Factorize this equation:
6=x^2-x

It's easier to sketch if you simplify [tex]f(x)[/tex]. Factorize the numerator and denominator - simple to do with a difference of cubes or squares.

[tex]\dfrac{x^3 - 1}{x^2 - 1} = \dfrac{(x - 1)(x^2 + x + 1)}{(x - 1) (x + 1)}[/tex]

If [tex]x\neq1[/tex], we can cancel the factors of [tex]x-1[/tex]. Note that [tex]f(1)[/tex] itself is undefined. For all intents and purposes, aside from the singularity at [tex]x=1[/tex], the graph of [tex]f(x)[/tex] will look exactly like the graph of

[tex]\dfrac{x^2 + x + 1}{x + 1}[/tex]

Now, rewrite this as

[tex]\dfrac{x(x + 1) + 1}{x + 1}[/tex]

Then when [tex]x\neq-1[/tex] (note that [tex]f(-1)[/tex] is also undefined), we can cancel [tex]x+1[/tex] to reduce this to

[tex]x + \dfrac1{x+1}[/tex]

On its own, the graph of [tex]x[/tex] is a line through the origin. When [tex]x[/tex] is a large number [tex]\frac1{x+1}[/tex] is small. But as [tex]x[/tex] gets closer to -1, the rational term blows up. Effectively, this means the graph of [tex]f(x)[/tex] looks like [tex]\frac1{x+1}[/tex] around [tex]x=-1[/tex], and far enough away it looks like [tex]x[/tex].

See the attached plot for a sketch of these details.

The angle of elevation for two parasailing boats traveling at the same speed is equal because they have the same length of tow line.

Parasailing is also referred to as parascending and it can be defined as a recreational activity which involves a person wearing an open parachute (canopy wing) and gliding through the air, while being towed by a boat.

By critically observing the image shown below, we can infer and logically deduce that the reason why the angle of elevation for two parasailing boats traveling at the same speed is equal, is simply because they have the same length of tow line.

Read more on parasailing here: https://brainly.com/question/11450151

#SPJ1

Complete Question:

Why is the angle of elevation for two parasailing boats traveling at the same speed equal?

There is no relationship between the number of hours cycled and the number of hours worked (Option D).

A scatterplot is a graph that is used to show the association between two variables. The relationship between the variables is shown by the use of  line of best fit.

From the scatterplot shown, we can conclude that there is no relationship between the number of hours cycled and the number of hours worked (Option D).

Learn more about scatterplot:https://brainly.com/question/25280625

#SPJ1

The balance in the Work in Process Inventory on January 1, if this was the only unfinished job for Ryan Company, is $18,200.

The work-in-process inventory is made up of the costs of direct materials, direct labor, and manufacturing overhead at the beginning or end of the period.

Work in Process Balance on January 1:

Direct materials $6,300

Direct labor $7,000

Manufacturing overhead $4,900

Total = $18,200

What was the balance in the Work in Process Inventory on January 1 if this was the only unfinished job?

Thus, the balance in the Work in Process Inventory on January 1, if this was the only unfinished job for Ryan Company, is $18,200.

Learn more about calculating work in process inventory at https://brainly.com/question/12944780

#SPJ1

Answer:

[tex]967.6cm^{2} (1 d.p)[/tex]

Step-by-step explanation:

Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]

Given from the question, r = 7 cm and h = 15cm

Lets Substitute r and h into the formula to find the Total Surface Area of the cylinder.

Total Surface Area of Cylinder = [tex]2\pi (7)(15)+2\pi (7)^{2} \\=210\pi +98\pi \\=308\pi cm^{2} \\=967.6cm^{2} (1 d.p)[/tex]

Answer:

[tex]\sf x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}[/tex]

Explanation:

[tex]\sf Given : x^2 + x + 1 = 0[/tex]

Solve it using quadratic formula

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad \:when\: \: ax^2 + bx + c = 0[/tex]

So, here constants are: a = 1, b = 1, c = 1

When the value's are substituted inside the formula

[tex]\sf \rightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(1)} }{2(1)}[/tex]

[tex]\sf \rightarrow x = \dfrac{-1 \pm \sqrt{-3} }{2}[/tex]

[tex]\sf \rightarrow x = \dfrac{-1 \pm i\sqrt{3} }{2}[/tex]

[tex]\sf \rightarrow x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}[/tex]

The answers are :

This problem can be solved using the quadratic equation.

x = -1 ± √1² - 4(1)(1) / 2a

x = -1 ± √1 - 4 / 2a

x = -1 ± √-3 / 2a

x = -1 ± i√3 / 2a (∴ i = √-1)

The possible values of x are :

Answer:

24ft high

Step-by-step explanation:

Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.

