In a right-angled triangle ABC, if angle B = 90°, then which of the
following is true?
(a) AB² = BC² + AC² (b) AC² = AB² + BC²
(c) AB = BC + AC (d) AC = AB + BC

Answer:

n > 3

Step-by-step explanation:

2n - 5 > 1

Add 5 on both sides

2n > 6

Divide by two on both sides to isolate n

n > 3

Answer:

Yes

Step-by-step explanation:

Plug in x and y:

17(-9)+12(8)<8

-153+96<8

-57<8

This is true so the point must satisfy the inequality.

Answer:

A. (18, 1)

Step-by-step explanation:

Step-by-step explanation:

the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.

Answer:

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

-1 is not equal to -5/3

The 200 km, 100 km, and 400 km distances traveled by the airplane at bearings of 335°, 170°, and 288°, respectively, indicates;

a) The displacement of the airplane when it lands is 485.56 kilometers

b) The bearing the airplane could have flown to complete the journey directly is 288.27°

A bearing is the measurement in degrees of an angle from the north direction

a) The path of the airplane can be represented using vectors as follows;

A bearing of 335° = N 25° W

Therefore;

[tex]\vec{d_1}[/tex] = -200·sin(25°)·i + 200·cos(25°)·j

A bearing of 170° = S 10° E

Therefore;

[tex]\vec{d_2}[/tex] =  100·sin(10°)·i - 100·cos(10°)·j

A bearing of 280° = N 80° W

Therefore;

[tex]\vec{d_3}[/tex] = -400·sin(80°)·i + 400·cos(80°)·j

The resultant displacement of the airplane, can be found by adding the above displacement vectors as follows;

R = (100·sin(10°)-200·sin(25°) - 400·sin(80°))·i + ((200·cos(25°) - 100·cos(10°) + 400·cos(80°))·j = -461.08·i + 152.24·j

The distance of the airplane from the start is therefore;

|R| = √((-461.08)² + 152.24²) ≈ 485.56

b) The direction of the airplane obtained from the resultant vector can be presented as follows;

[tex]\theta = arctan\left(\dfrac{152.24}{-461.08\right)}\approx -18.27^{\circ}[/tex]

From the other possible values of the angle, θ, we get;

θ = 180° - 18.27° ≈ 161.73°

The 161.73° is measures from the positive x-axis, and therefore is in Quadrant II

The bearing is therefore 270° + the measure of the 161.73° above the negative x-axis, which indicates;

The bearing = 270° + 180° - 161.73° = 288.27°

Learn more about bearings in mathematics here:

https://brainly.com/question/22013596

#SPJ1

The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3

Index form of a number can simply be described as that number written in the form of an exponential expression.

The number can also be written as a single number which is raised to another number.

Some rules of indices to note;

Given that;

(8^(5))/(8^(-9))

Then, we have;

8^5-(-9)

8^5+9

Add the powers

8^14

Hence, the value is 8^14

Learn more about index forms here:

https://brainly.com/question/15361818

#SPJ1

If a credit card has an APR of 32.47%, and its billing cycle is 30 days long. The credit card's periodic interest rate is 2.67%.

A credit card periodic rate can be defined as the interest amount that a person pays on the balance of their credit card.

Given data:

Billing cycle = 30 days long

APR = 32.47%

Using this formula to find the credit card periodic interest rate

Credit card periodic interest rate = APR / (Number of days in a year /Billing cycle)

Where:

Credit card periodic interest rate =?

Annual percentage rate (APR) = 32.47%  

Number of days in a year =365 days

Billing cycle = 30 days

Now let find the credit card periodic interest rate

There is 365 days in a year.

Credit card periodic interest rate = 32.47% ÷ (365 days / 30 days)

Credit card periodic interest rate =32.47% / 12.17

Credit card periodic interest rate = 2.67%

Therefore the  periodic interest rate is 2.67%

Learn more about credit card periodic interest rate here:https://brainly.com/question/21444304

#SPJ1

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]

The time it will take both the boat and whale to meet is 18minutes(nearest minutes)

Displacement is defined as the change in position of an object in a specified direction. It is measured in meters and it's a vector quantity.

Since velocity = displacement/time

displacement = velocity ×time

The total space between the boat and the whale is 5miles.

Using addition of vectors

5= v2t - v1t

5= 46t - 30t

5 = 16t

t= 5/16 = 0.3hrs

to minutes, = 0.3 ×60 = 18minutes(nearest minutes)

Therefore it will take the boat and the whale 18minutes to meet.

learn more about displacement from

https://brainly.com/question/14422259

#SPJ1

answer:18

Step-by-step explanation:

From the figure, we can see that ABC and A'B'C are similar triangles.

Because Segment A'B' is parallel to segment AB.

then angleA'B'C=ABC  CA'B'=CAB  A'CB'=ACB

A'B':AB=8:20         rate=0.4

A'C:AC=12:?

