,

number of **beads** used to make the necklaces = 315

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Passes through the coordinates -2,2 parallel to the line whose slope is -1

The **equation** of the** line** is y-2x= 6.

Here the problem we are dealing with is related to the **slope** of the line, where, a slope of a line is the alter in the **y coordinate **about the alter in the **x coordinate**. The net change in the y-coordinate is spoken to by Δy and the net change in the x-coordinate is spoken to by Δx. The equation for the slope of a straight line is given by** y − y1 = m(x − x1)**, where m is the slope and (x1,y1) are the points that pass through it,whereas the **slope-intercept form **of the line is given by **y = mx + b, **where b is the y-intercept. Since if two lines are **parallel **at that point it said the slope of both those lines are equal i.e** m₁= m₂**

Since it is given that the coordinates (-2,2) and the slope of the parallel to it, m=2

so the equation for the line is

=>y − y1 = m(x − x1)

=>y − 2 = 2(x +2)

=>y − 2 = 2x+4

=>y-2x= 6

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Find the eqaution of the line that passes through the coordinates -2,2 parallel to the line whose slope is -1.

2. The design of the Trieste was based on the design of a hot air balloon built by Auguste Piccard, Jacques's father. In 1932, Auguste rode in his hot-air balloon up to a record-breaking height.A. Auguste's ascent took 7 hours and went up 51,683 feet. Write a relationship y = kx to represent his ascent from his starting location.B. Auguste's descent took 3 hours and went down 52,940 feet. Write another relationship to represent his descent. C. Did Auguste Piccard end up at a greater or lesser altitude than his starting point? How much higher or lower?

**ANSWER**

A. y = 7383.3x

B. y = 17646.7x

C. Lesser altitude; 1257 feet

**EXPLANATION**

A. We want to write a proportional relationship between the time it took him to ascend and the total height he reached:

y = kx

where x = time taken

y = distance (height reached)

k = constant of proportionality

We have to** find k for the relationship.**

So, we have that:

[tex]\begin{gathered} 51683\text{ = k }\cdot\text{ }7 \\ \Rightarrow\text{ k = }\frac{51683}{7} \\ k\text{ = }7383.3\text{ ft/hr} \end{gathered}[/tex]**This constant of proportionality **(between distance and time) **is called speed**.

Therefore, **the relationship for his ascent** is:

**y = 7383.3x**

B. For his descent, we also have to find k in:

y = kx

We have that:

[tex]\begin{gathered} 52940\text{ = k }\cdot\text{ 3} \\ k\text{ = }\frac{52940}{3} \\ k=\text{ }17646.7\text{ ft/hr} \end{gathered}[/tex]Therefore, **the relationship for his descent **is:

**y = 17646.7x**

C. To find out if he reached a greater or lesser altitude than his starting point, we have** to subtract his altitude during ascent from his altitude during descent.**

If the value is positive then he ended up at a lesser altitude but if it is negative, he ended up on a greater altitude.

That is:

52940 - 51683

= **1257 feet**

Since it is positive, that means that he descended more feet than he ascended and so, **he ended up at a lesser altitude than his starting point, 1257 higher**.

Describe the

transformation from the

graph of of to the graph

of g.

In the picture, there is table with **functions**. g(x)=-f(x)

The **graph **of g is negative 1 times of **graph **of f.

Given that,

In the picture, there is table with **functions**.

We have to find the transformation from the **graph **of f to the **graph **g.

The table has **functions **with the numbers.

x values as -2,-2,0,1

**Function **f(x) as 4,1,0,1

**Function **g(x) as -4,-1,0,-1

The f(x) **function **we can write as

f(x)=x²

And the g(x) **function **we can write as

g(x)=-x²

Therefore, g(x)=-f(x)

The **graph **of g is negative 1 times of **graph **of f.

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A pool fills up 3 gallons of water in one minute. How many pints does it fill in one minute?

