which relation is a function ​

The length of shorter leg is 15 inches, length of longer leg is 36 inches and the length of hypotenuse is 39 inches.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.

Let,

x = Longer leg of triangle

y = Shorter leg of triangle

h = Hypotenuse of triangle

Given: The length of the longer leg of a right triangle is 6inches more than twice the length of the shorter leg.

The length of the hypotenuse is 9inches more than twice the length of the shorter leg.

⇒  x = 6 + 2y

    h = 9 + 2y

The given triangle is a right angled triangle.

⇒                                 x^2 + y^2 = h^2

                          (6 + 2y)^2 + y^2 = (9 + 2y)^2

                36 + 24y + 4y^2 + y^2 = 81 + 36y + 4y^2

                          36 + 24y + 5y^2 = 81 + 36y + 4y^2

36 - 81 + 24y - 36y + 5y^2 - 4y^2 = 0

                             -45 - 12y + y^2 = 0

                               y^2 - 12y - 45 = 0

                       y^2 - 15y + 3y - 45 = 0

                        y(y - 15) + 3(y - 15) = 0

                                 (y - 15)(y + 3) = 0

y - 15 = 0,   y + 3 = 0

y = 15,     y = -3

Since the length is not negative.

So, y = 15

Hence,

Shorter leg = 15 inchs

Longer leg = 6 + 2y = 6 + 2(15) = 36 inches

Hypotenuse = 9 + 2y = 9 + 2(15) = 39 inches

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Answer:

15/8

Step-by-step explanation:

Answer:

40+32=342

Step-by-step explanation:

Using the commutative of addition change the position of 302 and 40 the expression is 40+302=342 [analysis]

The points on the rhombus M(?, 0) and H(5, 0), and the location of the point O of the rhombus, indicates that the length of a side of a rhombus is 5 units from which Pythagorean Theorem indicates that the x-coordinate of the point M is 3

Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equivalent to the square of the length of the hypotenuse side of a right triangle.

The shape of the quadrilateral RHOM = A rhombus

The specified coordinates of the vertices of the rhombus are;

Point M = (?, 4)

Point H = (5, 0)

A rhombus is a parallelogram that have all four sides of the same length

The length of side OH, which is on the x-axis  = 5 - 0 = 5

Therefore, the length of OM = 5 (properties of a rhombus)

Let x represent the x-coordinate of the point M

According to Pythagorean Theorem, we get;

x² + 4² = 5²

Where x = The horizontal distance of the point M from the y-axis

x² = 5² - 4² = 9

x = √9 = 3

The x-coordinate of the point M, x = 3

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The original selling price is $80 if A store is selling an NBA jersey for $60 that has been discounted by 25%.

The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Given,

Discount = 25%

Selling price = $60

Original price = x

Original price

= Selling price/1 - discount

= 60/ 1 - 0.25

= 60/ 0.75

= 80

The original selling price is $80 if A store is selling an NBA jersey for $60 that has been discounted by 25%.

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Answer:

20

Step-by-step explanation:

A parallelogram has 4 sides.

Each pair of opposite sides is congruent.

To find the perimeter, find the length of 2 adjacent sides and multiply by 2.

Length of side (0, 0) to (5, 0) is 5.

Length of side (5, 0) to (8, 4) is the hypotenuse of a right triangle with legs of lengths 3 and 4.

a² + b² = c²

3² + 4² = c²

c² = 9 + 16

c² = 25

c = √25

c = 5

The hypotenuse measures 5 units.

perimeter = 2(5 + 5)

perimeter = 2(10)

perimeter = 20

Perimeter of the polygon is [tex]5x^{2} +y^{2}+3x+4y[/tex]

What do you mean by perimeter of polygon?

A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface.

The total of a polygon's sides is referred to as the polygon's perimeter. A regular polygon's perimeter is provided by if it is one.

Regular polygon perimeter equals (number of sides) x (length of polygon's sides) units.

Given sides of the polygon are 4y , [tex]y^{2} , 4x^{2} -y^{2},3x,x^{2} +y^{2}[/tex]

Perimeter of the polygon is the sum of all sides of the polygon

Perimeter of the polygon = [tex]4y+4x^{2} -y^{2}+3x+x^{2} +y^{2} +y^{2}[/tex]

                                          = [tex]5x^{2} +y^{2}+3x+4y[/tex]

Therefore, perimeter of the polygon is [tex]5x^{2} +y^{2}+3x+4y[/tex]

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Answer:

To factor the expression 2/3x + 4, we first need to find the greatest common factor (GCF) of the coefficients of the terms in the expression. In this case, the GCF is 2/3, so we can write the expression as (2/3)(x + 12/2). This is the factored form of the expression, and it can be simplified to (1/3)(2x + 6).

Step-by-step explanation:

the area between the curves y=[tex]x^{2}[/tex] and y=-3x is 9/2 sq units

By performing a definite integral between the two point, one may determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a & x = b. With the specified restrictions, integration may be used to compute this area.

