Rachel is working on simplifying the following rational expression, but something has gone wrong…can you find her error? Write out or explain all the steps (5 points) involved and give the new answer (5 points)
Problem:
x2+3x32+6x
Work:
x3+3x22+6x

x3+x2+2
x3+x4

Step-by-step explanation:

✧ \( \underline{ \underline{ \large{ \tt{G\: I \: V \: E\: N}}} }: \)

♨ \( \underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I\: N\: D}}}} : \)

♨ \( \underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T\: I\: O \: N}}}} : \)

☪ \( \boxed{ \bf{ {h}^{2} = {p}^{2} + {b}^{2} }}\)

~Plug all the known values and then simplify!

⇾ \( \large{ \bf{ {9}^{2} = {8}^{2} + {b}^{2} }}\)

⇾ \( \large{ \bf{81 = 64 + {b}^{2} }}\)

⇾ \( \large{ \bf{64 + {b}^{2} = 81}}\)

⇾ \( \large{ \bf{ {b}^{2} = 81 - 64}}\)

⇾ \( \large{ \bf{ {b}^{2} = 17}}\)

⇾ \( \large{ \bf{b = \sqrt{17}}} \)

We know ;

⟿ \( \large{ \bf{cot \theta = \frac{b}{p} = \boxed{ \bf{ \frac{ \sqrt{17} }{8}}}}} \)

⤷ \( \boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : { \tt{ \frac{ \sqrt{17} }{8} }}}}}}}\)

( Correct me if I'm wrong )

Hope I helped ! ♡

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☄ Let me know if you have any questions regarding my answer !

\( \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}\) !! ✎

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Answer:

8 miles

Step-by-step explanation:

6/9 = x/12

6/9*12 = 8

8 miles

Answer:

y = 2/3x - 3

Step-by-step explanation:

Given equation :-

Transformations :-

Solving :-

Answer:

Domain is x-values'

ranges y-values'

domain: x>=1

Range: y<=0

Step-by-step explanation:

The square factor for the pair of similar triangles is 1.25.

For a pair of similar triangles, the ratio of their corresponding sides is constant. Let the length of the corresponding sides of the first triangle be x and the length of the corresponding sides of the second triangle be y. Then we can write:

x / 15 = y / 12 (ratio of corresponding sides)

Since the triangles are similar, the ratio of their bases must also be the same as the ratio of their corresponding sides:

20 / 16 = x / y

Simplifying this expression, we get:

5 / 4 = x / y

Multiplying this by the previous equation, we get:

(5/4) * (x / 15) = (x / y) * (y / 12)

Simplifying, we get:

x = 25

Therefore, the length of the corresponding sides of the first triangle is 25 m. Since the sides of a square are all equal, the square factor for the pair of similar triangles is the ratio of the length of the corresponding sides to the base of the first triangle:

Square factor = 25 / 20

Square factor = 1.25

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Answer: 83.5

Step-by-step explanation:

\(\frac{\sin x}{34}=\frac{\sin 26^{\circ}}{15} \\\\\sin x=\frac{34 \sin 26^{\circ}}{15}\\\\x=sin^{-1} \left(\frac{34 \sin 26^{\circ}}{15} \right) \approx \boxed{83.5}\)

Answer:

  x ≈ 83.5° or 96.5°  (two possible values)

Step-by-step explanation:

The relationship between side lengths of a triangle and their opposite angles is given by the Law of Sines: side lengths are proportional to the sines of their opposite angles.

__

In this problem, the Law of Sines tells us ...

  sin(A)/BC = sin(C)/AB

  sin(C) = sin(A)·AB/BC

Using x for angle C, solving for x, and using the inverse sine function, we find ...

  x = arcsin(sin(26°)·34/15) ≈ arcsin(0.993641)

The arcsine function returns a value in the range 0–90°, but the supplemental angle in the rangle 90°–180° can have the identical sine value.

  x ≈ 83.5° or 96.5°

_____

Additional comment

For the graph in the attachment, we have set the angle mode to degrees. The solutions to f(x)=0 are solutions to the problem: 83.5° and 96.5°.

The triangle in the figure appears to be an acute triangle. The value of x for an acute triangle would be 83.5°. Often, we cannot take these figures at face value.

