what is the quotient when x^3-5x^2+3x-8 is devided by x-3

ANSWER

One real root.

EXPLANATION

The graph of the function

[tex]f(x) = {x}^{3} + 6{x}^{2} + 12x + 8[/tex]

is shown in the attachment.

According to the Fundamental Theorem of Algebra, this function must have 3 roots including real and complex roots.

The x-intercepts gives the number of real roots.

Observe that the graph has only one intercept.

This implies that, the equation:

[tex]{x}^{3} + 6{x}^{2} + 12x + 8 = 0[/tex]

has only one real solution.

Answer:

This should help you !!!

Four 2 bedroom apartments and two 3 bedroom apartments were vacant.

It is given that Campus rentals rents 2 and 3 bedrooms apartments for $700 and $900 a month respectively. Last month they had six vacant apartments and reported $4600 in lost rent.  

We have to find out that how many of each type of apartment were vacant ?

What is algebra ?

Algebra is the branch of mathematics that deals with various symbols and the arithmetic operations and the symbols are called variables.

Let's assume that ;

Number of vacant 2 bedroom apartments = x

Number of vacant 3 bedroom apartments = y

∵ The total number of vacant apartments were 6 ; the equation will be ;

x + y = 6 -------- Equation 1

or

x = 6 - y

The loss reported is $4600.

We can write it as ;

x × 700 + 900 × y = 4600

700 × ( 6 - y ) + 900 × y = 4600

4200 - 700 y + 900 y = 4600

200 y = 400

y = 2

putting this in equation 1 we get ;

x = 6 - 2 = 4

Thus , four 2 bedroom apartments and two 3 bedroom apartments were vacant.

To learn more about algebra click here ;

https://brainly.com/question/11164534

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Answer:

95:95:19

Step-by-step explanation:

1.Divide 209 by 11.(209÷19)

2.Multiply 19×5 since 5/11 of the coins are nickels.(19×5=95)

3.Multiply 19×5 again since 5/11 of the coins are dimes.(19×5=95)

4.Multiply 19×1 since there would be 1/11 left of the coins which are quarters. (19×1=19)

5.Check your awnser by adding 95+95+19.(95+95+19=209)

Answer:

a) The equation is (y - 1)² = -8 (x - 4)

b) The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

Step-by-step explanation:

a) Lets revise the standard form of the equation of the parabola with a

   horizontal axis

# (y - k)² = 4p (x - h), (h , k) are the coordinates of its vertex and p ≠ 0

- The focus of it is (h + p , k)

* Lets solve the problem

∵ The focus is (2 , 1)

∵ focus is (h + p , k)

∴ h + p = 2 ⇒ subtract p from both sides

∴ h = 2 - p ⇒ (1)

∴ k = 1

∵ It opens left, then the axis is horizontal and p is negative

∴ Its equation is (y - k)² = 4p (x - h)

∵ k = 1

∴ Its equation is (y - 1)² = 4p (x - h)

- The parabola contains point (2 , 5), substitute the coordinates of the

 point in the equation of the parabola

∴ (5 - 1)² = 4p (2 - h)

∴ (4)² = 4p (2 - h)

∴ 16 = 4p (2 - h) ⇒ divide both sides by 4

∴ 4 = p (2 - h) ⇒ (2)

- Use equation (1) to substitute h in equation (2)

∴ 4 = p (2 - [2 - p]) ⇒ open the inside bracket

∴ 4 = p (2 - 2 + p) ⇒ simplify

∴ 4 = p (p)

∴ 4 = p² ⇒ take √ for both sides

∴ p = ± 2, we will chose p = -2 because the parabola opens left

- Substitute the value of p in (1) to find h

∵ h = 2 - p

∵ p = -2

∴ h = 2 - (-2) = 2 + 2 = 4

∴ The equation of the parabola in standard form is

  (y - 1)² = 4(-2) (x - 4)

∴ The equation is (y - 1)² = -8 (x - 4)

b) Lets revise the equation of the ellipse

- The standard form of the equation of an ellipse with  center (h , k)