For any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies.  The Pythagorean Theorem describes the relationship between side lengths as [tex]a^2+b^2=c^2[/tex], where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle).  Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".

Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.

Substitute known values, and simplify...

[tex]a^2+(10)^2=(26)^2[/tex]

[tex]a^2+100=676[/tex]

Subtract 100 from both sides...

[tex](a^2+100)-100=(676)-100[/tex]

[tex]a^2=576[/tex]

Apply the square root property...

[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]

[tex]a=\pm 24[/tex]

[tex]a=24[/tex]  or  [tex]a=- 24[/tex]

Since the distance height the ladder will reach is not a negative number, we reject the negative solution.  Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.

The equivalent expression of [tex]\sqrt{-12}[/tex] is [tex]2\sqrt{-3}[/tex]

The expression is given as:

[tex]\sqrt{-12[/tex]

Express -12 as 4 * -3

[tex]\sqrt{-12} = \sqrt{4 * -3}[/tex]

Expand the expression

[tex]\sqrt{-12} = \sqrt{4} * \sqrt{-3}[/tex]

Take the positive square root of 4

[tex]\sqrt{-12} = 2 * \sqrt{-3}[/tex]

Evaluate the product

[tex]\sqrt{-12} = 2\sqrt{-3}[/tex]

Hence, the equivalent expression of [tex]\sqrt{-12}[/tex] is [tex]2\sqrt{-3}[/tex]

Read more about equivalent expression at:

https://brainly.com/question/27911936

#SPJ1

The equation  that can be used to calculate the surface area of the triangular prism net shown below is mathematically given as

SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)  

Generally, The region or area that is occupied by the surface of any particular item is referred to as that object's surface area.

In conclusion, the equation surface area of the triangular prism will be one that accommodates all parameters

SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)  

SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)  

Read more about the surface area

https://brainly.com/question/2835293

#SPJ1

The slope is 4 and the y-intercept is 6.

The slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

Attached is an image of the graph.

Answer:

  $959.68

Step-by-step explanation:

The loan amortization formula can be used to find the payment amount.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

A = payment amount; P = principal borrowed; r = annual interest rate; t = number of years; n = payments per year (and number of times interest is compounded per year).

For a principal amount of $33,000 at an interest rate of 3%, the 36 monthly payments will be ...

  A = $33000(0.03/12)/(1 -(1 +0.03/12)^(-12·3)) ≈ $959.68

The monthly payments will be $959.68.

The question was incomplete. Below you will find the missing content.

Use the system of equations and graphs below to complete the sentence.

x - 2y = 5

3x + 15y = -6

The graph that correctly represents the given system of equations is a graph ( ), and the solution to the system is ( , ).

The correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).

Given the first equation is x-2y=5

in this equation of line, the x-coordinate is:

x-(2.0)=5

⇒ x=5

The x-coordinate will be (5,0).

in this equation of line, the y-coordinate is:

0- 2y=5

⇒y= -5/2

The y-coordinate will be (0,-5/2).

So the first line equation has x-coordinate (5,0) and y-coordinate (0,-5/2).

Similarly,

Given the second equation is 3x+15y=-6

in this equation of line, the x-coordinate is:

3x+(15.0)=-6

⇒ x=6/3=2

The x-coordinate will be (2,0).

in this equation of line, the y-coordinate is:

(3.0)+15y=-6

⇒y= -6/15= -2/5

The y-coordinate will be (0,-2/5).

So the second line equation has x-coordinate (2,0) and y-coordinate (0,-2/5).

Equation-1: x - 2y = 5

⇒x =2y+5

putting the value of x in equation-2

3x + 15y = -6

⇒ 3(2y+5)+15y=-6

⇒6y+15+15y=-6

⇒21y=-6-15=-21

⇒y=-21/21=-1

putting the value of y in equation of x

x= 2(-1)+5= -2+5= 3

The solution of system of equations will be (3,-1)

Checking all the options

In option B one line has  x-coordinate (5,0) and y-coordinate (0,-5/2) and another line has x-coordinate (2,0) and y-coordinate (0,-2/5).

And the point of intersection of two lines is (3,-1).

Therefore the correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).

Learn more about the system of equations

here: https://brainly.com/question/14323743

#SPJ10

Answer:

x=10000

Step-by-step explanation:

the intersection points are (1, 7) and (4, 13), So the correct option is A.

To see that, we need to see when the two equations:

y = -x²+7x+1

y = 2x + 5

Can be solved simultaneously for a point (x, y). So we need to solve a system of equations.

y = -x²+7x+1

y = 2x + 5

We can rewrite:

-x²+7x+1 = y =  2x + 5

Then we can solve this for x:

-x²+7x+1 =  2x + 5

x² - 5x + 4 = 0

This is just a quadratic equation, the solutions are:

[tex]x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*(1)*(4)} }{2} \\\\x = \frac{5 \pm 3 }{2}[/tex]

So we have two values of x:

The correspondent values of y are:

y = 2*(4) + 5 = 13

y = 2*(1) + 5 = 7

Then the intersection points are (1, 7) and (4, 13)

Then the correct option is A. The dog will catch the frisbee.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer: 26 × 4

Step-by-step explanation: There are 26 letters in the alphabet lettered A through Z.