In this problem we have to use the convertion factor that is equal to 1 so:

[tex]\frac{1gal}{8pn}=1[/tex]so we can made the transormation:

[tex]3\text{gal}\cdot\frac{8pn}{1\text{gal}}=24pn[/tex]So in one minute it fills 24 pints

A sample of 342 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according tomajor ("blology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below.Biology Business Engineering Mathematics Computer scienceFemale4623501837Male4815461544What is the relative frequency of male students in the sample?Round your answer to two decimal places.0Х5.?

The relative frequency of an event is **the quotient of the division between the event and the total number of the sample**

From the given table

Add the numbers of males to find their total

[tex]48+15+46+15+44=168[/tex]Then add the numbers of females and males to find the total of the sample

[tex]168+46+23+50+18+37=342[/tex]Now, divide the number of males by the total to find the relative frequency

[tex]\begin{gathered} R\mathrm{}F=\frac{168}{342} \\ R\mathrm{}F=0.4912280702 \end{gathered}[/tex]Round it to 2 decimal places, then

**The relative frequency of the male students = 0.49**

Omar and Zina Aboud found that the dealers cost of the base price was $16.558.16 and the dealer's options cost was $611.60. The consumer paid the $476.00 destination charge. If the percent of the dealer's cost is 92% and the percent of dealer's options cost is 88%, find the car's sticker price.

We want to calculate the sticker price. The sticker price is given by the formula

[tex]\text{sticker price = base }price+\text{ options + destination charge}[/tex]We are told that the destination charge is 476. We should determine the base price and the options to find the price sticker.

We are told that the dealer's cost of the base price is 92% of the pase price. So we have the equation

[tex]16558.16=\frac{92}{100}\cdot\text{base price}[/tex]so if we divide both sides by 92 and multiply by 100 we get

[tex]\text{base price = }16558.16\cdot\frac{100}{92}=17998[/tex]Now, applying the same principal for the options, we have

[tex]611.60=\frac{88}{100}\text{options}[/tex]which means that

[tex]\text{options}=611.6\cdot\frac{100}{88}=695[/tex]Replacing these values in the original equation we have that

[tex]\text{sticker price = }17998+695+476=19169[/tex]**so the sticker price would be 19169**

write an equation of a line m= -7 b= -11

**Answer:**

y= -7x-11

**Step-by-step explanation:**

m= -7 (gradient)

b= -11 (y-intercept)

write in the form of y=mx+b

y=-7x-11

11A family went out to dinner. The cost of their meal was $689, before sales tax and tip.A sales tax of 8% was added.(a)The family then tipped 20% on the amount after the sales tax was added,Part AWhat was the amount, rounded to the nearest cent, of just the sales tax?Show all of your work and record your final answer in the space below.Click the box below to type your math work and answer.On the right side of the box, click thebutton to start a new line.

The cost of the meal before the sales tax and tip= $689

Sales tax = 8%

The family then tipped 20% on the ammount after the sales was added

PART A

The amount of the sales tax can be calculated as follows

Amount of sales tax = sales tax * the amount of the meal

Amount of sales tax = 8% x $689

Amount of sales tax = 8/100 x 689

Amount of sales tax = 0.08 x 689

Amount of sales tax = $55.12

**Therefore, the amount of sales tax is $55.12**

**PART B**

**What is the total amount paid by the family after adding the tax sales and 20% tipping**

The cost of the meal = $689

Amount of sales tax = $55. 12

20% tipping on the amount after the sales tax was added

Amount of the meal after the sales has been added = $689 + $55.12

**Amount of the meal after the sales tax has been added = $744. 12**

20% tipping of the total amount = 20% x 744.12

= 20/100 x 744.12

= 0.2 x 744.12

= $148.82

The total amount paid by the family = 689 + 55.12 + 148.82

**The total amount = $892.94**

**Therefore, the family paid a total amount of $892.94**

Now move the red distribution at the top to the right so that its mean is approximately 375 and then look at the middle and bottom distributions. Based on the location of 0 in the bottom distribution (meaning no difference in the means) what is the best conclusion?