Answer:

I did this question the other day, I think it is right, but I'm not 100% sure. Let me know if it is helpful

Step-by-step explanation:

The distance between Ibadan and Onitsha is 450km

The distance between Ibadan and Kafanchan is 636. 4km

To determine the distance, we have that;

The distance of Onitsha from Kafanchan is 450km

The distance between Ibadan and Onitsha is x

The distance between Ibadan and Kafanchan is y

Note that the third quadrant is 270 degrees

Then, the value of the angle = 270 - 225 = 45 degrees

Then, using the tangent identity, we have that;

tan 45 = x/450

cross multiply the values

x = 450km

Also, using the sine identity

sin 45 = 450/y

cross multiply the values

y = 636. 4 km

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Hey there!

Before we get to know an Integer and Rational Number, we have to know the Real Number system first.

1. What is Real Number System?

But do you know that the Real Number system can be broken into two categorizes? And what are them?

Real Numbers can be broken into these main two categorizes which are:

These numbers can also be broken into other categorizes as well! Crazy, ain't it? Well that's how maths work!

Anyways, we will skip Irrational Number since it is off-topic and not related to your question. We will talk about Rational Number instead.

2. What is Rational Number?

Now we know the meaning of Rational Number. But like I said, the Rational Number can be broken into other categorizes which are:

And Integers can also be broken into:

3. Conclusion and Answer

Hope this helps, and let me know if you have any doubts regarding Real Number system.

The snail will take approximately 0.43 hours or 25.8 minutes to travel 12 feet at the speed of 8.5 meters per hour.

Given, A snail moves at a speed of 8.5 meters per hour, 1m = 3.28ft. Let's convert meters per hour into feet per hour by multiplying it with 3.28ft/m. So, 8.5 meters per hour = 8.5 × 3.28 feet per hour ≈ 27.88 feet per hour.

Now, to calculate the time taken by a snail to travel 12 feet, we can use the formula: Time = Distance ÷ Speed

Time taken = 12 feet ÷ 27.88 feet per hour ≈ 0.43 hours (rounded to two decimal places)

Now, let's convert 0.43 hours to minutes by multiplying it with 60 minutes per hour: 0.43 hours × 60 minutes per hour ≈ 25.8 minutes (rounded to one decimal place). Therefore, it will take approximately 0.43 hours or 25.8 minutes for the snail to travel 12 feet at the speed of 8.5 meters per hour.

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The required width of the carpet is 9 meters, which corresponds to option B.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

We are given that the area of the carpet is 6 square meters, and the length is 4/6 meters. So we can write:

6 = (4/6) x Width

To solve for the width, we can multiply both sides by 6/4:

6 x 6/4 = (4/6) x Width x 6/4

9 = Width

Therefore, the width of the carpet is 9 meters.

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Answer:

hi

Explanation:

hi

Answer:

0.35

Step-by-step explanation:

\(\frac{7}{20}\)

  20 ) 7   ( 0.35

          0

           70

          60

            100

            100

                0

Answer:

7\20 as a decimal is

0.35

The actual cost to see the game is $150, as that is the amount you paid for the ticket. The cost in this scenario can be considered an opportunity cost. By choosing to attend the game instead of selling the ticket for $400, you forgo the opportunity to earn that additional $400.

In this scenario, the cost of attending the game refers to the actual amount of money you spent on the ticket, which is $150. This is the out-of-pocket expense that directly affects your financial resources.

On the other hand, the opportunity cost is the potential benefit or value that you give up by choosing one option over another. In this case, if you had sold the ticket for $400, you would have received a higher amount of money, which represents the opportunity cost of attending the game. By deciding to go to the game, you forego the opportunity to earn that additional $400.

Opportunity cost is a concept in economics that emphasizes the value of the next best alternative forgone when making a decision. It helps assess the trade-offs involved in different choices and helps in evaluating the true cost of a decision beyond the immediate financial expenses.

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The length of the pendulum using equation is 43.56 feet.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation that represent the time of pendulum for one swing is

=> T = \(\frac{2\sqrt L}{3.3}\)

Now T = 4 sec then ,

=> 4 = \(\frac{2\sqrt L}{3.3}\)

=> 4*3.3 = 2\(\sqrt L\)

=> \(\sqrt L = 2\times3.3 = 6.6\)

=> L = 43.56 feet.
Hence the length of the pendulum using equation is 43.56 feet.

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Answer: Choice C

\(0 \le d \le 2\)

Graph with filled in circles at d = 0 and d = 2, shading in between

==========================================

Explanation:

d = amount downloaded in gigabytes

The smallest amount is d = 0. We cannot download a negative amount of data, so this is why d = 0 is the smallest.

The largest amount allowed is d = 2. This is the cap that the ISP has set up.

