Find the value of x that makes m ∥ n.

Geometry: CC 2015 > Chapter 3: Proofs with Parallel Lines > Section Exercises 3.3

Answer:

158.2 mm^2

Step-by-step explanation:

You can think of this figure as a rectangle in which a triangle from the bottom was moved to the top.

The area of the figure is the area of the rectangle.

A = LW = 14 mm * 11.3 mm = 158.2 mm^2

Answer:

answer is Afridi.AB=CB

The temperature difference between the optimum temperatures of bacteria X and Y is 25°C.

To find the temperature difference between the optimum temperatures of bacteria X and Y, we subtract the temperature of bacteria Y from the temperature of bacteria X.

Temperature difference = Optimum temperature of bacteria X - Optimum temperature of bacteria Y

Temperature difference = -31°C - (-56°C)

When we subtract a negative number, it is equivalent to adding its positive value. Therefore, -(-56°C) is the same as +56°C.

Temperature difference = -31°C + 56°C

To add these temperatures, we need to consider the sign of the result. In this case, we have a negative temperature (-31°C) and a positive temperature (+56°C). When adding numbers with different signs, we subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.

Absolute value of -31°C = 31°C

Absolute value of +56°C = 56°C

Since 56°C > 31°C, the result will have a positive sign.

Temperature difference = 56°C - 31°C = 25°C

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Answer:

-0.7

Step-by-step explanation:

\(x-y=0.7\)

You can choose any digits you wish for \(x\) and \(y\) but the difference must be 0.7. I chose 1.0 and 0.3.

\(x=1\\y=0.3\\x-y=0.7\\\\y-x=\\0.3-1=\\-0.7\)

To determine the depth of the fish we just need to multiply the total depth by the fraction, then we have:

Therefore, the depth of the fish is 28 ft.

Step-by-step explanation:

Angles q and r are complementary, so the measure of angle r is 90-38=52 degrees.

Since angles s and r are vertical angles, they are congruent, so angle s measures 52 degrees.

I suppose you mean

\(f(x) = \dfrac{x+5}{x+1}\)

Then

\(f(3) = \dfrac{3+5}{3+1} = \dfrac84 = 2\)

and the difference quotient is

\(\dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5}{x+1}-2}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5-2(x+1)}{x+1}}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{-x+3}{(x+1)(x-3)} \\\\ \dfrac{f(x)-f(3)}{x-3} = \boxed{-\dfrac{x-3}{(x+1)(x-3)}}\)

If it's the case that x ≠ 3, then (x - 3)/(x - 3) reduces to 1, and you would be left with

\(\dfrac{f(x)-f(3)}{x-3}\bigg|_{x\neq3} = -\dfrac1{x+1}\)

Answer:

A, B, E

Step-by-step explanation:

Notice that A, B, and E all maintain their common ratios, while C and D do not.

Answer:

The large number is 17

Step-by-step explanation:

x+y=31⟹x=31−y

2x=y+11⟹x=y+11/2

2(y+11/2)=2(31−y)

y+11=62−2y

3y=51

y=17    x=14

Hope this helps, have a nice day! :)

The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.

To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.

First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.

Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.

The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.

(3/10) * 100 = 0.3 * 100 = 30%

Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.

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Answer:

28

Step-by-step explanation:

Substitute x = - 2 into the expression, that is

(- 2)² - 7(- 2) + 10 = 4 + 14 + 10 = 28

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

x=25

Step-by-step explanation:

2x-14=36

2x=50

x=25

The volume of water in the lake in m³ is 49100000 m³

From the question, we have the following parameters that can be used in our computation:

The volume of water in a lake is 0.0491 km³.

This means that

Volume = 0.0491 km³

the volume of water in the lake in m³ is calculated as

Converted volume = Volume * 1000000000

Substitute the known values in the above equation, so, we have the following representation

Converted volume = 1000000000 * 0.0491 km³

Evaluate

Converted volume = 49100000 m³

Hence. the volume of water in the lake in m³ is 49100000 m³

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Answer:

36

Step-by-step explanation:

8 doesn't go into 2, so we move on

8 goes into 28 (3) times

8 times 3 is 24

28-24 equals 4

8 goes into 48 6 times

8 times 6 is 48

48-48=0

36 times

Hope this helps :-)

The result of the number 288 divided by 8 is 36.