12/0.4=AC=30

AC-A’C=30-12=18

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Rectangular coordinates of a point is written like (x, y, z)

Cylindrical coordinates of a point  is written like (r, θ, z)

Spherical coordinates of a point is written like (p, θ, φ)

First talk about Rectangular vs Cylindrical.

x = rcosθ

y = rsinθ.

z = z

x^2 + y^2  = r^2

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

r^2 = 4+4 = 8.

r = [tex]\sqrt{8}[/tex]

r = 2[tex]\sqrt{2}[/tex]

θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .

z = -1.

So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).

Now let's us talk about Rectangular vs Spherical Coordinates.

x =  pcosθsinφ.

y= psinθsinφ.

z = pcosφ.

p^2 =  x^2+y^2+z^2.

tanθ = y/x

cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3

θ = [tex]tan -1[/tex](y/x) =  0.78rad .

φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad

So Spherical coordinates is (3, 0.78rad, 1.91rad).

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Given Question is incomplete, Complete Question here

The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,

To know more about cylindrical and spherical coordinates here.

https://brainly.com/question/4465072

#SPJ4

Answer:

I think it is true, please let me know if I am wrong:)

The correct option regarding the heights of the trees include:

The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:

(12 - 5) > (12 - 7)

7 > 5

The mean of tree heights at Yard Works is 8 feet.

The mean of tree height at The Grow Station is 9 feet.

The mean absolute deviation of the tree heights at both yards is 2.

Learn more about mean on:

https://brainly.com/question/10002748

#SPJ1

Answer:

Step-by-step explanation:

y = 2x - 1  

when you sub in 0 in x and -1 in y, the y-intercept is -1.

Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

Answer:

1/2

Step-by-step explanation:

-1(15+4-27)/16

Add 15 and 4 to get 19.

Now you have -1(19-27)/16

Subtract 27 from 19 to get −8.

-1(-8)/16

Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.

-(-1/2)

Simplify

1/2

Answer:

1/2

Step-by-step explanation:

⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆

Calculate:

-(15 + 4 - 27) / 16

-(19-27)/16

-(-8) / 16

= 8/16

Simplify:

= 1/2

The interval of convergence is given as: ⟹|x|<1

What is Maclaurin series?

Given the values of the function's successive derivatives at zero, a Maclaurin series is a power series that enables one to construct an approximation of a function with input values close to zero.

We will utilize the common power series representation of the functions, such as sine and the logarithmic function, to find the first three non-zero terms of the Maclaurin series representation for the function. We shall multiply the terms of each expression to obtain the final expression.

[tex]sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}[/tex]

[tex]ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}[/tex]

The series representation shown above is only accurate when ⇒|x| < 1.

Given that;

f(x) = 4 sin(x) ln(1+x)

We are familiar with how functions are represented by power series:

[tex]sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}[/tex]

[tex]ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}[/tex]

The series representation shown above is only accurate when ⇒|x| < 1.

[tex]sin(x) ln(1+x) = [x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........][x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........][/tex]

[tex]sin(x) ln(1+x) = x^2 -\frac{x^3}{3}+\frac{x^4}{4} +\frac{x^5}{5} +........[/tex]

Finally, the function's power series representation is given as:

⇒ [tex]f(x) = 4 sin(x) ln(1+x) = 4 [x^2 - \frac{x^3}{2}+\frac{x^4}{6} +\frac{x^5}{6}+..... ][/tex]

The interval of convergence is given as: ⟹|x|<1.

Learn more about Maclaurin series click here:

https://brainly.com/question/28170689

#SPJ4

Answer:

m=[tex]-\frac{3}{2}[/tex]

Step-by-step explanation:

The slope is found with the equation m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]:

[tex](x_1,y_1)=(3,1)\\(x_2,y_2)=(1,4)\\m=\frac{(4)-(1)}{(1)-(3)}\\m=\frac{3}{-2}[/tex]

The angular velocity of a person standing on the equator is ω = 1.026 × 10⁻⁴ rad/s

Angular velocity is the number of revolution per second of an object.

Since a planet rotates through one complete revolution every 17 hours and since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. We thus require its angular velocity.

The angular velocity is given by ω = 2π/T where T = period of revolution

Since the planet rotates through one complete revolution every 17 hours, its period, T = 17 hours = 17 h × 60 min/h × 60 s/min = 61200 s

So, substituting the period into the equation for the angular velocity, we have

ω = 2π/T

ω = 2π/61200 s

ω = π/30600 s

ω = 0.0001026 rad/s

ω = 1.026 × 10⁻⁴ rad/s

So, the angular velocity is ω = 1.026 × 10⁻⁴ rad/s

Learn more about angular velocity here:

https://brainly.com/question/28155635

#SPJ1

The equivalent expression to the given expression is, 7 to the fourth power.

What is equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.

Consider, the given expression

7 · 7 · 7 · 7

By using:

If a = b · b · b

Here there is multiplication of b 3 times.

So, [tex]a = b^3[/tex]

In the given expression 7 is occur 4 times,

Hence it becomes, [tex]7^4[/tex].

That is  7 to the fourth power.

Therefore, the equivalent expression to the given expression is, 7 to the fourth power.