So basically d can be anything between d = 0 and d = 2, including both endpoints. This means \(0 \le d \le 2\)

We use filled in circles for both endpoints to show to the reader "include these endpoints". Shading is done in between to show the entire solution set of possible d values. For instance d = 1 is in that region so it is possible to have this solution. Something like d = 4 is outside the region and not possible.

The transformation on a line such that a line is obtained which is pependicular to previous line is possible only when it is reflected through y = x axis. This can be understood as,

When line is reflected about x-axis, the x coordinate remain same where as y-coordinate changes in opposite sign with same magnitude. So reflection of line x = 3 about x axis remain same.

Simillarly reflection of line x = 3 about x = 1 remain same as x = 3.

The reflection of line x = 3 about y-axis results n a parallel line passing through x = -3.

So answer is reflection across y = x.

Answer:

15% increase

Step-by-step explanation:

to find the percent increase from an initial value to a final value, first find the difference:

2070-1800=270

then divide the difference by the initial value:

270/1800= 0.15

and multiply by 100

0.15*100=15

so there is a 15% increase

Answer:

The probability of rolling a six on this cube is A. 1/6

Step-by-step explanation:

Just... Think about it. The cube has six sides (the total, or denominator). There is only one six (the numerator). So, the answer is 1/6.

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The percentage of pupils that miss class each day is the most appropriate indicator to track with a p chart. P charts are a specific kind of control chart used to track the percentage of nonconforming products produced over time in a process.

It is frequently applied to attribute data, where the data can be categorised as conforming or nonconforming depending on particular standards.The percentage of pupils that skip class daily in the given alternatives can be categorised as either a conforming (present) or nonconforming (missing) feature. We can track the variation in absenteeism and see any patterns or trends that might need attention or intervention by using a p chart to track the percentage of pupils who are missing over time.

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The results obtained by central limit theorem are given below-

μ = 170 customers per day

σ = 45 customers per day

n = 31

\(\begin{aligned}&\mu_{x}=170 \\&\sigma_{x}=8\end{aligned}\)

The Central Limit Theorem proves that the distribution of a sample means of size n can be estimated to the normal distribution with mean  (μ) and standard deviation (σ) for one random normally distributed variable X, with mean (μ) and standard deviation (σ);

\(s=\frac{\sigma}{\sqrt{n}}\)

This Central Limit Theorem may also be applied to skewed variables if n is at least 30.

She observes that the rival business averages 170 clients per day, with a standard deviation of 45 clients.

Thus, \(\mu=170, \sigma=45\)

Let's say she selects a random sampling of 31 days.

So, n = 31

Now, the mean is according to the Central Limit Theorem is

\(\mu_{x}=170\), and

standard deviation = \(\sigma_{x}=\frac{45}{\sqrt{31}}=8\)

Therefore, by using central limit theorem the data is obtained as,

μ = 170 customers per day

σ = 45 customers per day

n = 31

\(\begin{aligned}&\mu_{x}=170 \\&\sigma_{x}=8\end{aligned}\)

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The complete question is-

A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary:

μ = _____customers per day

σ = _____customers per day

n = ____

\(\mu_{x}\) =____

\(\sigma_{x}\) = ____

The dimensions of the tank with minimum weight are approximately x ≈ 14.55 ft and h ≈ 34.34 ft.

To find the dimensions of the tank with minimum weight, we need to consider the relationship between the volume of the tank and the weight of the sheet steel.

Let's assume the side length of the square base of the tank is x, and the height of the tank is h.

The volume of the tank is given as 8788 ft³, so we have the equation x²h = 8788.

To determine the weight, we need to consider the surface area of the tank. Since the tank has an open top and a square base, the surface area consists of the base and four sides.

The base area is x², and the area of each side is xh. Therefore, the total surface area is 5x² + 4xh.

The weight of the sheet steel is directly proportional to the surface area. Thus, to minimize the weight, we need to minimize the surface area.

Using the equation for volume, we can express h in terms of x: h = 8788/x².

Substituting this expression for h into the surface area equation, we have A(x) = 5x² + 4x(8788/x²).

Simplifying the equation, we get A(x) = 5x² + 35152/x.

To find the dimensions of the tank with minimum weight, we need to minimize the surface area. This can be achieved by finding the value of x that minimizes the function A(x).

We can differentiate A(x) with respect to x and set it equal to zero to find the critical points:

A'(x) = 10x - 35152/x² = 0.

Solving this equation, we get x³ = 3515.2, which yields x ≈ 14.55.

Since the dimensions of the tank need to be positive, we discard the negative solution.

