Three personal watercraft vehicles launch from the same dock. The first vehicle leaves the dock traveling due northeast, while the second vehicle travels due northwest. Meanwhile, the third vehicle leaves the dock traveling due north.
The first and second vehicles stop about 300 yards from the dock, while the third stops about 212 yards from the dock.
(d) Write a coordinate proof to prove that the positions of all three watercrafts are approximately collinear and that the third watercraft is at the midpoint between the other two.

Answer:  [tex]A^{2} + B^{2}[/tex] correct answer.

Step-by-step explanation:

What is Pythagorean Theorem?

Image result for Pythagorean theorem

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation.

                               [tex]A^{2} + B^{2} + C^{2}[/tex]

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.

So, We can write,

Consider the triangle given above:

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

                    [tex]Hypotenuse^{2}[/tex] = [tex]Perpendicular^{2}[/tex] + [tex]Base^{2}[/tex]

                           [tex]C^{2} = A^{2} + B^{2}[/tex]

Hence,

                              [tex]A^{2} + B^{2}[/tex] correct answer.

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The domain of f is [-5, ∞) because the vertex is the global minimum of a parabola that opens up.

The domain of any polynomial, including quadratics, is (–∞, ∞).

The domain of a parabola is always all real numbers (sometimes written (−∞,∞). The domain is all real numbers because every single number on the x− axis results in a valid output for the function (a quadratic).

When x=−b2a, y=c−b24a. Therefore the maximum or minimum value of the quadratic is c−b24a. Whether it is the maximum or minimum can be determined by examining the sign of a. If a is positive, then the range is y≥c−b24a

Hence, The range here is [-5, ∞), because the vertex is the global minimum of a parabola that opens up, and the global minimum is the lowest value.

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Answer:

[tex] 81g^4 [/tex]

Step-by-step explanation:

When you raise a product to a power, raise each factor of the product to the power.

Rule:

[tex] (ab)^n = a^nb^n [/tex]

Our problem:

[tex] (3g)^4 = 3^4g^4 = 81g^4 [/tex]

The new mean of a distribution of tests would be 175 and the new standard deviation of a distribution of tests would be 10 which is unchanged.

We have been given that in the question:

Mean of data = 80

Standard deviation = 10.

Then,  every score is doubled and 15 is added to each score.

The mean of a distribution is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

a) Mean of new data

The mean of the data rises by the same amount when a constant value is applied to each observation.

Mean of new score =

μ' = 2μ + 15 = 2(80) + 15 = 175

b) Standard deviation of new data

Every observation has a constant value added to it, therefore the standard deviation stays constant.

The standard deviation of the new score =

σ' = σ = 10

Therefore, the new mean and standard deviation would be 175 and 10 respectively.

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Answer:

7/8 if you divide you will get your answer

The restrictions on the variables x and y of the equation

(3y-12)/(2y+4) ÷ (6y-24)/(8+4y) be y ≠ 4 and y ≠ -2

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)

Let the equation be (3y-12)/(2y+4) ÷ (6y-24)/(8+4y)

simplifying the equation, we get

(3y-12)/(2y+4) × (8+4y)/(6y-24)

⇒ (3y-12)/(2y+4) × 2(4+2y)/2(3y-12)

⇒ 2/2 = 1

If y = 4 ⇒ denominator (6 × 4 - 24) = 0 = ∞

Similarly, If y = -2 ⇒ denominator ((2 × -2) + 4) =0 = ∞

So, y ≠ 4, y ≠ -2

How to find restrictions on the variables?

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C. y = 1/3 x - 9

The slope-intercept form is one way to represent a linear function that is set equal to y.

Simplifying and Solving

To find slope-intercept form from point-slope you should simplify the equation and then solve for y.

Firstly, distribute the 1/3.

Then, subtract the 6 from both sides.

This means that the slope-intercept form is y = 1/3 x - 9.

What Slope-Intercept Form Shows

We use slope-intercept form for 2 main reasons; it shows the slope and the y-intercept of a line (hence the name). The formula of slope-intercept is y = mx + b. In this formula, m is the slope and b is the y-intercept.

So, the slope of the line above is 1/3. The y-intercept of the line is -9.

Answer:

the answer is 225

Step-by-step explanation:

[tex] \frac{300 \times 25}{100} = 75[/tex]

this is the amount of discount

so remove it from the original price

300 - 75 = 225

which is the price after the 25% discount

hope this helps

The given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference

What is an arithmetic sequence?

An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.

here the given sequence is 0,1,3,6,10,......is an arithmetic sequence

then the common difference between the consecutive terms is constant

lets check take two consecutive terms as 0 and 1 then the difference is 1

take 1 and 3 then common difference is 3-1 =2

take 3 and 6 then common difference is 6-3 =3

take 6 and 10 then common difference is 10-6=4

.............in the same way we check for other terms also

and found that the common difference is not same

Hence the given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference

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Answer:

The conditional statement is true.

Step-by-step explanation:

If a and b are negative, it doesn't matter what numbers they are; the sum will always be negative.

According to the question, the region is bounded by the curve with the given data as [tex]x = y^{3} , x=1, y=0.[/tex]

To compute the volume of the solid, use the disk method. The given object is rotated along the horizontal axis with the disk cross sectional area and the volume can be written as:

[tex]v=\int\limits^a_b {\pi x^{2} } \, dx[/tex]

As per question, when x = 1 then the value of y is: y = 1

Now, substituting calculated values in the expression:

[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx[/tex]

Substitute the value of the variable 'x':

Therefore, the expression can be written as:

[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx=\int\limits^0_1 {\pi (y^{3}) ^{2} } \, dx=\frac{\pi }{7}=0.448[/tex]

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The probability that the marble that you drew was either blue or green is 0.7.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

There are 4 blue ,3 green , 1 yellow and 2 red

In total there are 10 balls.

probability of getting blue or green ball is = 7/10

P (blue or green) = 0.7

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Answer:

b(x) = 4x + 1

Step-by-step explanation:

If x starts from 1, we can give the equation as follows:

b(x) = 4x + 1

Let's check it, for the first one

x = 1, b(x) = 5

for the second, x = 2, b(x) = 4(2)+1 =9

The answer to your question would be, 171.5

Solution:

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.

As you stated the formula of a rectangle is P (perimeter) = 2W (the two widths added together) + 2L (the two lengths added together).

To solve this algebraically you need to define your variable, or unknown, which in this case is the width or "W".

Now set this same equation with any symbol you wish, "x" is often used, and solve for x.  You could keep W instead of X also if it makes it easier to work on the problem.

P= 2x + 2L

isolate the 2x by subtracting 2L from both sides.

P-2L=2x

Now isolate the x by dividing both sides by 2 and you have

P-2L/2=x

x will be W.  Just put in the numbers P and L and you will have solved for W.

One More Solution :

The perimeter of a rectangle is given by the following formula:    

P = 2W + 2L

To solve this formula for W, the goal is to isolate this variable to one side of the equation such that the width of the rectangle (W) can be solved when given its perimeter (P) and length (L).

P = 2W + 2L

subtract 2L from both sides of the equation

P - 2L = 2W + 2L - 2L

P - 2L = 2W

divide both sides of the equation by 2

(P - 2L)/2 = (2W)/2

(P - 2L)/2 = (2/2)W

(P - 2L)/2 = (1)W

(P - 2L)/2 = W

Thus, given that the perimeter (P) of a rectangle is defined by    P = 2W + 2L ,

then its width (W) is given by    W = (P - 2L)/2

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Using basic mathematical operations such as addition and subtraction, the beaker now has 5.2 ml of liquid.

Basic mathematical operations include addition, subtraction, multiplication, and division.

Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.

If a scientist measures 4.62 ml of a chemical into a beaker, then takes out 0.67 ml of the chemical, and finally adds 1.25 ml of water into the beaker, subtracting the amount of chemical taken out from the initial amount of chemical and adding the amount of water, we can solve how much liquid is in the beaker.

4.62 ml - 0.67 ml + 1.25 ml = 5.2 ml

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Answer:

2

Step-by-step explanation:

Given equations:

[tex]\begin{cases}ab=a-b\\\\\dfrac{a}{b}+\dfrac{b}{a}-ab\end{cases}[/tex]

Rewrite the second equation as a rational expression:

[tex]\begin{aligned}\implies \dfrac{a}{b}+\dfrac{b}{a}-ab & = \dfrac{a}{b} \cdot \dfrac{a}{a}+\dfrac{b}{a} \cdot \dfrac{b}{b}-ab\cdot \dfrac{ab}{ab} \\\\&=\dfrac{a^2}{ab}+\dfrac{b^2}{ab}-\dfrac{(ab)^2}{ab}\\\\&=\dfrac{a^2+b^2-(ab)^2}{ab}\\\\\end{aligned}[/tex]

Substitute the first equation  [tex]ab=a-b[/tex]  into the rational expression:

[tex]\begin{aligned}\implies \dfrac{a^2+b^2-(a-b)^2}{ab}&=\dfrac{a^2+b^2-(a^2-2ab+b^2)}{ab}\\\\&=\dfrac{a^2+b^2-a^2+2ab-b^2}{ab}\\\\&=\dfrac{2ab}{ab}\\\\&=2\end{aligned}[/tex]

Therefore, the possible value of the given expression is 2.

Answer:

Coefficient(s):9

Variable(s):x,y

Constant(s):-22

Step-by-step explanation:

its stem and leaf just took the test

Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.