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k )  

- The coordinates of the foci are (h ± c , k), where c² = a² - b²  

* Now lets solve the problem

∵ Its vertices are (-4 , 4) and (6 , 4)

∵ The coordinates of the vertices are (h + a , k ) and (h - a , k)  

∴ k = 4

∴ h + a = 6 ⇒ (1)

∴ h - a = -4 ⇒ (2)

- Add (1) and (2) to find h

∴ 2h = 2 ⇒ divide both sides by 2

∴ h = 1

- Substitute the value of h in (1) or (2) to find a

∴ 1 + a = 6 ⇒subtract 1 from both sides

∴ a = 5

∵ The foci at (-2 , 4) and (4 , 4)

∵ The coordinates of the foci are (h + c , k) , (h - c , k)

∴ h + c = 4

∵ h = 1

∴ 1 + c = 4 ⇒ subtract 1 from both sides

∴ c = 3

∵ c² = a² - b²

∴ 3² = 5² - b²

∴ 9 = 25 - b² ⇒ subtract 25 from both sides

∴ -16 = -b² ⇒ multiply both sides by -1

∴ 16 = b²

∵ a² = 25

∵ The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1

∴ The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) How to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

 then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

∵ x² + 4y² - 6x - 7 = 0

∵ The general form of the conic equation is

   Ax² + Bxy + Cy² + Dx + Ey + F = 0  

∴ A = 1 and C = 4

∵ If A and C are nonzero, have the same sign, and are not equal  to

  each other, then the graph is an ellipse.

∵ x² + 4y² - 6x - 7 = 0 ⇒ re-arrange the terms

∴ (x² - 6x ) + 4y² - 7 = 0

- Lets make x² - 6x completing square

∵ 6x ÷ 2 = 3x

∵ 3x = x × 3

- Lets add and subtract 9 to x² - 6x to make the completing square

 x² - 6x + 9 = (x - 3)²

∴ (x² - 6x + 9) - 9 + 4y² - 7 = 0 ⇒ simplify

∴ (x - 3)² + 4y² - 16 = 0 ⇒ add 16 to both sides

∴ (x - 3)² + 4y² = 16 ⇒ divide all terms by 16

∴ (x - 3)²/16 + 4y²/16 = 1 ⇒ simplify

∴ (x - 3)²/16 + y²/4 = 1

∴ The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

Answer: I'm pretty sure it's 200x - 120x = 1,200

Step-by-step explanation:

Answer:

200x - 120x = 1,200

Step-by-step explanation:

The break-even point is when the amount of money he spends equals the amount he earns.  

Let's see how much he earns and how much he spends per month:

He earns $200 per hour. If x represents the number of hours per month, we can write the earns as 200x.

He spends $1,200 per month and $120 per hour. We can write it as 1,200 + 120x.

So, we need 200x = 1,200 + 120x

We don't have this exact equation in our options but if we subtract 120x from both sides, we have:

200x - 120x = 1,200 + 120x - 120x

200x - 120x = 1,200

The correct answer is the first equation.

Answer:

29

Step-by-step explanation:

(5k-3) + (9+k) = 180

6k + 6 = 180

6k = 174

k = 29

mark brainliest please (button next to the thanks button)

Answer:

k equals 29 degrees

Step-by-step explanation:

a line equals 180 degrees so you set the sum of the variables equal to 180 and solve for k

Answer:

Step-by-step explanation:

Put the value of x = 0.3 to the equation 5x + 2y = 20, and solve it for y:

5(0.3) + 2y = 20

1.5 + 2y = 20           subtract 1.5 from both sides

2y = 18.5          divide both sides by 2

y = 9.25

Answer:

-1.25, 2, 3.5

Step-by-step explanation:

(x-2)(2x-7)(4x+5)=0

(2x^2-7x-4x+14)(4x+5)=5

from now on you know that either

(2x^2-7x-4x+14)=0 or

(4x+5)=0

By solving the first eqation (2x^2-7x-4x+14)=0

you get x = 2 or 3.5

By solving the second equation (4x+5)=0

you get x = -1.25

Answer:

x=8*2

Step-by-step explanation:

Answer:

[tex]8(2)^{x-1}[/tex]

Step-by-step explanation:

Pacey's computer is infected with a virus. The number of files the virus corrupts doubles every 8 minutes.

