8. Fill in the missing statements and reasons to complete the following proof

Answer: First find your given information:

D=6 miles (3 miles there + 3 miles back)

T=1 hour

Vwind= 3 mph

We're going to assume that the wind's velocity is always in opposite direction to Mr. Lee so:

VFinal = VMr. Lee - Vwind

We also know that VFinal=D/T

So D/T = VMr. Lee - Vwind

Rearrange to get VMr. Lee = D/T + Vwind

Plug in your given info to get VMr. Lee = (6 miles)/(1 hours) + 4 mph or 10 mph

Tno wind= D/VMr. Lee or (6 miles/10 mph)

Tno wind=0.6 hours

Step-by-step explanation:

Answer:

Step-by-step explanation:

3 3/4 + 11 1/4 = 15

1/3 of 11 1/4 is 3.75 or 3 3/4. I added 3 3/4 to 11 1/4, and checked my answer, which was 15, by dividing it by four.

I know its confusing sorry, I hope you understand ^^

The cubic equation is given by A = x³ - 7x² + 14x - 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The coordinates of the points are A ( 1 , 0 ) , B ( 2 , 0 ) , C ( 0 , -8 ) , D ( 4 , 0 )

Now , the equation will be

f ( x ) = a ( x - 1 ) ( x - 2 ) ( x - 4 )

So , when x = 0 , the value of y = -8

-8 = a ( -1 ) ( -2 ) ( -4 )

-8 = a ( -8 )

8a = 8

Divide by 8 on both sides of the equation , we get

a = 1

Substitute the value of a in the equation , we get

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

f ( x ) = x³ - 7x² + 14x - 8

Hence , the equation is f ( x ) = x³ - 7x² + 14x - 8

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The required amount of sauce in each bottle is given by fraction 5/7. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Sum the total amount of sauce in the 7 bottles present at each booth,
Total sauce = 0 × 2 + 1/2×1 + 1×3 + 1 1/2 × 1
                 = 1/2 + 3 + 3/2
                 = 2 + 3 = 5

Now, the ratio of the total sauce to the total number of bottles will give the amount of sauce in each bottle.

So,
= 5/7

Thus, the required amount of sauce in each bottle is given by fraction 5/7.

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Answer:

Step-by-step explanation

It seems like you are to use trig functions to find the missing sides.

soh - cah - toa

Sin(what degree angle you have) = opposite of the angle over the hypotenuse

cosine (what degree angle you have) = adjacent (side that is next to angle that isn't hypotenuse) over hypotenuse

tangent (what degree angle you have) = opposite side from angle over adjacent side to angle

for number 1:

sine59 = d/ 37

cross multiply

sin59 multiplied by 37 which equals 31.7

so this means d is 31.7

use the trig functions to find the rest. it is just a pattern and SOH-CAH-TOA will help.

lmk if you have questions

Eulerian path can be implemented in linear time because it follows a specific rule: a connected graph can have an Eulerian path if and only if it has either zero or two vertices of odd degree.

This means that the algorithm can quickly determine whether or not a graph has an Eulerian path by simply counting the number of odd degree vertices. This can be done in linear time, making the implementation of Eulerian path efficient and fast.

On the other hand, Hamiltonian path does not follow a specific rule, and there is no known efficient algorithm to determine whether or not a graph has a Hamiltonian path.

This means that the implementation of Hamiltonian path requires checking all possible paths in the graph, which can take a long time and is not efficient. Therefore, Hamiltonian path cannot be implemented in linear time like Eulerian path can.

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The difference between AIC and BIC penalty lies in their approach to model selection.

AIC (Akaike Information Criterion) is a measure of the goodness of fit of a statistical model. It is used to compare different models and select the one that fits the data best. AIC is based on the principle of maximum likelihood, which means it is more focused on finding the model that fits the data best.

On the other hand, BIC (Bayesian Information Criterion) is a criterion for model selection based on the Bayesian approach. It is also used to compare different models, but it takes into account the complexity of the model. BIC tends to favor simpler models, and it is more focused on finding the model that is most likely to be true given the data.

In summary, AIC is more focused on finding the model that fits the data best, while BIC is more focused on finding the model that is most likely to be true given the data.

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A quarter pound hamburger is counted as one servings which is four ounces.