Based on the location of 0 in the bottom **distribution** (meaning no difference in the means), the best conclusion is:

A- The **distribution** of differences between the **sample means** of each group has a mean at or near zero making it likely the two groups are not statistically different.

In mathematics, **distribution** describes the **probability** that a system or a data set will take on a specific value or set of values.

**Probability distribution** shows how data values are distributed. It is also known as **statistical distribution** because it demarcates values into common and uncommon (left and right), making a bell-shaped normal distribution.

Thus, when there is no difference in the means, the best conclusion of the **statistical distribution** is Option A.

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Question Completion with Answer Options:A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.

B- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are not statistically different.

C- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are statistically different.

D- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are statistically different.

consider functions f and g. f(x) = -x^3g(x) = | 1/8x-1| what is the value of ( g • f)(4)a: -9b: -1/8 c: 9 d: 1/8

**The solution:**

Given the functions:

[tex]\begin{gathered} f(x)-x^3 \\ \\ g(x)=|\frac{1}{8}x-1| \end{gathered}[/tex]Required:

To find the value of g(f(4))

Step 1:

Substitute 4 for x in f(x).

[tex]f(4)=-(4)^3=-64[/tex]Step 2:

Substitute -64 for x in g(x).

[tex]\begin{gathered} g(-64)=|\frac{1}{8}(-64)-1| \\ \\ g(-64)=|(1\times-8)-1| \\ \\ g(-64)=|-8-1|=|-9|=9 \end{gathered}[/tex]Therefore, **the correct answer is 9 [option C]**

Use substitution to solve the following system of equations. What is the value of y? {3x+2y=12{5x−y=7 A) y = -3B) y = 3C) y = -2D) y = 2

*Answer*

**B) y = 3**

*Step-by-step explanation*

Given the system of equations:

[tex]\begin{gathered} 3x+2y=12\text{ \lparen eq. 1\rparen} \\ 5x-y=7\text{ \lparen eq. 2\rparen} \end{gathered}[/tex]Isolating x from equation 1:

[tex]\begin{gathered} 3x+2y-2y=12-2y \\ 3x=12-2y \\ \frac{3x}{3}=\frac{12-2y}{3} \\ x=\frac{12}{3}-\frac{2}{3}y \\ x=4-\frac{2}{3}y\text{ \lparen eq. 3\rparen} \end{gathered}[/tex]Substituting equation 3 into equation 2 and solving for y:

[tex]\begin{gathered} 5(4-\frac{2}{3}y)-y=7 \\ 5\cdot4-5\cdot\frac{2}{3}y-y=7 \\ 20-\frac{10}{3}y-y=7 \\ 20-\frac{13}{3}y=7 \\ 20-\frac{13}{3}y-20=7-20 \\ -\frac{13}{3}y=-13 \\ (-\frac{3}{13})\cdot-\frac{13}{3}y=(-\frac{3}{13})\cdot-13 \\ y=3 \end{gathered}[/tex]

**Answer:**

y=3

**Step-by-step explanation: **

**Got it right :/**

Please Help . I'm Running Out Of Time!

-5/4 can be shown as -1 1/4, and plotted on the number line as the first quarter tick past -1. Its opposite, 1 1/4, is the same way, the first quarter tick past 1.

**Answer: On the plot line 5/4 is 5 tic marks passed 0 so -5/4 would be 6 tic marks before. Hope this helps**

**If this is wrong I am deeply sorry.**

Please asnwer corrrectly and if you could explain or not

**Answer:**

y = 4·0.5^x

**Step-by-step explanation:**

If x is increased by 1, y is multiplied by 0.5.

x | y

0 | 4

1 | 4·0.5

2 | 4·0.5·0.5

3 | 4·0.5·0.5·0.5

what is the price of a line jacket at discount Heaven?

**The price of the lined jacket at discount heaven is 32.**

To find the price of the lined jacket at the house of denim we use the rule of three.