Therefore, the dimensions of the tank with minimum weight are approximately x ≈ 14.55 ft and h ≈ 8788/(14.55)² ≈ 34.34 ft.

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The value of segment AC is 7 units.

A line may be defined as a 2-dimensional figure which consists of a group of points that are joined together and extend infinitely in both the directions. There are two types or categories of lines they are line segment which has two end points and other one is a ray which has one initial point, and it can extend indefinitely on the other side represented by an arrow.

According to the given question a line with many segments is given.

Segment BC = 3, Segment BD = 5, Segment AD = 9 and we have to find Segment AC.

As, AC = AB + BC.

Now, AB = AD - BD then,

AC = [(AD - BD) + BC]

AC = [(9 - 5) + 3].

AC = 4 + 3

=> AC = 7.

Thus, the value of segment AC is 7 units.

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Answer: x= -3

Step-by-step explanation:

1) Set up the equation with triangle sum

35 + x + 58 + 90 = 180

2) Solve

183 + x = 180

x = -3

Answer:

It loses -0.04 milliliters per minute.

Step-by-step explanation:

The pipe loses 1 1/5 milliliters (I'mma just call it ml from now on) every 30 minutes. The question is asking how many ml it loses every one minute. To find this, divide 1 1/5 ml by 30. This is very difficult with fractions tho, so convert the fraction into a decimal. (1 1/5 as a decimal is 1.2) Then divide 1.2 by 30 and you get -0.04 ml per minute.

Make sure you put that it loses *negative* 0.04 ml per minute!

Answer: The differential equations is

y3 3x3logx = 8x3.

Step-by-step explanation:

break the given original- value problem. The DE is homogeneous. xy2dy/ dx = y3- x3; y( 1) = 2.

result

Given a homogenous discriminational equation, xy2 dy/ dx = y3- x3

xy2dy/ dx = y3- x3

dy/ dx = ( y3- x3)/ xy2

dy/ dx = (( y/ x) 3- 1)/( y2/ x2)---( 1)

Put y/ x = v ⇒ y = xv

separatew.r.t x

dy/ dx = x.dv/ dx v

Equation( 1) becomes,

⇒ dv/ dx v = ( v3- 1)/ v2

⇒ dv/ dx = (( v3- 1)/ v2)- v

⇒ dv/ dx = ( v3- 1- v3)/ v2

v2. dv = -1/x.dx

Integrate on both sides, we get

∫ v2. dv = ∫- 1/x.dx

v3/ 3 = - logx C

1/3( y3/ x3)) log x = C( 2)

Now, given that y( 1) = 2

Substituting y = 2 and x = 1 in equation( 2)

(1/3) ×(23/13)) log 1 = C

C = 8/3

From equation( 2), we get

⇒( y3/ 3x3) logx = 8/3

thus, the needed differential equation is y3 3x3logx = 8x3.

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Step-by-step explanation:

Since 4104 students are employed sophomores, juniors, or seniors, the total number of unemployed students is 11,989 - 4104 = 7885.

And since 745 students are employed freshman, the number of unemployed freshman is 7885 - 745 = 7140.

So, the total number of freshman is 745 + 7140 = 7885.

The Venn diagram would look like this:

[ Freshmen ] [ Sophomores, Juniors, Seniors ]

[ 7885 ] __________ [ 4104 ]

| 745 |

__________

[ 7140 ]

So, there are 7885 freshman.

The paint cans and the spaces serve as examples of equivalent ratios. 5.5 cans of paint will be required to cover 2200 sq. unit.

Two ratios that have the same values are said to be equivalent. The same number can be used to multiply or divide both sums to get an equivalent ratio. The method is the same as determining equivalent fractions. When two or more ratios are reduced to their most basic form, they have the same value. Examples of equivalent ratios are 1:2, 2:4, and 4:8. In their most basic form, all three ratios have the same value, which is 1:2. They are in proportion if two ratios are equal. Equations in algebra are said to be equivalent if their solutions or roots are equal. When the same amount or expression is added to or removed from both sides of an equation, the result is the same.

To paint a 2200 square unit space, 5.5 cans are required.

The given parameter is:

Cans: Area\(=1:400\)

Express as fraction

Cans/Area\(=1/400\)

Multiply both sides by Area

Cans\(=\frac{1}{400}*Area\)

When the area is 2200, we have:

Cans\(=\frac{1}{400}*2200\)

Cans\(=5.5\)

5.5 cans are therefore required to paint a 2200 units square space.

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