The area between the curves y=[tex]x^{2}[/tex] and y=-3x

y=[tex]x^{2}[/tex] and y=-3x

firstly calculated the point of intersection. y = y

[tex]x^{2}[/tex]  = -3x

[tex]x^{2}[/tex]  + 3x = 0

x( x+ 3) = 0

x = 0 , x = -3

point of intersection is 0 , -3

Area = [tex]\int\limits _ {} \, x^{2} + 3xdx[/tex] from -3 to 0

Area  = [ [tex]x^{3}/3 + 3x^{2} /2[/tex] ] from -3 to 0

Area =   [ -27/3 + 27/2 ]

Area  = [ -9 + 27/2]

Area = [-18 + 27] / 2

Area = 9/2 sq units

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Answer:

35

Step-by-step explanation:

The area of the parallelogram will be equal to 28 units squared. Hence, option B is correct.

The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.

As per the data obtained from the given values,

Length of base (b) of parallelogram = 7

Length of height (h) of parallelogram = 4

Use the formula of area (A) of a parallelogram,

[tex]Area = Base*Height[/tex]

A = 7 × 4

A = 28 units squared.

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The answers to all the subparts using the probability formula are shown:

(A) P(red ball): 5/8

(B) P(NOT Yellow): 7/8

(C) P(white or yellow): 3/8

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

PRobability formula: P(E) = favourable events/Total events

(A) P(red ball):

P(E) = favorable events/Total events

P(E) = 5/8

(B) P(NOT Yellow)

P(E) = favorable events/Total events

P(E) = 7/8

(C) P(white or yellow)

P(E) = favorable events/Total events

P(E) = 3/8

Therefore, the answers to all the subparts using the probability formula are shown:

(A) P(red ball): 5/8

(B) P(NOT Yellow): 7/8

(C) P(white or yellow): 3/8

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Answer:

s = 9

Step-by-step explanation:

calculate the slope m through the 2 points using the slope formula and equate to - 5

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )

m = [tex]\frac{-7-3}{s-7}[/tex] = [tex]\frac{-10}{s-7}[/tex]

equate m to slope of - 5

[tex]\frac{-10}{s-7}[/tex] = - 5 ← multiply both sides by s - 7

- 10 = - 5(s - 7) ← divide both sides by - 5

2 = s - 7 ( add 7 to both sides )

9 = s

The equations that represent a line passing through the point (–2, 5) with a slope of 4 are:

Equation of the line of slope = 4 passing through point (-2, 5) is calculated using the point slope formula which is

(y - y') = m(x - x')

y' = 5

slope, m = 4

x' = -2

substituting the known variables and solving

(y - 5) = 4(x - ( -2 ) )

y -5 = 4( x + 2)

y - 5 = 4x + 8

y = 4x + 8 + 5

y = 4x + 13

the equation of the line with a slope of 4 and passing through point (-2, 5) is  y = 4x + 13

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Answer:

Step-by-step explanation:

Probably "1+1=window" was discovered by some cheeky primary school student, and then it spread without attribution. We will never know for sure who originally came up with that.

Answer:

Step-by-step explanation:

First question. Answer is

A quadratic equation's solutions can be found using the quadratic formula, which is option D.

Explanation:

2x^2 - 5x +5 = 0.

x = - 5 +-[tex]\sqrt{5[/tex].

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A quadratic equation's solutions can be found using the quadratic formula, which is option D.

Any quadratic problem can be resolved using the quadratic formula. First, we change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. Then, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). View examples of how to apply the formula to a range of equations.

If necessary, simplify the right side while writing the left side as a square. Create two linear equations by combining the positive and negative square roots of the right side with the square root of the left side. Each of the two linear equations must be resolved.

2x^2 - 5x +5 = 0.

x = - 5 [tex]\pm[/tex] √5

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Answer:

Step-by-step explanation:

0.15625

Answer:

112

Step-by-step explanation:

Answer:

A reflection over the x axis

Step-by-step explanation:

x is the horizontal line we are reflecting one across it to get the other

the breadth of the river is [tex]20\sqrt{3} m[/tex] or 34.614 m

as per given in the question ,

the length of the tower (l) = 20m

the angle of elevation of the top of the tower from the opposite bank

[tex]\theta[/tex] = [tex]30^{0}[/tex]

the breadth of the river should be found

let the breadth of the river be x,

to find breadth,

[tex]tan\theta=\frac{opposite\ side}{adjacent\ side}[/tex]                        ----(1)

the opposite side will be the length of the pole i.e, 20m

the adjacent side will be the breadth of the river i.e, x

now substitute all the values in equation (1)

[tex]tan\theta=\frac{20}{x}[/tex]

=> [tex]tan 30^0= \frac{20}{x}[/tex]             ( the value of [tex]tan30^0 =\frac{1}{\sqrt{3} }[/tex] )

=> [tex]\frac{1}{\sqrt{3} } =\frac{20}{x}[/tex]

=> [tex]x=20\sqrt{3}m[/tex]

so,  

     the breadth of the river is [tex]20\sqrt{3} m[/tex] or we can write 34.614m

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Answer: 1000 different flags

Step-by-step explanation:

So for the flag there are 10 color options and you need to have 3 different stripes. Where you are able to use a color more than once.