To know more about equivalent expression, click on the link

https://brainly.com/question/24734894

#SPJ4

Answer:

In a triangle LMN, the measure of angle M is 15

Step-by-step explanation:

The value of c, if In triangle LMN, m ∠ L = (2c + 51)°. If the exterior angle to ∠ L measures 83° is 23, so option B is correct.

Triangles are basic three-sided polygons with three internal angles. It is one of the basic geometric shapes, symbolized by the symbol, and has three vertex connections.

Given data:

m ∠ L = (2c + 51)°,

∠ L = 83°

Calculate the remaining measure of the angle,

S = 180 - 83

S = 97°

Calculate the value of c as shown below,

97° = 2c + 51

2c = 97 - 51

c = 46 / 2

c = 23

Therefore, the value of c, if In triangle LMN, m ∠ L = (2c + 51)°. If the exterior angle to ∠ L measures 83° is 23.

To know more about Triangles:

https://brainly.com/question/16886469

#SPJ2

By using the concept of compact set, it can be proved that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

What is compact set?

A set K is said to be compact if every open cover of K has a finite subcover.

Let K⊆Rn is compact  f:K→R is continuous, and ϵ>0

Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,

Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.

So,  |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,

Since f is continuous,

We can write

|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,

This is true for infinite many [tex]n_k[/tex]

So ||x - y|| = 0

|f(x) - f(y)| > ϵ, a contradiction since f is continuous

So,  there is a number A>0 such that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

To learn more about compact set, refer to the link-

https://brainly.com/question/17175854

#SPJ4

Answer: the answer is 72

Step-by-step explanation:

if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240

Now we need to determine 30% of 240 and the procedure explaining it as such

Step 1: In the given case Output Value is 240.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 240 = 100%.

Step 4: In the Same way, x = 30%.

Step 5: On dividing the pair of simple equations we got the equation as under

240 = 100% (1).

x = 30% (2).

(240%)/(x%) = 100/30

Step 6: Reciprocal of both the sides results in the following equation

x%/240% = 30/100

Step 7: Simplifying the above obtained equation further will tell what is 30% of 240

x = 72%

Therefore, 30% of 240 is 72

I hope this helps

Answer:

  72

Step-by-step explanation:

You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.

The 30% you want will be the difference between 80% and 50%:

  80% -50% = 30%

  192 -120 = 72

30% of the same number is 72.

Answer:

  12.903

Step-by-step explanation:

You want the measure of BC in right triangle ABC with A=90°, B=47° and AB=8.8.

The relations between sides and trig functions of the angles in a right triangle are summarized by the mnemonic SOH CAH TOA. Useful here is the relation between the side adjacent to the given acute angle and the hypotenuse:

  Cos = Adjacent/Hypotenuse

  cos(47°) = AB/BC

Solving for BC, we get ...

  BC = AB/cos(47°) = 8.8/cos(47°)

The calculator (2nd attachment) shows this to be ...

  BC = 12.903

It takes 51.33 min or 6/7 hrs to travel upstream 4 km.

What is relative velocity?

it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.

speed of boat = 7 km/hr

speed of river = r km/hr

speed upstream = 7-r km/hr

speed downstream = 7+r km/hr

time taken to go upstream 4 km = 4/(7-r)

time taken to go downstream 8 km = 8/(7+r)

as time taken is equal in both scenario:

4/(7-r) = 8/(7+r)

on solving we get:

r = 7/3 km/hr

put this value in time taken for upstream

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

to learn more about relative speed:

https://brainly.com/question/29523095

#SPJ4

Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

Think about two trains that are traveling in the same direction and at the same pace.

Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.

The other train seems to be moving at a constant speed.

So, we know that:

Speed of boat = 7 km/hr

Speed of river = r km/hr

Now,

Speed upstream = 7-r km/hr

Speed downstream = 7+r km/hr

Time taken to go upstream 4 km = 4/(7-r)

Time taken to go downstream 8 km = 8/(7+r)

As the time taken is equal in both scenarios:

4/(7-r) = 8/(7+r)

On solving we get:

r = 7/3 km/hr

Put this value in time taken for upstream as follows:

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

Learn more about relative speed here:

https://brainly.com/question/29523095

#SPJ4

If the polygon is a square the other 2 coordinates are

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (0, 0) and (3, 2) is the diagonal of the polygon calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(3 - 0)² + (2 - 0)²}

d =√{9 + 4}

d = √13 units

this is the hypotenuse

from Pythagoras theorem

let length of one side be x

√13² = x² + x²

13 = 2x²

6.5 = x²

x = 2.5495

x = 2.55 units

In ordered pair this is 2.55 units from the origin in the x and y direction

(0, 2.55) and (2.55, 0)

Learn more about length of line segment  here:

https://brainly.com/question/24778489

#SPJ1

Answer:

tan R = [tex]\frac{45}{28}[/tex]; tan S =[tex]\frac{28}{45}[/tex]

Step-by-step explanation:

The tangent proportion is [tex]\frac{opposite}{adjacent}[/tex].

When R is the reference angle TS (45) is the opposite side and TR is the adjacent side (28).

When S is the reference angle, TR is the opposite side (28) and TS is the adjacent side (45).