Deepak is given the choice of picking a four letter password of his liking, using any four letters. Since the letters he uses can be repeated, it is 26 * 4 possibilities, since there are 26 different possibilities of letters from the alphabet he could choose, for 4 times. Also, since letters can be repeated, 26 stays the same. If letters could not be repeated, it would be 26 * 25 * 24 * 23.

Answer:

B.  26⁴

Step-by-step explanation:

If the password is 4 letters long and he can repeat letters then:

Therefore, to find the total number of passwords he can create, simply multiply the number of permutations for each letter of his password:

⇒ 26 × 26 × 26 × 26 = 26⁴

Fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A

The given parameters are:

Energy A = 5.1 * 10^7

Energy B = 1.5 * 10^11

The amount of energy B in proportion to energy A is calculated as

Proportion = Energy B/Energy A

So, we have:

Proportion = (1.5 * 10^11)/(5.1 * 10^7)

Divide 1.5 by 5.1

Proportion = 0.2941 * 10^11/10^7

Divide 10^11 by 10^7

Proportion = 0.2941 * 10^4

Evaluate

Proportion = 2941

Hence, fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A

Read more about quotient at:

https://brainly.com/question/673545

#SPJ1

The value of x is 3 units.

We know that a portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

Given that FH is a line segment and FH = 18 units. G is a point on FH such that FG = 4x units and GH = 2x units.

So, we can write

4x + 2x = 18

i.e. 6x = 18

i.e. x = 18/6 = 3

Then, the value of x is 3 units. So, the first option is correct.

Learn more about line segments here -

https://brainly.com/question/20049098

#SPJ10

Answer: A / 3

Step-by-step explanation: edge 2022

Answer: Multiplying these factors gives the approximate volume of the original body

Step-by-step explanation:

The given convex body can be approximated by a sequence of nested bodies, eventually reaching one of known volume (a hypersphere), with this approach used to estimate the factor by which the volume changes at each step of this sequence.

Given :

Midpoint formula :

[tex]\boxed {M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})}[/tex]

Let's input the values !

⇒ M = (4 - 4 / 2, -5 + 5 / 2)

⇒ [tex]\boxed {M = (0,0)}[/tex]

The midpoint between the points is (0, 0).

The slope of the given line containing the given points is; 7.

The formula for slope of a line between two coordinates is;

Slope(m) = (y2 - y1)/(x2 - x1)

Now, let us take the last 2 coordinates which are;

(-1, 35) and (2, 56).

Thus, the slope is;

m = (56 - 35)/(2 - (-1))

m = 21/3

m = 7

Thus, the slope of the given line containing the given points is 7.

Read more about slope of a line at; https://brainly.com/question/3493733

#SPJ1

Answer:

B and D

Step-by-step explanation:

Both B and D cross over the point (4, 8) therefore they share the solution (4, 8)

33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long

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

12 inch = 1 ft

Total perimeter of patio not counting the side against the house = 12 + 12 + 14 = 38 feet

38 feet = 38 feet * 12 inch per feet = 456 in

Number of stone pavers needed = 456 in / 14 in = 32.57 ≅ 33

33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The end behavior of the function is the one in option C.

"One end increases and one end decreases"

Here we have the function:

f(x) = -ln(2x) + 4.

Remember that for the natural logarithm, as x tends to zero the function tends to negative infinity.

And as x tends to infinity, the natural logarithm tends to infinity.

So, for our function where we have a negative sign before the logarithm, as x tends to zero the function tends to infinity and as x tends to infinity the function tends to zero.

Then the correct option is C:

"One end increases and one end decreases"

If you want to learn more about end behaviors:

https://brainly.com/question/1365136

#SPJ1

The required mass of the solid is 8.52g. Hence option B is correct.

We have,
mb = mass/89.0, ΔTb = 2.42° C and Kb = 2.53°C•kg/mol.

Mass of the object is defined as the space occupied by an object.

Given equation, ΔTb=Kb x mb
2.42 = 2.53 x mb
mb =0.95
mass / 89.0 x 0.1 = 0.95
mass = 8.52 g

Thus, the required mass of the solid is 8.52g.

learn more about mass here:
https://brainly.com/question/19694949

#SPJ1

A circle is a curve sketched out by a point moving in a plane. If the distance from A to C is 6 units, then the distance from C to B is 6 units.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

If the distance from A to C is 6 units, then the distance from C to B is 6 units. This is because AC and BC are the radii of the circle, therefore, both are equal to each other.

