Two opposite sides of a parallelogram are 3x-8 and 10x+13. Find the measure of all sides

Answer:

31.74 million

Step-by-step explanation:

Answer:

\((2 \sqrt{2} )(2 - \sqrt{3} ) \\ = 4 \sqrt{2} - 2 \sqrt{6} \)

(2 · √2) (-√3 + 2)

2 · √2 (-√3 + 2)

2 · √2 (-√3) + 2 · √2 · 2

-2 · √2 · √3 + 2 · 2 · √2

-2 · √2 · 3 + 4 · √2

-2 · √6 + 4 · √2

Answer:

Step-by-step explanation:

1. -10+18+6=8+6=14

2. -1+84=83

3. -2×(−6)2 +7=12×2+7=24+7=31

4. 50-(−6)2 +(−8)=50+12-8=62-8=54

5. (-2+2)× (−3)3=0× (−3)3=0

6. 30+8-42=38-42=-4

7. -9-2-1=-12

8. -32+6+6=-20

9. -10×3÷5+9=-30÷5+9=-6+9=3

10. -24÷ 8 + 33=-3+33=30

Answer:36.33333333 but rounded it is basically 36

Step-by-step explanation:

what you have to do is 327 divided by 9 then you get your answer then round

The general solution to the given differential equation is sin x + x ln y + C, where C is the constant of integration.

The given equation is (cos x + ln y) dx + (x/y + \(e^y\)) dy = 0.

Taking the partial derivative of the coefficient of dx with respect to y, we get (∂/∂y)(cos x + ln y) = 1/y.

Taking the partial derivative of the coefficient of dy with respect to x, we get (∂/∂x)(x/y + \(e^y\) ) = 1/y.

Since the partial derivatives of the coefficients are equal, the given differential equation is exact.

To solve the exact equation, we need to find a function F(x, y) such that (∂F/∂x) = (cos x + ln y) and (∂F/∂y) = (x/y +  \(e^y\)).

By integrating the first equation with respect to x, we obtain F(x, y) = sin x + x ln y + g(y), where g(y) is an arbitrary function of y.

Next, we differentiate F(x, y) with respect to y and set it equal to the second equation.

(∂F/∂y) = x/y +  \(e^y\) + g'(y).

Comparing this with (∂F/∂y) = (x/y +  \(e^y\)), we find that g'(y) = 0, which implies that g(y) is a constant.

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Answer:

The answer is B.

Step-by-step explanation:

When you reflect (2,5) over the x axis, you get (2,-5).

The length of AL, BK and CH are 12, 9 and 6 respectively.

Similar triangles are those triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

Given a figure of a big triangle.

We can clearly see that angles made by each of the triangles ALE, BKE, CHE and DGE are equal and thus they are similar triangles.

The sides of similar triangles are proportional.

DG / GE = CH / HE = BK / KE = AL / LE

We have DG = 3, GE = 5,HG = 5, KH = 5, LK = 5

HE = 5 + 5 = 10

KE = 5 + 5 + 5 = 15

LE = 5 + 5 + 5 + 5 = 20

Substituting,

Consider DG / GE = CH / HE

3 / 5 = CH / 10

CH = (3/5) × 10 = 6

Consider DG / GE = BK / KE

3 / 5 = BK / 15

BK = (3/5) × 15 = 9

Consider DG / GE = AL / LE

3 / 5 = AL / 20

AL = (3/5) × 20 =  12

Hence the length of AL is 12, length of BK is 9 and length of CH is 6.

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Therefore , the solution of the given problem of speed comes out to be

30.22 minutes taken to cover the distance.

Speed at a distance is a measure of how swiftly something is moving. A moving object's speed determines how far it travels in a given amount of time. Speed is determined by the formula: speed = distance x  time. Meters every second (m/s), kilometers / hour (km/h), and kilometres per second (mph) are the most often used units for measuring speed (mph).

Here,

Similar to part b, but with the knowledge of the cruise distance and the necessity to solve for time, maximum cruising time is achieved.

1) Accelerating: 13.2 seconds, d = 871.2 feet.

2) Deceleration: 13.2 seconds, d = 871.2 feet.

3) When cruising: d = 45 miles - 871.2 feet - 871.2 feet = 237600 feet - 1742.4 feet = 235857.6 feet

t = 235857.6/132 = 1786.8s

Total: 1786.8 + 13.2 + 13.2 = 1813.2 seconds, or 30.22 minutes.