A pound is usually a unit which is used to measure the weight of a body.  It is known as one pound is approximately equal to 454 grams. One kilogram is roughly the same as equal to 2.2 lbs. There are 16 ounces in one pound which is mentioned.

This question can be solved due to the rule of proportions.

A pound is an imperial unit of mass or weight measure, it is abbreviated as lb, lbm and one pound is considered to be equal to 0.4535 kilograms.

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Answer:

[tex]\huge\boxed{\sf c = 3.1\ yards}[/tex]

Step-by-step explanation:

a = 2.7 yards

b = 1.6 yards

c = hypotenuse

Using Pythagoran Theorem:

[tex]c^2=a^2+b^2[/tex]

c² = (2.7)² + (1.6)²

c² = 7.29 + 2.56

c² = 9.85

c = √9.85

[tex]\rule[225]{225}{2}[/tex]

Based on the information provided, it's not possible to say who is winning without knowing the specific game and how points are scored and awarded.

The statement "has -6 points give or take 4 points" doesn't provide a specific range of points that your friend could have, so we can't use this information to determine a winner.

Additionally, using a number line to compare two points of -3 and -6 is not helpful in determining who is winning in the game because it only shows their relative values, not the actual rules of the game and how points are scored.

It would be best to ask the friend to clarify their score and the rules of the game to determine who is winning.

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Each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.

The angles m∠MON and m∠LOM form one of the interior angles of a rectangle, hence they are complementary as they add up to 90°.

we shall solve for x as follows:

2x + 7x + 9 = 90

9x + 9 = 90

9x = 90 - 9 {subtract 9 from both sides}

9x = 81

x = 81/9 {divide through by 9}

x = 9

m∠MON = 7(9) + 9 = 72°

m∠LOM = 2(9) = 18°

The angles m∠LOM and m∠POQ are vertical angles formed by the two straight lines MA and LP, hence;

m∠LOM = m∠POQ = 18°

In conclusion, each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.

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Based on the ratio of the​ office's area to the area of the home, the deductible amount is $760.

The ratio refers to the relative quantity of one value contained in another.

Generally, ratios are depicted as fractions, decimals, or percentages.

Total home area = 2400 ft²

Office area =380 ft² (20 x 19)

The ratio of office to home area = 380/2400

The percentage of office use of the home-related expense = 15.83% (380/2400 x 100)

The Electricity bill for the year = $4,800

The deductible amount for office use = $760 ($4,800 x 380/2400) or ($4,800 x 15.83%)

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Answer:

74.2

Step-by-step explanation:

Median is another word for average amount.

So if you add the numbers 56, 65, 77, 81, and 92 you would end up with 371.

To get an average, or the median, you take the numbers, add them together, then divide the answer by how ever many numbers you had.

In this case, you had 5, so

56+65+77+81+92=371

then divide by 5 so

371/5=74.2

Answer:

2(-3x+2)^2 -1

Step-by-step explanation:

so first you would find that f(g(x)) = f(-3x+2)

next plug in

f(-3x+2) = 2x^2-1

to every x

f(-3x+2) = 2(-3x+2)^2-1

Answer:

2

Step-by-step explanation:

sqrt 16/4 is 4/2

4/2 is 2

The end behavior of this the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity.

The end behavior of a polynomial can be determined by looking at the degree (highest exponent) and the leading coefficient (coefficient of the highest degree term). If the degree is even and the leading coefficient is positive, the end behavior of the polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. Similarly, if the degree is even and the leading coefficient is negative, the end behavior of the polynomial is negative, meaning that as x approaches positive and negative infinity, the y values approach negative infinity. If the degree is odd and the leading coefficient is positive, the end behavior of the polynomial is positive, and if the degree is odd and the leading coefficient is negative, the end behavior of the polynomial is negative.For example, consider a polynomial of degree 5, f(x) = 3x5 + 2x4 - 3x2 + 4. The leading coefficient is 3, which is positive, and the degree is 5, which is odd. Therefore, the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. This can be verified by using the formula: End Behavior = Leading Coefficient x ∞limitx→±∞ End Behavior = 3 x ∞limitx→±∞  End Behavior = +∞.