[tex]\begin{gathered} 35.25\rightarrow100 \\ x\rightarrow10 \end{gathered}[/tex]Then the discount is:

[tex]x=\frac{10\cdot35.25}{100}=3.525[/tex]Hence, the price of the lined jacket at house of denim is:

[tex]35.25-\text{3}.525=31.725=\text{31}.73[/tex]**Therefore, the price of the lined jacket at house of denin is $31.73.**

Sequence: 0, 4, 8, 12,...

Find the 18th term.

**Answer:**

68

**Step-by-step explanation:**

Bryant measured a house and made a scale drawing the scale he used was 1 inch = 1 foot what scale factor does the drawing use?

The **scale factor **which is being used by this drawing is 1 : 12.

A **scale factor** can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar **geometric** figures such as equilateral triangles, river, planets in our solar system, etc.

Mathematically, the **scale factor **of a **geometric** figure can be calculated by using tis formula:

Scale factor = Dimension of image/Dimension of original figure

Generally speaking, an appropriate **conversion factor** to an equal value must be used when it is necessary to perform any mathematical **conversion**.

Conversion:

1 inch = 1 foot

12 inches = 1 foot

Therefore, the **scale factor **for this drawing is 1 : 12.

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A cosine function has an amplitude of 1/4 , period of pi/2, horizontal shift of 2pi, and vertical shift of -4.

What is the y-value of the positive function when x = 2π?

y = ?

The **value** of y when y = y = 0.25sin(4(x+2π))-4. and x = 2pi is -4.

Some functions (like Sine and Cosine) repeat forever and are called **Periodic Functions**.The Amplitude is the height from the center line to the peak (or to the trough).The Phase Shift is how far the function is shifted horizontally from the usual position.The Vertical Shift is how far the function is shifted vertically from the usual position.

We can have all of them in one equation:

y = A sin(B(x + C)) + D

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

So, for the given question we have amplitude is 0.25, period is 2π/4, **phase** shift is 2π, vertical shift is -4

So,

y = 0.25sin(4(x+2π))-4.

when x = 2π

y = 0.25sin(16π)-4

y = 0-4

y = - 4

Therefore, y = 0.25sin(4(x+2π))-4, and its y - **value** when x = 2π is -4.

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A sequence of positive integers with 2020 terms is called an FT sequence if each

term after the second is the sum of the previous two terms. For example, if the

first two terms of an FT sequence are 8 and 7, the sequence would begin

8,7,15, 22, 37,.... For some positive integer m, there are exactly 2415 FT sequences

where the first two terms are each less than 2m and the number of odd-valued

terms is more than twice the number of even-valued terms. What is the value of m?

(A) 21

(B) 69

(C) 115

(D) 35

(E) 105

The value of m will be 35.

Consider the **FT **0, 1, 1, 2, 3, 5, 8, 13, 21, 24,45,.......

The numbers are arranged in order of even, odd, odd, even, odd, odd, even, odd, odd, even,.......

Hence, the loop contains 3 elements. If the number of terms is 2020 terms, then we have 673 loops + 1 element. (That is 3* 673 +1 = 2020) The last element will start the new loop and it is an even number.

In the other hand with 2019 terms, we have number of odd = 2* number of even. But the last term is even. That makes number of odd < twice number of even and it contradicts with the condition.

However in this case, the 2020th term is even and so there are fewer than twice as many odd valued terms as there are even-valued terms.

Thus, there are m2 + m × (m − 1) **FT** **sequences **that satisfy the required conditions.

Since there are 2415 such **FT sequences**, we may solve m2 + m × (m − 1) = 2415 by trial and error.

Evaluating m2 + m × (m − 1) when m = 30, we get 302 + 30 × 29 = 1770, and so m is greater

than 30.

When m = 33, we get 332 + 33 × 32 = 2145.

When m = 34, we get 342 + 34 × 33 = 2278.