Therefore , the solution of the given problem of speed comes out to be

30.22 minutes taken to cover the distance.

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Answer:

Slope is undefined

Step-by-step explanation:

slope = \(\frac{\Delta y}{\Delta x}\)

\(\frac{5-8}{-7-(-7)}=\frac{-3}{0}\)

Anything divided by zero is undefined

This should make sense visually as the points describe a vertical line at \(x=-7\)

The image of (-4, -2) after a reflection over the line y = -x is (2, -4).

In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.

Generally, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis is given by this rule (x, y) → (-x, y). Thus, line y = -x would become:

(-4, 2) → (2, -4).

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The ratio of the number of circles to the number of triangles in simplest form is 3:4. The number of circles that need to be added to make the ratio 1 : 1 is 3.

First of all, we would have to determine the total number of circles and the number of triangles based on the information provided in the chart (see attachment) as follows;

Total number of circles, C = 9 circles.

Total number of triangles, T = 12 triangles.

Therefore, the ratio of the number of circles to the number of triangles is given by

C:T = 9:12

Dividing both sides of the ratio by 3, we have the following ratio in simplest form:

C:T = 3:4

In order to make the ratio 1:1, the number of circles that need to be added can be calculated as follows;

9 + x:12=1:1

(9 + x)/12 = 1/1

9 + x = 12

x = 12 - 9

x = 3 circles.

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The water level dropped from 15 feet at 8 A.M. to 3 feet at 2 P.M. The time interval between these two points is 6 hours. Therefore, the rate of change of the water level at noon was 2 feet per hour.

By analyzing the given information, we can deduce that the period of the sinusoidal function is 12 hours, representing the time from one high tide to the next. Since the high tide occurred at 8 A.M., the midpoint of the period is at 12 noon. At this point, the water level reaches its average value between the high and low tides.

To find the rate of change at noon, we consider the interval between 8 A.M. and 2 P.M., which is 6 hours. The water level dropped from 15 feet to 3 feet during this interval. Thus, the rate of change is calculated by dividing the change in water level by the time interval:

Rate of change = (Water level at 8 A.M. - Water level at 2 P.M.) / Time interval

Rate of change = (15 - 3) / 6

Rate of change = 12 / 6

Rate of change = 2 feet per hour

Therefore, the water level was dropping at a rate of 2 feet per hour at noon.

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The equation of the table in slope intercept form is y = - 5 / 2x - 1

Linear equation can be represented in various form, such as standard form, point slope form and slope intercept form.

But the equation of the table below will be represented in slope intercept form.

The equation in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, using (-4, 9)(-2, 4)

m = 4 - 9 / -2 + 4

m = - 5 / 2

Hence, let's find the y-intercept using (0, -1)

y = - 5 / 2x + b

-1  = - 5 / 2(0) + b

b = -1

Therefore, the equation is y = - 5 / 2x - 1

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By using the approximation of 62,500 inches to the mile, you can simplify and expedite various calculations involving distances and conversions between inches and miles, providing a convenient tool for numerical analysis and problem-solving

The approximation of 62,500 inches to the mile is commonly used in various calculations, especially in scenarios where conversions between inches and miles are involved. This approximation simplifies the conversion process and allows for easier calculations.

For example, if you need to convert a distance from miles to inches, you can simply multiply the number of miles by 62,500 to obtain the equivalent distance in inches. Conversely, if you have a measurement in inches and want to convert it to miles, you divide the number of inches by 62,500 to get the distance in miles.

Additionally, this approximation can be useful in other applications, such as determining the number of inches in a given number of miles, or calculating the length of a specific distance in miles based on its measurement in inches.

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.

x = 10,  y = 50

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

Explanation:

The 85 degree angle up top and the (3x+55) degree angle at the bottom are one pair of vertical angles.

Vertical angles are always equal in measure.

3x+55 = 85

3x = 85-55

3x = 30

x = 30/3

x = 10

The other pair of vertical angles are the 95 and (2y-5). Vertical angles don't have to align vertically. They simply need to be opposite one another in the X configuration as shown.

2y-5 = 95

2y = 95+5

2y = 100

y = 100/2

y = 50

We can now add up the values of x and y

x+y = 10+50 = 60 which is the final answer.

-------------

Another approach:

The angles 95 and (3x+55) form a straight angle of 180 degrees.

The angles are supplementary so they must add to 180.

95+(3x+55) = 180

3x+150 = 180

3x = 180-150

3x = 30

x = 30/3

x = 10

We arrive at the same x value found earlier.