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The  Bernoulli equation of given differential equation Xdydx + y = 1y² is ln (1 - x/y - x) = c

Any equation with one or more derivates and one or more terms of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)

-1/y = u

y¹/y² = u¹

xy¹ - (1 + x)y = xy²

now take the y² on other side,

xy¹/y² - (1 + x)/y = c

now replace the values by u¹,

xu¹ + (1 + x)u = x

xu¹ + u + ux = x

xu = s      ....[1]

Substitute the value of xu as s

u + xu¹ = s¹

s¹ + s = v

s - x  = t

s¹ - 1 = t¹

t¹ + 1 + t = 0

Now take the integration of both the sides,

dt/dx = - ( 1 + t)

-∫ dt/1+t =  ∫dx

-ln ( 1+ t ) = x + c

now ,put the value of t,

-in ( 1 + s - x ) = x + c

now put the value of s,

-ln ( 1 + xu - x ) = x + c

-ln ( 1 - x/y - x) = c.

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Answer:

Step-by-step explanation:

The rate of deflation of the hot-air balloon is 0.25 feet per minute. Let's represent the diameter of the balloon at any time t in minutes as D(t).

We know that D(0) = 14 feet (initial diameter) and we want to find x when D(x) = 8 feet.

Using the fact that the rate of change of D with respect to time is -0.25 (negative because the diameter is decreasing), we can set up a differential equation:

dD/dt = -0.25

Separating variables and integrating, we get:

∫(1/D) dD = ∫(-0.25) dt

ln|D| = -0.25t + C

where C is the constant of integration.

Using the initial condition D(0) = 14, we get:

ln|14| = C

C = ln(14)

Substituting this value of C into the equation, we get:

ln|D| = -0.25t + ln(14)

Taking the exponential of both sides, we get:

|D| = e^(-0.25t + ln(14)) = e^ln(14) e^(-0.25t) = 14 e^(-0.25t)

Since we are only interested in the positive value of D, we can drop the absolute value sign:

D = 14 e^(-0.25t)

Now we can solve for x by setting D = 8:

8 = 14 e^(-0.25x)

Dividing both sides by 14, we get:

e^(-0.25x) = 8/14 = 4/7

Taking the natural logarithm of both sides, we get:

ln(e^(-0.25x)) = ln(4/7)

-0.25x = ln(4/7)

x = -4 ln(4/7) / 0.25

x ≈ 6.21

Therefore, it will take about 6.21 minutes for the balloon to shrink to a diameter of 8 feet.

The triangle with side lengths of  48 in., 56 in., and 83 in.  is obtuse, because 832> 48² +56²

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

The side lengths of the triangles are 48 in., 56 in., and 83 in

The smallest side lengths are: 48 in., 56 in

The sum of the squares of these side lengths is

48^2+ 56^2

For the triangle to be obtuse, then the following must be true

83^2> 48² +56²

Evaluate the exponents

6889> 5440

The above inequality is true.

Hence, the triangle is obtuse, because 83^2> 48² +56²

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(C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.

In number theory, the breakdown of a composite number into a sum of smaller integers is known as integer factorization.

The procedure is known as prime factorization if these factors are further limited to prime numbers.

The technique of expressing all numbers as the product of primes is known as prime factorization.

So, let's take something like the number 20 as an example.

It can be divided into two components.

"Well, that's 4 times 5," we can respond.

Observe that 5 is a prime number. The number 4 is not a prime.

So, it is necessary to write 48 as the product of its prime elements:

2 * 3 * 2 * 2 * 2

Then,

√48 = √(2 * 2 * 2 * 2 * 2)

Lower radical form: √48

Hence, (C) could be the correct option.

Therefore, (C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.

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Correct question:

Which calculation correctly uses prime factorization to write V48 in simplest form?

A. 48 = V2 -2 -2 -2 - 3 = 2V12

B. 48 = 14 - 12 = 2/12

C. 48 = V2 -2 -2 -2 - 3 = 4V3

D. V48 = 16 - 3 = 4V3​

Answer:

please give the complete question..

Step-by-step explanation:

please give the complete question..

The solution to the system of equations is given as follows:

x = 2.31, y = 0.93.

The system of equations for this problem is defined as follows:

To solve by elimination, we first multiply the first equation by 4, and then add the first equation with the second, hence:

Hence the solution for x is given as follows:

13x = 30

x = 30/13

x = 2.31.

Then the solution for y is of:

y = 3x - 6

y = 3(2.31) - 6

y = 0.93.

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To solve the exponential equation 23^x = 6, take the logarithm base 23 of both sides to get x = log base 23 of 6.