When m = 35, we get 352 + 35 × 34 = 2415, as required.

Hence, Answer: (D)

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A rectangle is 4 inches long and 2x inches wide. The value of the perimiter is equal to the value of the area

When a rectangle has a **perimeter **equal to the area and is 4 inches long and 2x inches wide, the value of x is 2.

GIVEN:

The perimeter (in inches) of a rectangle with dimensions of 4 inches long by 2 inches wide equals the area (in square inches) specified in the question.Rectangle perimeter (P) equals 2x plus 2L.Rectangle area (A) equals LWAs per the stated circumstance,

P = A LW = 2W+2L 2x(4) = 2(2x)+2(4) (4) 8x = 4x +8 4x = 8 x=2HENCE,The value of x is 2 when a rectangle has a **perimeter **equal to the area, is 4 inches long, and is 2x inches broad.

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The US postal charges $.34 for the 1st ounce and $.23 for each additional ounce. use inequality to find the maximum number of whole ounces that can be mailed for $8.27

Answer:Explanations:

The charges for the first ounce = $0.34

Charges for each additional ounce = $0.23

Let the number of additional ounces be n

The maximum total charges = $8.27

The inequality that represents the given illustration is:

0.34 + 0.23n ≤ 8.27

0.23n ≤ 8.27 - 0.34

0.23n ≤ 7.93

n ≤ 7.93 / 0.23

n ≤ 34.48

Maximum number of whole ounces = Number of additional ouces + Initial ounce

Maximum number of whole ounces = 34.48 + 1

Maximum number of whole ou

Someone help me out pls!

**Answer:**

look my photo. hope it can help

Assume that all interest is simple interestBerger Car rental borrow $8500 at 4% interest to cover the increase cost of the auto insurance find the term of the loan if the interest is $170.

we know that

The formula of simple interest is equal to

[tex]I=P(rt)[/tex]In this problem

we have

I=$170

P=$8,500

r=4%=4/100=0.04

t=?

substitute given values in the formula

[tex]\begin{gathered} 170=8,500(0.04t) \\ Solve\text{ for t} \\ t=\frac{170}{8,500*0.04} \\ t=0.5\text{ years} \end{gathered}[/tex]therefore

0.5 years=6 months

The answer is 6 monthsThe answer to which situation is best estimated by -7? How can you estimate decimal amounts?A The temperature falls 1.9°F from 4.3°F.B A hot air balloon rises 4.1 meters from the ground and then rises 2.3 meters more.C A submarine goes 3.8 feet below the surface of the ocean and then goes 2.5 feet farther downD The amount of money Sarah has after she buys milk for $3.85 and bread for $2.45.

**Answer:**

C A submarine goes 3.8 feet below the surface of the ocean and then goes 2.5 feet farther down

**Explanation:**

Option A

[tex]\begin{gathered} 4.3^0F\approx4^0F \\ 1.9^0F\approx2^0F \\ \text{Estimated change in temperature=}4^0F-2^0F=2^0F \end{gathered}[/tex]Option B

[tex]\begin{gathered} 4.1\text{ meters}\approx4\text{ meters} \\ 2.3\text{ meters}\approx2\text{ meters} \\ \text{Estimated change in the balloons's height}=4-2=2\text{ meters} \end{gathered}[/tex]Option C

[tex]\begin{gathered} -3.8f\exponentialE et\approx-4\text{ feet} \\ -2.5f\mathrm{e}et\approx-3\text{ feet} \\ \text{Estimated change in depth=}-4-3=-7\text{ feet} \end{gathered}[/tex]Option D

[tex]\begin{gathered} \$3.85\approx\$4 \\ \$2.45\approx\$2 \\ \text{Change in the amount Sarah has=-}\$4-\$2=-\$6 \end{gathered}[/tex]**The situation that is best estimated by -7 is Option C.**

Use the graph below for this question: graph of parabola going through negative 3, negative 1 and 5, negative 1. What is the average rate of change from x = −3 to x = 5? (1 point) A) −1