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ1

Answer: c and 6

Step-by-step explanation:

The value of y when x= 2401 is -10

An inverse variation is represented as:

[tex]y = \frac{k}{\sqrt x}[/tex]

Where k is the proportionality constant

When y = -70, x = 49

So, we have:

[tex]-70 = \frac{k}{\sqrt {49}}[/tex]

Take the square root of 49

[tex]-70 = \frac{k}{7}[/tex]

Multiply through by 7

k = -490

Substitute k = -490 in [tex]y = \frac{k}{\sqrt x}[/tex]

[tex]y = -\frac{490}{\sqrt x}[/tex]

When x =2401, we have

[tex]y = -\frac{490}{\sqrt {2401}}[/tex]

Evaluate the square root

[tex]y = -\frac{490}{49}[/tex]

Divide

y = -10

Hence, the value of y when x= 2401 is -10

Read more about variation at:

https://brainly.com/question/14254277

#SPJ1

Answer:

9

Step-by-step explanation:

I believe the question is stating he can run 3 miles in 1 minute? Though it does make sense, here's the breakdown. :)

3 x 45 = 135 Miles total

135 / 15 = 9 "15" miles ran after 45 minutes.

If this is not what you meant to ask, let me know!

Answer:

3

Step-by-step explanation:

[tex]\frac{y+x}{xy} =3\\x+y=3xy\\xy+x+y=4\\xy+3xy=4\\4xy=4\\xy=1\\x^2y+xy^2=xy(x+y)=xy(3xy)=3(xy)^2=3(1)^2=3[/tex]

Answer:

3

Step-by-step explanation:

So we're given: [tex]\frac{1}{x} + \frac{1}{y} = 3[/tex] and that: [tex]xy+x+y=4[/tex]. And now we need to solve for: [tex]x^2y+xy^2[/tex].

Original equation:

[tex]\frac{1}{x} + \frac{1}{y} = 3[/tex]

Multiply both sides by xy

[tex]y+x=3xy[/tex]

Now take this and plug it as x+y into the second equation:

Original equation:

[tex]xy+x+y=4[/tex]

Substitute 3xy as x+y

[tex]xy + 3xy = 4[/tex]

Combine like terms:

[tex]4xy = 4[/tex]

Divide both sides by 4

[tex]xy=1[/tex]

Divide both sides by x:

[tex]y=\frac{1}{x}[/tex]

Original equation:

[tex]x^2y+xy^2[/tex]

Substitute 1/x as y

[tex]x^2(\frac{1}{x})+x(\frac{1}{x})^2[/tex]

Multiply values:

[tex]\frac{x^2}{x}+\frac{x}{x^2}[/tex]

Simplify:

[tex]x+\frac{1}{x}[/tex]

Substitute y as 1/x back into the equation:

[tex]x+y[/tex]

so now we just need to solve for x+y

Look back in steps to see how I got this:

[tex]y+x=3xy[/tex]

Divide both sides by 3

[tex]\frac{x+y}{3}=xy[/tex]

Original equation:

[tex]xy+x+y=4[/tex]

Substitute

[tex]\frac{x+y}{3}+x+y=4[/tex]

Multiply both sides by 3

[tex]x+y+3x+3y=12[/tex]

Combine like terms:

[tex]4x+4y=12[/tex]

Divide both sides by 4

[tex]x+y=3[/tex]

So now we finally arrive to our solution 3!!!!! I swear I felt like I was going in circles, and I was about to just stop trying to solve, because I had no idea what I was doing, sorry if I made some unnecessary intermediate steps.

Answer:

I am pretty positive it is thirty if you need work shown just let me know if it is wrong for some reason then I apologize.

Step-by-step explanation:

If the model is 15 inches. Then the length of the table will be 10 feet.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A table blueprint uses the scale 3 inches :2 feet.

The scale factor will be 2 feet: 3 inches.

If the model is 15 inches.

Then the length of the table will be

⇒ (2 feet/ 3 inches) x 15 inches

⇒ 2 x 5

⇒ 10 feet

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ2

The type of solution set of the given equation is; "No Solution"

Let's solve for x in the given equation;

8(3x - 2) - 4 = 8x + 4(4x - 3)

Expanding the bracket gives;

8(3x) + 8(-2) - 4 = 8x + 4(4x) + 4(-3)

24x - 16 - 4 = 8x + 16x - 12

24x - 20 = 24x - 12

Subtract 24x from both sides to get;

-20 = -12

This is a false equation as both sides are not the same number and as such the type of solution set is "No Solution"

Read more about equation solutions at; https://brainly.com/question/2972832

#SPJ1