That means at every 8 minutes interval sequence becomes 8, 8 × 2, 8 × 2 × 2,.....

So the sequence is a geometric sequence.

Explicit formula of geometric sequence is

[tex]A_{x}=A_{0}(r)^{x-1}[/tex]

When[tex] A_{x}[/tex] = xth term

[tex]A_{0}[/tex] = first term

x = number of term

and r = common ratio

Here [tex]A_{0}[/tex] = 8 and r = [tex]\frac{8\times2}{8}[/tex] = 2

So expression representing the number of files corrupted will be [tex]A_{x}[/tex] = [tex]8(2)^{x-1}[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-3y-2z=-3&(1)\\3x+2y-z=12&(2)\\-x-y+4z=3&(3)\end{array}\right\\\\\text{add both sides of the equations (1) and (3):}\\\\\underline{+\left\{\begin{array}{ccc}x-3y-2z=-3\\-x-y+4z=3\end{array}\right}\\.\qquad-4y+2z=0\qquad\text{add 4y to both sides}\\.\qquad2z=4y\qquad\text{divide both sides by 2}\\.\qquad\boxed{z=2y}\\\\\text{Put it to (2)}:\\\\3x+2y-2y=12\\3x=12\qquad\text{divide both sides by 3}\\\boxed{x=4}\\\\\text{Put the value of x to (1) and (3):}[/tex]

[tex]\left\{\begin{array}{ccc}4-3y-2z=-3&\text{subtract 4 from both sides}\\-4-y+4z=3&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3y-2z=-7&\text{multiply both sides by 2}\\-y+4z=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-6y-4z=-14\\-y+4z=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-7y=-7\qquad\text{divide both sides by (-7)}\\.\qquad\boxed{y=1}\\\\\text{Put the value of y to the second equation:}[/tex]

[tex]-1+4z=7\qquad\text{add 1 to both sides}\\4z=8\qquad\text{divide both sides by 4}\\\boxed{z=2}[/tex]

Answer:

C≈1256.64in

Step-by-step explanation:

C=πd=π·400≈1256.63706in

Hope this helps!

Answer:

i  need mesurements

Step-by-step explanation:

It took 45 square units of gold foil to cover the entire pyramid trophy, including the bottom.

To find the amount of gold foil needed to cover the square pyramid-shaped trophy, we need to calculate the total surface area of the pyramid, including the base.

A square pyramid consists of the following surfaces:

1. The base (which is a square)

2. Four triangular faces

First, let's find the area of the base. Since it's a square, we can use the formula for the area of a square:

[tex]\[ \text{Area of the base} = \text{side}^2 \][/tex]

Given that the side of the square base is 3 units, the area of the base is:

[tex]\[ \text{Area of the base} = 3^2 = 9 \text{ square units} \][/tex]

Next, let's find the area of each triangular face. Since it's a regular pyramid, all four triangular faces have the same dimensions and area. We'll use the formula for the area of a triangle:

[tex]\[ \text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Given that the base of each triangular face is the side length of the square base (which is 3 units) and the height of the pyramid is 6 units, the area of each triangular face is:

[tex]\[ \text{Area of a triangle} = \frac{1}{2} \times 3 \times 6 = 9 \text{ square units} \][/tex]

Since there are four identical triangular faces, the total area of all four faces combined is:

[tex]\[ \text{Total area of all four triangular faces} = 4 \times 9 = 36 \text{ square units} \][/tex]

Now, let's calculate the total surface area of the pyramid by adding the area of the base and the total area of all four triangular faces:

[tex]\[ \text{Total surface area} = \text{Area of the base} + \text{Total area of all four triangular faces} \][/tex]

[tex]\[ = 9 + 36 = 45 \text{ square units} \][/tex]

Therefore, it took 45 square units of gold foil to cover the entire pyramid trophy, including the bottom.