For the first stripe there are 10 options so it can be any of the 10 choices.

For the second option you are able to use any of the 10 colors again so it can be any of the 10 colors.

For the last option for stripe 3 you can pick from ay of the 10 colors so there are 10 color options is could be.

Now that you know the how many choices of color there can be for each stripe you multiple the color choice for each stripe by each other to get the number of combinations for different flags.

colors for stripe 1x  colors for stripe 2x colors for stripe 3= # of different flags

10x10x10=1000

so there can be 1000 different 3 stripe flags that can be made with 10 colors

$92000 is the James’s current equity in the home.

Equity, also known as shareholders' equity or owners' equity for privately held businesses, is the sum of money that, in the event of a company's liquidation, would be distributed to its shareholders after all of the company's assets have been sold and its debt has been fully repaid.

In an acquisition scenario, it is equal to the sum of the company's sales less any liabilities that were not transferred to the new owner.

A company's book value can also be represented by shareholder equity. A payment-in-kind arrangement may occasionally include equity. Furthermore, it represents the proportionate ownership of a company's shares.

James’s current equity =  (180000 × 1.25) - ((180000 × 0.8) -11000)

                                       = 92000

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The domain of s = 13.5h is (0, 1, 2, 3, 4).

The range of s = 13.5h is (0, 13.5, 27, 40.5, 54).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

s = 13.5h

For h = 0,

s = 0

For h = 1,

s = 13.5

For h = 2,

s = 27

For h = 3,

s = 40.5

For h = 4,

s = 54

Thus,

The domain is (0, 1, 2, 3, 4).

The range is (0, 13.5, 27, 40.5, 54).

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The fuel efficiency for the speed of 60 mph is (d) 38.55 mpg

From the question, we have the following least-squares regression line equation that can be used in our computation:

ln(Fuel Efficiency) = 1.437 +0.541 In(Speed)

Also from the question, we have the following parameters:

Speed = 60 mph

This means that we substitute 60 mph for speed in the given equation

ln(Fuel Efficiency) = 1.437 + 0.541 In(Speed)

So, we have the following representation

ln(Fuel Efficiency) = 1.437 + 0.541 In(60)

Take the natural logarithm of 60

This gives

ln(Fuel Efficiency) = 1.437 + 0.541 * 4.09434456222

Evaluate the products

So, we have the following representation

ln(Fuel Efficiency) = 1.437 + 2.21504040816

Evaluate the sum

So, we have the following representation

ln(Fuel Efficiency) = 3.65204040816

Take the exponent of both sides

Fuel Efficiency = e^(3.65204040816)

Evaluate

Fuel Efficiency = 38.5532502162

Approximate

Fuel Efficiency = 38.55 mpg

Hence, the fuel efficiency  is (d) 38.55 mpg

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Answer:

[tex]\dfrac{2(x+4)}{x}[/tex]    or     [tex]2 + \dfrac{8}{x}[/tex]

Step-by-step explanation:

Rewrite the problem as a fraction.

[tex]\dfrac{6(x+4)^2}{3x(x+4)}[/tex]

Then, represent the squared term on the top as two values to make it easier to cancel.

[tex]\dfrac{6(x+4)(x+4)}{3x(x+4)}[/tex]

Now, cancel an x+4 from the top and bottom.

[tex]\dfrac{6(x+4)}{3x}[/tex]

Finally, divide the numerator and denominator by 3.

[tex]\dfrac{2(x+4)}{x}[/tex]     or     [tex]2 + \dfrac{8}{x}[/tex]

[tex]\bf{\dfrac{6(x+4)2}{3x(x+4)} \iff \ Eliminate \ (x+4).}\\ \\ \bf{That\:is, isolating\:the \ common \ factor \ \dfrac{\not{6}\times2 }{\not{3}x} \ \--\to\dfrac{2\times2}{x}=\dfrac{4}{x} } \\ \\ \boldsymbol{\sf{\dfrac{4}{x} }}\bf{\iff}\boxed{\boxed{\bf{Answer}}}[/tex]

The function is determined using speed and is found to be d = 120t.

Speed is generally the change in distance per unit time. (rate of change of distance)

To calculate speed, we will use speed = distance/time.

speed = 360/3

           = 120km/hr

Since, the train is moving with a constant speed the ratio of distance and time will be equal to 120 throughout the journey.

120 = d/t

Hence, d = 120t.

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Answer:correct

Step-by-step explanation: If you distribute the 3 to 9 and 15 you will get this,

3x9 + 15x3

27 + 45

the slope of the line is zero, as change in y cordintae is 0.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

In the given line in the graph, the change in y coordinate is 0.

We know that slope = change in y / change in x

As the change in y coordinate is 0.

The slope of the line will be zero.

Hence, the slope of the line is zero.

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The solution of the inequality –5 ≥ –1 + s will be less than or equal to negative 4.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

–5 ≥ –1 + s

Simplify the inequality, then the value of the variable 's' is given as,

–5 ≥ –1 + s

–5 + 1 ≥ s

s ≤ –4

The solution of the inequality –5 ≥ –1 + s will be less than or equal to negative 4.

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