Angie, to solve the exponential equation 23^x = 6, you need to find the value of x such that when you raise 23 to the power of x, you get 6. To do this, you can use logarithms.

In particular, you can use the logarithmic function log_23. The log_23 of a number y is the exponent x such that 23^x = y. So, to solve the equation 23^x = 6, you can take the log_23 of both sides:

log_23(23^x) = log_23(6)

x = log_23(6)

The right side of this equation can be evaluated using a calculator or logarithmic tables. Once you have the value of x, you will have solved the exponential equation.

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The number of centimeters in 9 meters is 900.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Given that, the measure is 9 meters.

We know that, 1 meter = 100 centimeters

Now, 9 meters

= 9×100

= 900 centimeters

Therefore, the number of centimeters in 9 meters is 900.

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The solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54

by elimination are respectively:

x = -4, y = -4

x = 3, y = -1

x = 5, y = 1

x = -6, y = 4

we shall write the equations as:

7x - 4y = -12...(1)

x - 2y = 4...(2)

multiply equation (2) by 7 to get equation (3)

7x - 14y = 28...(3)

subtract equation (1) from (3) to eliminate x

7x - 14y - 7x + 4y = 28 + 12

-10y = 40

divide through by -10

y = -4

put the value -4 for y in equation (2) to get y

x - 2(-4) = 4

x + 8= 4

x = -4

x - y = 4...(1)

2x + y = 5...(2)

Add equations (1) and (2) to eliminate y

2x + y + x - y = 5 + 4

3x = 9

divide through by 3

x = 3

put the value 3 for x in equation (1) to get y

3 - y = 4

y = -1

4x - 3y = 17...(1)

2x - 5y = 5...(2)

multiply equation (2) by 2 to get equation (3)

4x - 10y = 10...(3)

subtract equation (3) from (1) to eliminate x

4x - 3y - 4x - 10y = 17 - 10

7y = 7

divide through by 7

y = 1

put the value 1 for y in equation (2) to get y

2x - 5(1) = 5

2x - 5 = 5

x = 5

5x + 6y = -6...(1)

7x - 3y = -54...(2)

multiply equation (1) by 7 to get equation (3) and equation (2) by 5 to get equation (4)

35x + 42y = -42...(3)

35x - 15y = -270...(4)

subtract equation (4) from (3) to eliminate x

35x + 42y - 35x + 15y = -42 + 270

57y = 228

divide through by 57

y = 4

put the value for y in equation (1) to get x

5x - 6(4) = -6

5x + 24 = -6

x = -6

Therefore, the solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54

by elimination are:

x = -4, y = -4

x = 3, y = -1

x = 5, y = 1

x = -6, y = 4

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The area of given trapezoid is 92 square yards.

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (a+b)×h.

where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).

Given that, a right-angled trapezoid with length of two parallel sides measuring 10 yards and 13 yards.

The height of the trapezoid is 8 yards.

Here, area = 1/2 (10+13)×8

= 23×4

= 92

Therefore, the area is 92 square yards.

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Answer:

Quadrant I is located on the top right of the graph (Positive x, Positive y)

Quadrant II is located on the top left of the graph (Negative x , Positive y)

Quadrant III is located on the bottom left of the graph (Negative x, Negative y)

Quadrant IIII is located on the bottom right of the graph (Positive x, Negative y)

The origin is at the center of the graph with (0,0) as its x and y components

Step-by-step explanation: ^^ Please give 5 star and thanks.

One gallon is a unit of volume that is equivalent to 3.785 liters. This means that one gallon is equal to 3.785 liters.

The gallon is an imperial unit of measurement, which means that it is not used in most countries outside of the United States and the United Kingdom. In the US customary system, the gallon is divided into four quarts, each of which is equal to two pints. One US gallon is equivalent to approximately 0.83 imperial gallons, which are used in the UK.The gallon originated in medieval England as a measure for ale and other alcoholic beverages. It was adopted by the Romans during their invasion of Britain, and the term "gallon" is derived from the Latin term "galleta," which means "a pailful." The gallon was standardized in the 18th century by the British Imperial System.In the United States, the gallon is used in both the customary and imperial systems. In the customary system, the gallon is equal to 128 fluid ounces, while in the imperial system, it is equal to 160 fluid ounces. The US liquid gallon is divided into four quarts, which is equivalent to eight pints. One US dry gallon is equal to 4.4 liters.

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