Complete question:

Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the chair free including the bottom​.

Answer:

Jenn

Step-by-step explanation:

Natalie and Beth swim at about the same speed. Kara swims twice as fast as Beth so she also swims twice as fast as Natalie. So Kara is faster than Natalie and Jenn is faster than Kara. Therefore Jenn is faster than Natalie.

Hope This Helps :]

Final answer:

Jenn is faster than Natalie because she swims faster than Kara who swims almost twice as fast as Beth, and Natalie swims about the same speed as Beth.

Explanation:

The question pertains to comparing the speeds of different swimmers, which is a logical, rather than numerical comparison. Kara swims almost twice as fast as Beth, and Natalie swims about the same speed as Beth. Jenn swims faster than Kara.

Therefore, Jenn is the fastest swimmer among the four. Since the comparison is between Natalie and Jenn, and we have already established that Jenn swims faster than Kara, who in turn swims faster than Beth (and Natalie swims at the same speed as Beth), it is logical to conclude that Jenn is faster than Natalie.

Answer:

x = -8   &   at x = 3

Step-by-step explanation:

This is a rational function.

We can get the values of x at which vertical asymptotes occur by setting the denominator equal to 0 and solving for x.

Let's do this:

[tex]x^2+5x-24=0\\(x+8)(x-3)=0\\x=-8,3[/tex]

Hence, vertical asymptotes occur at x = -8 & at x = 3

-2z +2

-3z+z+2 distribute the - to make them positive

-3z+z equals -2z

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Inverse proportion equation has this form:

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

Where  "k" is the constant of variation.

We know that  "y" is inversely proportional to "x" and when [tex]x=3[/tex], [tex]y=6[/tex]

Then, we can substittute these values into the equation and solve for "k" to  find its value:

[tex]6=\frac{k}{3}\\\\6*3=k\\\\k=18[/tex]

Finally, we need to substitute "k" and [tex]y=9[/tex] into the equation and solve for "x":

[tex]9=\frac{18}{x}\\\\x=\frac{18}{9}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

y is inversely proportional to x is written as:

x ∝ 1/y

When the proportion is removed, a constant is introduced. We have to find the constant first to find the value of x in y = 9

So,

Removing the proportionality symbol will give us:

x=k/y

As we know that x=3 for y=6 so

3 = k/6

3*6=k

So,

k=8

Hence the value of proportionality constant is 8.

Now putting the value of y which is 9

x=k/y

=>x=18/9

=>x=2

Answer:

Step 2: Olivia incorrectly determined 1/2 of 10% of 720

Step-by-step explanation:

1/2 of 720 = 360

10% of 720 = .10*720 = 72

1/2 of 72 = 36

This is not the same as 31

This is the incorrect step

Step 2

Answer:

Step 2: Olivia incorrectly determined One-half of 10% of 720.Step-by-step explanation:

Answer: im sorry i dont knoey888888888888888888888hjk.

Step-by-step explanation:

Answer:

The mean of this data set is  [tex]\mu = 24[/tex]

Step-by-step explanation:

By definition, the mean of a data set [tex]x_1, x_2, x_3, ..., x_n[/tex] is

[tex]\mu = \frac{\sum^n_i x_i}{n}[/tex]

Where n is the total number of data.

In this case we have 7 data

12, 13, 15, 28, 28, 30, 42

So the mean is:

[tex]\mu = \frac{12+ 13 +15 +28 +28 +30+ 42}{7}[/tex]

[tex]\mu = 24[/tex]

Find the difference between the two prices:

617.40 - 420 = 197.40

Now divide the difference by the wholesale price:

197.40 / 420 = 0.47 = 47% markup.

The percent markup when retail price is $617.40 and wholesale price is 420.00 is 47%.

To calculate the percent markup on the snowblower, we need to find the difference between the retail price and the wholesale price, and then divide that by the wholesale price. The markup is the amount added to the cost of the goods to cover overhead and profit.