Given is a division problem.

We have to find the number 288 divided by 8.

Here,

Dividend = 288

Divisor = 8

Using the divisibility rule, the last 2 digits are divisible by 8 and the first digit 2 is a factor of 8.

So 288 is divisible by 8.

Using long division,

28 = (3 × 8) + 4

Remainder is 4.

First digit of the quotient is 3.

Adding the lat digit from the dividend to the remainder 4, we get 48.

48 = 6 × 8

Next digit of the quotient is 6.

Hence the result is 36.

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We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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x= 9-2

x= 7

14+y=9

y= 14-9

y= 5

The equation of the line will be y = - 2x + 4.

        y = mx + c

      [m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

        [c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

       Other possible equations of lines are -

We have a line that passes through the point (-1, 6) and is parallel to the line 2x + y = 9.

Assume the equation of line to be -

y = mx + c

We can write 2x + y = 9 as -

y = - 2x + 9

Since the line is parallel to 2x + y = 9, we can write -

m = - 2

-For point (-1, 6), we can write -

6 = - 2 x - 1 + c

6 = 2 + c

c = 4

Therefore, the equation of the line will be y = - 2x + 4.

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I would need a bit more to answer that one my friend

Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)

Thus, the minimum exam score to be awarded an A is about 8.52.

Answer:

\( \sqrt{ {13.5}^{2} - {8.6}^{2} } = \sqrt{108.29} = 7 \sqrt{2.21} = \frac{7}{10} \sqrt{221} \)

V = (1/2)(8.6)(.7√221)(22.4) = 1,002.33 square meters

The closest answer is 1,001.73 square meters.

Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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Answer:

3x=-x-60

Step-by-step explanation:

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Answer:

its 2

Step-by-step explanation:

you eat one chip, then you eat one more, you have now eaten two chips

Answer:

y = 1/10x - 5/2

Step-by-step explanation:

I think you mean perpendicular to the line y = -10x + 7, and the point is (5, -2).

The slopes of perpendicular lines are negative reciprocals, so the perpendicular line has slope 1/10.

y = mx + b

y = (1/10)x + b

-2 = (1/10)(5) + b

-2 = 1/2 + b

-5/2 = b

y = 1/10x - 5/2

According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.

To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.

In this case we can conclude that the total yardage traveled was 140 yards because:

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Given

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

To find:

How tall, to the nearest tenth of a meter, is the lighthouse?

Explanation:

It is given that,

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

That implies,

Also,

Therefore,

Then,

Hence, the height of the light house is, 91.5m.

The probability of a point randomly chosen in region A is 3/16

The probability of a point randomly chosen in region A or B is 1/4

The probability of a point randomly chosen in region B is 5/16

The probability of a point randomly chosen in regions A, B, or C is 9/16

The probability of a point randomly chosen in region C is 7

The probabilities are found as follows:

Area of region A = πB² - πA²

Area of region A = π(4² - 2²)

Area of region A = 12π

The total area of the figure is the area of the largest circle with radius 8 inches:

Total area = π(8²)

Total area = 64π

The probability of a point randomly chosen in region A = 12π / 64π

The probability of a point randomly chosen in region A = 3/16

Area of region A or B = π(4²)

Area of region A or B = 16π

The probability of a point randomly chosen in region A or B = 16π / 64π

The probability of a point randomly chosen in region A or B = 1/4

Area of region B = π(6² - 4²)

Area of region B = 20π

The probability of a point randomly chosen in region B = 20π / 64π

The probability of a point randomly chosen in region B = 5/16

Area of region A, B, or C = πC²

The probability of a point randomly chosen in region A, B, or C = πC² / 64π

The probability of a point randomly chosen in region A, B, or C = 9/16

Area of region C = π(8² - 6²)

Area of region C = 28π

The probability of a point randomly chosen in region C = 28π / 64π

The probability of a point randomly chosen in region C = 7

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Answer:

what is force ? write its S.I unit