B) 0

C) 1

D) 8

The **average rate **of change of the function at the interval x = -3 to x = 5 has a value of (b) 0

From the question, we have the following points

**Parabola **going through (-3, -1) and (5, -1).

Also from the question, the **interval **is given as

x = −3 to x = 5

This **interval **can also be represented as

(a, b) = (-3, 5)

The **points **in the question can be expressed as

f(a) = f(-3) = -1

f(b) = f(5) = -1

The value of the **average rate of change **of the graph at the **interval **is then calculated as

Rate = [f(b) - f(a)]/[b - a]

Substitute the known values in the above equation

So, we have the following equation

Rate = [f(5) - f(-3)]/[5 + 3]

So, we have the following equation

Rate = [-1 + 1]/[5 + 3]

Evaluate the above **quotient**

Rate = 0

Hence, the **average rate **of change of function f is (b) 0

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. Find the slope and y-intercept of the line shown below.to10-8--10-8-6-4-2.co6-4-2---2--4--6--8--10-yX4 6 8 10

**Solution:**

Given the graph:

Using two points on the line to find the slope, **m**:

Thus, **the y-intercept and slope, m of the line respectively are:**

Leonard is 68 years less than quadruple Sheldon's age. In 12 years, Leonard's age will be 24 years less than two times Sheldon's age. What are their 2 ages?

Sheldon is** 16 4/7 **years old, while **Leonard is 21 1/7.**

We are given the **correlations **between **two numbers **in this sort of query, specifically the data when their ages are contrasted now and in the **future**.

Let **x **represent** Leonard's age.**

We can infer **Sheldon's age **from the question as being** 4x - 68.**

The following **equation **results from the question:

**x + 12 = 2((4x - 68) + 12) - 24**

Fix x,

=> **x + 12 = 2(4x - 68 + 12) - 24**

x + 12 = 2(4x - 56) - 24

x + 12 = 8x - 112 - 24

x - 8x = -136 - 12

-7x = - 148

**x = 148 / 7 or 21 1/7**

Now, simply multiply **4x by 68 **to get Sheldon's age.

=> 4x - 68

=> 4 * 148/7 - 68

=> 592/7 - 68

=>** 116/7 or 16 4/7**

Leonard is therefore** 21 1/7 years old, **while Sheldon is** 16 4/7.**

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Please help me with this question

**Step-by-step explanation:**

substitution means to use one equation to express one variable only in terms of the other variable and constants.

let's use

6f + 11b = 317

for that purpose.

6f = 317 - 11b

f = (317 - 11b)/6

now we use that my substituting "f" by its identical expression in b in the second equation :

7(317 - 11b)/6 + 5b = 221

to avoid handling fractions we multiply everything by 6 :

7(317 - 11b) + 30b = 1326

2219 - 77b + 30b = 1326

893 - 47b = 0

893 = 47b

b = 893/47 = 19 cents

f = (317 - 11b)/6 = (317 - 11×19)/6 = (317 - 209)/6 =

= 108/6 = 18 cents

a piece of fudge is 18 cents.

a piece of bubble gum is 19 cents.

Express the trig ratios as fractions in simplest form.Drop down menu: (a) are equal (b) are not equal

**ANSWER**

**EXPLANATION**

We want to express the trigonometric ratios as fractions in the simplest terms.

The trigonometric ratios SOHCAHTOA for right triangles for sine and cosine are:

[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \\ \cos\theta=\frac{adjacent}{hypotenuse} \end{gathered}[/tex]Therefore, for the given triangle, we have that:

[tex]\begin{gathered} \sin O=\frac{34}{35} \\ \\ \cos N=\frac{34}{35} \end{gathered}[/tex]As we see from the equations above, the sine of O and the cosine of N **are equal.**

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When the equation, ___O2 + ___C 6H 14 ___CO2 + ___H2O is balanced, the coefficient of O2 is: