Andrew is kayaking in a river with a 6 mph current. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. Find the speed (mph) of Andrew’s kayak in still water

If point P(2k, k) is equidistant from A(-2, 4) and B (7,-5), the numerical value of k is 3.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

The distance between P(2k, k) and A(-2, 4) is:

d = √((2k - (-2))² + (k - 4)²)

d = √((2k +2)² + (k - 4)²)

The distance between P(2k, k) and B(7, -5) is:

d = √((2k - 7)² + (k - (-5))²)

d = √((2k - 7)² + (k + 5)² )

Since the distances are equal, we can set the two equations for d equal to each other and solve for k.

√((2k +2)² + (k - 4)²) = √((2k - 7)² + (k + 5)² )

Square both sides

(2k +2)² + (k - 4)² = (2k - 7)² + (k + 5)²

(2k +2)² + (k - 4)² = 5k² - 18k + 74

5k² + 20 = 5k² - 18k + 74

Collect like terms

5k² - 5k² + 18k = 74 - 20

18k = 74 - 20

18k = 54

k = 54/18

k = 3

Therefore, the value of k is 3.

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A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.

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Answer:

C.   Function 1:  Difference of 1

Step-by-step explanation:

Function 1

m = ∆y / ∆x = 6/2 = 3

Function 2

Slope intercept form

m = 2

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

Function 1 is greater

Difference

3 - 2 = 1

Answer:

its B

Step-by-step explanation:

Answer:

[tex]a = \frac{bq}{n}[/tex]

Step-by-step explanation:

If we are trying to solve for "a", then we need it to be alone on one side of the equation.

[tex]\frac{n}{q} = \frac{b}{a}[/tex]

[tex]\frac{an}{q} = b[/tex]

[tex]a = \frac{bq}{n}[/tex]

Answer:

35[tex]yd^{2}[/tex]

Step-by-step explanation:

6x5=30

2x5(1/2)=5

30+5=35

Answer:

[tex]\huge\mathfrak\red{Answer...} \\ \\\huge\mathfrak\purple{angle \: z} \\ \\ \huge\mathfrak\pink{hope \: it \: helps..}[/tex]

Answer:

Step-by-step explanation:

Answer:

domain[-5,-3)U(4,3)

range-(4,-4)

Step-by-step explanation

parentheses are used when the circle is open and brackets are used when the circle is filled in, domain is the x axis and range is the y axis

Answer:

y = ax^2 + bx + ct

Step-by-step explanation:

Answer:

392 m^2

Step-by-step explanation:

I made a video explaining it for you! I promise it’s not unrelated to the question. Here it is:

https://youtu.be/AcVNod4o-_w

The measure of angle B is 82°

What is angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

∠A = 180° - 143°

     = 37°

∠A + ∠B + ∠C = 180°

37° + ∠B + 61° = 180

∠B = 180 - 61 - 37

     = 82°

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Answer:

10 yards

Step-by-step explanation:

We know that to find the perimeter you have to multiply the length and width by 2 and add

We already know that the length is 14 yards

Multiply 14 by 2

    14*2=28

Subtract 48 by 28 (the total of both the length and width multiplied by 2)

    48-28=20

Divide 20 by 2

   20/2=10

And your answer is 10 yards as the width

10+10+14+14=48 yards

Answer:

1.3

Step-by-step explanation:

3.5 - y

y= 2.2

So substitute the Values and do 3.5 - 2.2 and you get 1.3 as answer

I hope This helped!

Answer:

1.3

Step-by-step explanation:

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Answer: 106 km/h,2.5 hr

Step-by-step explanation:

Given

The train travels 315 km in the same time car travels 265 km

The average speed of the train is 20 kmph faster than car

Suppose, speed of the car is v and it travels 265 km in t hours

[tex]\therefore \dfrac{315}{v+20}=\dfrac{265}{v}\\\\\Rightarrow 315v=265\left (v+20\right)\\\\\Rightarrow 315v=265v+5300\\\Rightarrow 50v=5300\\\Rightarrow v=106\ km/h[/tex]

Time taken to travel is

[tex]\Rightarrow t=\dfrac{265}{106}}\\\\\Rightarrow t=2.5\ h[/tex]

Answer:

x=12√3

Step-by-step explanation:

we can split the triangle into two right triangles

since we know that DEF is an equilateral triangle, that means that we will be dealing with a 30°-60°-90° special right triangle

since it is a 30°-60°-90° triangle,

x=12√3

6th terms of given geometric progression whose common ratio is 3/2 and first term is 4  is 243/8 using the farmula ar^(n-1).

What is a geometric sequence?

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.

Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).

a = First term where

The common Ratio is r.

nth term = ar^(n-1)

6th terms ar^(6-1) = ar^5.

given is that r =3/2. a = 4.

6th term = 4 * (3/2)^5

= 4 * 3^5/2^5

=4*243/4*8

=243/8.

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Answer:

x = 39

y = 129

Step-by-step explanation:

to find x you do

x +51 = 90

subtract 51 from both sides

x = 39

to find y

we already know part of y is a right angle (90 degrees)

so we need to find the tiny other part

this tiny other part is equal to x

so

90 +39 = 129

Answer:

Adam took 132 minutes longer than Steve.

Step-by-step explanation:

Let's find the time that takes Steve and Adam to complete the race. We will use the equation:

[tex] V = \frac{d}{t} [/tex]              

Where:

d: is the distance = 26 miles

t: is the time =?

V: is the speed

For Steve we have the following time:

[tex] t_{s} = \frac{d}{V_{s}} = \frac{26 mi}{4 mi/h} = 6.5 h*\frac{60 min}{1 h} = 390 min [/tex]

And the time of Adam is:

[tex] t_{a} = \frac{d}{V_{a}} = \frac{26 mi}{3 mi/h} = 8.7 h*\frac{60 min}{1 h} = 522 min [/tex]

So, the difference between the time of Adam and Steve is:

[tex] \Delta t = t_{a} - t_{s} = 522 min - 390 min = 132 min [/tex]

Hence, Adam took 132 minutes longer than Steve.

I hope it helps you!

Answer:

[tex]4\frac{7}{20}[/tex]

Step-by-step explanation:

Answer:[tex](1,1),\ \dfrac{1}{3}[/tex]

Step-by-step explanation:

Given

Equation of the curves are [tex]y=x^2,\ y^2=x[/tex]

The intersection of the curve is

[tex]\Rightarrow y^4-y=1\\\\\Rightarrow y(y^3-1)=0\\\\\Rightarrow y=0,1\\[/tex]

So, x coordinates are [tex]x=0,1[/tex]

points of intersection are[tex](0,0),(1,1)[/tex]

So, the area bounded between the curves

[tex]\Rightarrow I=\int_{0}^{1}\left ( \sqrt{x}-x^2\right )dx\\\\\Rightarrow I=\int_{0}^{1}\sqrt{x}dx-\int_{0}^{1}x^2dx\\\\\Rightarrow I=\left ( \frac{2}{3}x^{\frac{3}{2}} \right )_0^1-\left ( \frac{1}{3}x^3 \right )_0^1\\\\\Rightarrow I=\frac{2}{3}\left ( 1-0 \right )-\frac{1}{3}\left ( 1^3-0 \right )\\\\\Rightarrow I=\frac{2}{3}-\frac{1}{3}\\\\\Rightarrow I=\frac{1}{3}[/tex]

The area bounded by them is [tex]\frac{1}{3}[/tex]

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Answer:

  3x +2y = 6

Step-by-step explanation:

The scale of the axes of the supplied graph are not shown. We must infer what they are from the equation of the given line.

The given equation is in slope-intercept form, so we can read the y-intercept from the equation as being -1. This is 1 major grid square below the x-axis.

  y = mx + b . . . . . . . line with slope m and y-intercept b

The x-intercept is found by setting y=0 and solving for x.

  y = x -1

  0 = x -1

  1 = x . . . . . . add 1 to both sides

The x-intercept of 1 is shown on the graph as 2 major grid squares from the y-axis. This tells us each major grid square is 1/2 unit in the x-direction and 1 unit in the y-direction.

__

Knowing the scaling of the axes, we can determine that the x-intercept of line L is 2, and the y-intercept is 3.

There are several different useful forms of the equation for a line. One of them is "intercept form":

  x/(x-intercept) + y/(y-intercept) = 1

Using the above intercept values, this is ...

  x/2 + y/3 = 1

Multiplying by 6 puts this in standard form:

  3x +2y = 6 . . . . . . . standard form equation for line L

__

If we solve for y, we can find the slope-intercept form.

  2y = -3x +6

  y = -3/2x +3

The amount of mold after n days is 3 × (1.5)ⁿ⁻¹.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

At first, mold was 3 cm², then 4.5 cm², and it was increasing each day by 50%.

a₁ = 3

a₂ = 4.5

a₃ = 4.5 + (4.5 × 50%) = 6.75

.............

Here the common ratio, r = a₂/a₁ = a₃/a₂ = ..... = 1.5

n th term of a GP = a rⁿ⁻¹, where a is the first term and r is the common ratio.

Area of mold after n days = 3 × (1.5)ⁿ⁻¹

Hence the mold at any time can be calculated by the formula 3 × (1.5)ⁿ⁻¹.

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Elimination is a very easy method when it comes to solving simultaneous equations.

First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.

The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given

Now take one of the equations and multiply it by -1.

Add the equations up to eliminate the variable and derive the other variable(s)

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Answer:

Amount of peanut butter each student get = 533.34 gram (Approx.)

Step-by-step explanation:

Given:

Amount of peanut butter Mr black has = 32 kg

Total number of students = 60 students

Find:

Amount of peanut butter each student get

Computation:

Amount of peanut butter Mr black has = 32 kg

Amount of peanut butter Mr black has = 32 x 1,000 gram

Amount of peanut butter Mr black has = 32,000 gram

Amount of peanut butter each student get = Amount of peanut butter Mr black has / Total number of students

Amount of peanut butter each student get = 32,000 / 60

Amount of peanut butter each student get = 533.33

Amount of peanut butter each student get = 533.34 gram (Approx.)