Use similar logic to add up the other pair of supplementary angles to solve for y.

85 + (2y-5) = 180

2y+80 = 180

2y = 180-80

2y = 100

y = 100/2

y = 50

We arrive at the same y value as earlier.

So we'll arrive at x+y = 10+50 = 60 as the final answer.

Answer:

Width: 6 cm

Length: 9 cm

Step-by-step explanation:

Width: x

Length: x + 3

2(x)+2(x+3) = 30cm

2x + 2x + 6 = 30

4x = 30-6

x = 24/4

x = 6

The function rule c = 40n + 210 establishes a relationship between the number of months (n) and the corresponding cost (c) in dollars.

The given function rule, c = 40n + 210, provides a mathematical formula to calculate the cost (c) in dollars based on the number of months (n). The rule implies that there is a fixed cost of 210 dollars (represented by the constant term) added to a variable cost determined by multiplying the number of months by 40 dollars (represented by the coefficient of n). This indicates that as the number of months increases, the cost will also increase linearly according to the rate of 40 dollars per month. Conversely, when the number of months is zero, the cost will be the initial fixed cost of 210 dollars. By plugging in different values for n, one can determine the corresponding cost (c) at any given month and analyze the relationship between the two variables.

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Answer:

\( \huge{ \boxed{ \sf{ \sqrt{18} \: units}}}\)

Step-by-step explanation:

\( \star{ \sf{ \:Sea \: M (2, 2) \: (x1, y 1) \: y \: N (5, -1) \: sea \: (x2, y2).}}\)

\( \star{ \sf{ \: Usando \: la \: fórmula \: de \: la \: distancia}} : \)

\( \boxed{ \sf{distancia = \: \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}\)

\( \mapsto{ \sf{distancia \: = \: \sqrt{ {(5 - 2)}^{2} + {( - 1 - 2)}^{2} } }}\)

\( \mapsto{ \sf{distancia = \sqrt{ {(3)}^{2} + {( - 3)}^{2} } }}\)

\( \mapsto{ \sf{distancia \: = \sqrt{9 + 9}}} \)

\( \mapsto{ \sf{distancia = \sqrt{18} \: units}}\)

\( \sf{¡Espero \: haber \: ayudado!}

\)

\( \sf{¡Atentamente!}\)

~\( \text{TheAnimeGirl}\)

Answer:

the two-digit number is 65.

Step-by-step explanation:

Let's assume that the tens and units digits of the two-digit number are x and y, respectively.

According to the given condition,

10x + y < 6(x + y) - 1 (less than 6 times the sum of its digits by 1)

Simplifying the above equation, we get:

4x - 5y < -1 (dividing both sides by 2)

Also, it is given that the difference between the digits is 1, so we can write:

x - y = 1 (difference between the digits is 1)

Now, we need to solve these two equations to find the values of x and y.

Multiplying the second equation by 4, we get:

4x - 4y = 4

Adding this equation to the first equation, we get:

4x - 5y + 4x - 4y = 3

Simplifying the above equation, we get:

8x - 9y = 3

Now, we can solve these two equations simultaneously to find the values of x and y.

Multiplying the second equation by 8, we get:

8x - 8y = 8

Subtracting this equation from the previous equation, we get:

y = 5

Substituting this value of y in the equation x - y = 1, we get:

x - 5 = 1

x = 6

Therefore, the two-digit number is 65.

In the "ones" place,

4₅ + 3₅ = (7)₅ = (5 + 2)₅ = 10₅ + 2₅ = 12₅

(a number in base 5 can only consist of the digits 0-4; anything larger, which I wrap in parentheses, needs to be split up further)

In the "tens" place, we carry over the 1 from the previous sum:

2₅ + 4₅ + 1₅ = (7)₅ = 12₅

In the "hundreds" place,

4₅ + 2₅ + 1₅ = (7)₅ = 12₅

In the "thousands" place,

1₅ + 2₅ + 1₅ = 4₅

So, we have

1424₅ + 2243₅ = 4222₅

(a) The sample mean can be used as an estimate of λ: 0.95.

(b) The expected number of observations in each class are

Class 0: 18.2

Class 1: 86.5

Class 2: 163.8

Class 3 or more:  31.5

(c) The distribution of X is not Poisson because we reject the null hypothesis that X has a Poisson distribution with parameter λ = 0.95.