In order to help visualize the shape of a distribution, a stem-and-leaf presentation or stem-and-leaf plot is a tool for displaying quantitative data in a graphical manner, comparable to a histogram. They are helpful tools for exploratory data analysis and developed from Arthur Bowley's work in the early 1900s.

This is simply accomplished by creating a draft of the unsorted leaves before arranging them in the final stem-leaf display. On the Undergraduate and graduate levels, you may find a number of examples that have been solved and even obtain expert assistance to learn the subject of stem and leaf plots.

A school is studying Math for Data and Financial Literacy standardized test scores.

Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.

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The average speed in miles per hour for the round trip is (D) 47.5.

To find the average speed:

Formula: Sum of terms/Number of terms

Therefore, the average speed in miles per hour for the round trip is (D) 47.5.

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Answer:

(2A)/(r^2)=pi

Step-by-step explanation:

The goal is to get pi by itself, so you have to move all the other elements over

2A=pir^2

(2A)/(r^2)=pi

By elimination, the solution of the system of equations, 20x + 5y = 120 and 10x + 7.5y = 80, is (5 , 4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Multiply first equation 2 by 2.

10x + 7.5y = 80     (equation 2)

20x + 15y = 160

Subtracting the two equations will eliminate the variable x.

20x + 15y = 160     (equation 2)

20x +  5y = 120     (equation 1)

0x + 10y = 40

y = 4

Substitute the value of y to any of the two equations and solve for x.

20x + 5y = 120     (equation 1)

20x + 5(4) = 120

20x = 120 - 20

20x = 100

x = 5

Hence, the solution of the system of equations is (5 , 4).

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Answer:

Solution

verified

Verified by Toppr

Correct option is C)

Perimeter of window P=2y+3x=16    

⇒y=

2

16−3x

​

  ....(1)

Area A=xy+

4

3

​

​

x

2

=

4

3

​

​

x

2

+x(

2

16−3x

​

)

A=8x+(

4

3

​

​

−

2

3

​

)x

2

dx

dA

​

=8+(

4

3

​

​

−

2

3

​

)2x

For maxima or minima,

dx

dA

​

=0

⇒4−

4

(6−

3

​

)

​

x=0.

∴x=

6−

(3)

​

16

​

=

36−3

16(6+

3

​

)

​

=

33

16(6+1.73)

​

=

33

16(7.73)

​

=

33

123.68

​

⇒x=3.75 nearly.

Now,  

dx

2

d

2

A

​

=2(

4

3

​

​

−

2

3

​

)<0

Hence A is maximum.

By (1),

y=2.375

Step-by-step explanation:

Answer:

36÷7.2=5

So this is the answer

Answer:

Step-by-step explanation:

[tex]−6(x−2)+50\\\\-6x+12+5\\\\\sf{-6x+17}[/tex]

we are done!! ~~

Answer:

-6x + 17

Step-by-step explanation:

We can use algebraic expansion and order of operations to solve for this expression.

[tex] - 6(x - 2) + 5 \\ = - 6x + 12 + 5 \\ = - 6x + 17[/tex]

The given sequence is geometric, with common ratio = -1.

Now, Given: -1, 1, -1, 1, ...

Here, a₁ = -1, r = [tex]\frac{1}{-1}=\frac{-1}{1} = \frac{1}{-1} = -1[/tex]

Hence, it is a geometric sequence, with common ratio = -1.

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Answer:

solve this

Step-by-step explanation:

260*9/4

Answer:

3 5,7,9,11,13,16,17 19,21,23,25,27,29

The distance between the given parallel lines is

In the given statement is :

The equations of the pair of each parallel lines is:

y = 4x and y = 4x - 17

To find the distance between each pair of parallel lines.

Two lines a₁x +b₁y + c₁=0   and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.

As we know that distance between the parallel lines (d) is given as:-

d = [tex]\frac{c_{2} -c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]

Parallel lines equation as:

y - 4x = 0

y - 4x + 17 = 0

Here,

a = -4 , b = 1, c1 = 0, c2 = 17

Therefore, putting the values

d = [tex]\frac{17 -0}{\sqrt{-4^{2}+1^{2} } }[/tex]

d = [tex]\frac{17}{\sqrt{17} }[/tex]

d = root 17

d = 4.12 units

Hence, The distance between the given parallel lines is 4.12 units

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The correct location on the table is:

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:

a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex] .

b= the constant term that represents the y-intercept.

For the given example: a=7 and b=2.

For solving  linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.

       x= 9*3

       x=27

      Therefore, x≠3

       x=-9+6

       x= -3

      Therefore, x≠3

       x= 5 -2

       x= 3

      Therefore, x=3

       x= 12/5 + 3/5

       x= 15/5

      x=3

      Therefore, x=3

       14x=42

       x=3

      Therefore, x=3

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