What is the domain of the function below?

f(x) = -3x³ + 2x² - 5
(-∞, 0.444)
[0, ∞)
(-∞, 0)
(-∞, ∞)

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

To know more about right triangle, click on the link

https://brainly.com/question/2437195

#SPJ1

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

Know more about probability here:

https://brainly.com/question/28924396

#SPJ1

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:

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]

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

$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

To know more about equity check the link below

https://brainly.com/question/28148396

#SPJ1

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

to learn more about similar questions:

https://brainly.com/question/17849908

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.

To learn more about speed visit the link below:

brainly.com/question/28224010

#SBJ4

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

Learn more about a rhombus here:

https://brainly.com/question/23432950

#SPJ1

The age of Lance and Chad are 7 years and 20 years respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let age of Lance's is  = L

Age of Chad's = C

Given that The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age.

The system of equations that represents this situation is;

L + c = 27

C - 6 = 2L

2L - c = -6------ (1)

Therefore,

⇒ ( 2L - c ) + (L + c) = 21

⇒ 3L = 21------- (2)

L = 7

C = 20

Therefore the age of each person;

7 years and 20 years

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

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

Read more about least-squares at

https://brainly.com/question/24309895

#SPJ1

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.

To know more about Parallelogram:

https://brainly.com/question/11220936

#SPJ2

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

Answer:

Step-by-step explanation:

0.15625

Answer:

15/8

Step-by-step explanation:

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].

To learn more about Quadratic equation's refer to:

https://brainly.com/question/1214333

#SPJ1

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

To learn more about Quadratic equation's refer to:

brainly.com/question/1214333

#SPJ1

Answer:

3 cats are orange and The other 1 is not

Because

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).

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

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.

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.

Learn more about Slope, by the following link

https://brainly.com/question/3493733

#SPJ1

Answer:

Step-by-step explanation:

First question. Answer is

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.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

Jack spend $15 on sweets

Jack spend $35 on magazines

Jack saves $50

Given,

Jack spends 15 % of his pocket money on sweets and 35 % on magazines.

Jack save the rest ; 100 - (15 + 35) = 100 - 50 = 50%

Here,

If Jack has a pocket money of $100

The money he spends on sweets = 15% of 100 = $15

The money he spends on magazines = 35% of 100 = $35

Then,

The money he saves = 50% of 100 = $50

Learn more about savings here;

https://brainly.com/question/14860498

#SPJ4

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]

To learn more about the perimeter of polygon from the given link.

https://brainly.com/question/15387363

#SPJ1

Answer:

[tex]y=-4x+5[/tex]

Step-by-step explanation:

The equation of a line with slope [tex]m[/tex] and [tex]y[/tex]-intercept [tex](0,b)[/tex] is [tex]y=mx+b[/tex].

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]

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

Answer:correct

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

3x9 + 15x3

27 + 45

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

Learn more about linear functions:

https://brainly.com/question/29213103

#SPJ1