(a) The sample mean can be used as an estimate of λ:

i = (110×0 + 61×1 + 17×2 + 9×3 + 3×4) / 200 = 0.95

(b) We can use the Poisson distribution to estimate the expected number of observations in each class. Let z = i = 0.95 be the estimated value of λ. Then the classes can be set up as follows:

Class 0: X = 0

Class 1: X = 1

Class 2: X = 2

Class 3 or more: X ≥ 3

Using the Poisson distribution, we can calculate the expected number of observations in each class:

Class 0: P(X=0; λ=z) × n = e^(-z) × z^0 / 0! × 200 = 18.2

Class 1: P(X=1; λ=z) × n = e^(-z) × z^1 / 1! × 200 = 86.5

Class 2: P(X=2; λ=z) × n = e^(-z) × z^2 / 2! × 200 = 163.8

Class 3 or more: P(X≥3; λ=z) × n = 1 - P(X=0; λ=z) - P(X=1; λ=z) - P(X=2; λ=z) = 31.5

(c) To test the hypothesis that X has a Poisson distribution with parameter λ = 0.95, we can use the chi-squared goodness-of-fit test. The test statistic is given by:

χ^2 = Σ (Oi - Ei)^2 / Ei

where Oi is the observed frequency in the i-th class and Ei is the expected frequency in the i-th class. Using the classes from (b), we can calculate the test statistic:

χ^2 = [(110-18.2)^2 / 18.2] + [(61-86.5)^2 / 86.5] + [(17-163.8)^2 / 163.8] + [(9-31.5)^2 / 31.5] = 137.52

The critical value of chi-squared for 3 degrees of freedom and a significance level of 0.01 is 11.345. Since the calculated test statistic (137.52) is greater than the critical value (11.345), we reject the null hypothesis that X has a Poisson distribution with parameter λ = 0.95. Therefore, there is evidence that the distribution of X is not Poisson.

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The mean number of billionaires per state in these five Midwest states is approximately 10.2 (to the nearest tenth).

To find the mean number of billionaires per state in the given five states, we need to calculate the average by summing up the number of billionaires in each state and dividing it by the total number of states.

Given:

Illinois: 20 billionaires

Wisconsin: 10 billionaires

Michigan: 10 billionaires

Minnesota: 6 billionaires

Ohio: 5 billionaires

To find the mean number of billionaires, we sum up the number of billionaires in each state:

20 + 10 + 10 + 6 + 5 = 51

Next, we divide the total number of billionaires by the total number of states (which is 5):

51 / 5 = 10.2

Therefore, the mean number of billionaires per state in these five Midwest states is approximately 10.2 (to the nearest tenth).

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Answer:

They sold

20 Roses and 20 Carnations

Step-by-step explanation:

The total sales of 40 flowers is $100 not $10 as in the question

Roses=$3

Carnations=$2

Total flowers sold=40

Total sales=$10

Let Roses=r

Carnations=c

c+r=40. (1)

3r+2c=100 (2)

From (1)

c=40-r

Substitute c=40-r into (2)

3r+2c=100

3r+2(40-r)=100

3r+80-2r=10

r=100-80

r=20

Substitute r=20 into (1)

c+r=40

c+20=40

c=40-20

=20

c=20

r=20

Check:

3r+2c=100

3(20)+2(20)=100

60+40=100

100=100

Given that :

To find :

Solution :

•Let us take the units digit be x

•Then the tens digit will be 2x [As it is given that the tens digit is two times the units digit]

A/Q

↪2x + x = 66

↪3x = 66

↪x = 66/3

↪x = 22

Therefore,the units digit is 22

And the tens digit is 2x = 2 × 22 = 44

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Answer: 840 cm^3

Step-by-step explanation: I hope it helps you!

Residuals are leftover scores, also known as errors or residuals of prediction, in statistics.

They are the differences between the observed and expected dependent variable scores.

In other words, they are the differences between the actual values of the dependent variable and the predicted values based on a statistical model. Residuals are useful in assessing the accuracy of a statistical model and in identifying any patterns or trends in the data that may need to be addressed.

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Answer:

The answer is A

Step-by-step explanation:

The equation that should be used for determining the distance is |4.5| - | - 10.3| = -14.8.

Given that,

Based on the above information, the equation that should be used is  |4.5| - | - 10.3| = -14.8.

Therefore we can conclude that the equation that should be used for determining the distance is |4.5| - | - 10.3| = -14.8.

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Answer: 14

Step-by-step explanation:

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.