Therefore, the percent markup on the snowblower is 47%.

Answer:

[tex]-\frac{3}{4}[/tex]  meters

Step-by-step explanation:

From the answer choices, we basically need to find which of them is between   [tex]-\frac{1}{2}[/tex]  and  [tex]-1\frac{2}{3}[/tex]

Converting all of them to decimals would make it really easier:

So we need to find number between -0.5  and -1.67

Answer choice A is -2.33

Answer choice B is  -0.75

Answer choice C is  -0.25

Answer chioce D is  -1.83

So which number, from the choices, is between -0.5 & -1.67?

Clearly, it is -0.75, or,  [tex]-\frac{3}{4}[/tex]  meters

Answer:

B) y=3(1/3)^x

Step-by-step explanation:

Based on the graph, y intercept = 3

So you can plug in x =0 in each functions given in the options to see which one has y-intercept = 3

y= 3 (1/3)^x  ; when x = 0, y = 3 * 3^0 = 3 * 1 = 3

Answer:

The correct option is B) [tex]y=3(\frac{1}{3})^{x}[/tex]

Step-by-step explanation:

Consider the provided graph:

The general formula for equation of exponential decay is: [tex]y=ab^{x}[/tex] where [tex]b<1[/tex]

The graph of exponential decay [tex]y=ab^{x}[/tex] where [tex]b<1[/tex] as shown in figure 1:

From the figure 1, it is clear that a represents the y intercept and the coordinates are (0,a).

Now, consider the provided Graph:

The y intercept is (0,3)

Therefore, the value of a must be 3.

Now, consider the provided options, only option B) has the value of a = 3.

Therefore, the correct option is: B) [tex]y=3(\frac{1}{3})^{x}[/tex] .

Answer:

The value of (g*h) (-3)  is [tex]=-\frac{112}{3}[/tex]

Step-by-step explanation:

If [tex]g(x) = x+\frac{1}{x}-2[/tex] and [tex]h(x)=4-x[/tex]

We have to find (g*h) (-3)

First multiply g(x) with f(x)

[tex] (x+\frac{1}{x}-2)\times (4-x)[/tex]

[tex]Distribute\:parentheses[/tex]

[tex]=x\cdot \:4+x\left(-x\right)+\frac{1}{x}\cdot \:4+\frac{1}{x}\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab[/tex]

[tex]=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x[/tex]

simplify

[tex]=-x^2+6x+\frac{4}{x}-9[/tex]

Now, put x= -3 in above expression

[tex]=-(-3)^2+6(-3)+\frac{4}{-3}-9[/tex]

[tex]=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)[/tex]

[tex]=\left(-\frac{16}{3}\right)\left(4+3\right)[/tex]

[tex]=7\left(-\frac{16}{3}\right)[/tex]

[tex]=-\frac{16}{3}\cdot \:7[/tex]

[tex]=-\frac{112}{3}[/tex]

Therefore, the value of (g*h) (-3) is [tex]-\frac{112}{3}[/tex]

Answer:

Average rate of change = -6

Step-by-step explanation:

The average rate of change over the interval (a,b) is given by;

[ f(b) - f(a)] / (b-a)........................where interval is (a,b)

(a,b) interval =(-3,1)

Where;

f(x)= -12 (x+2)² +5

[tex]f(a)=f(-3)=-12(-3+2)^2+5\\f(a)=f(-3)=-12(-1)^2+5\\f(a)=f(-3)=-12(1)+5\\=-12+5=-7\\\\\\f(b)=f(1)=-12(1+2)+5\\f(b)=f(1)=-12(3)+5\\=-36+5=-31\\\\f(b)-f(a)=-31--7=-24\\\\b-a=1--3=4\\\\f(b)-f(a)/b-a=\frac{-24}{4} =-6[/tex]

Answer:

[tex]\sqrt{13}\ units[/tex]

Step-by-step explanation:

we have

[tex]R(1, -1), S(6, 1),T(8, 5),U(3, 3)[/tex]

Plot the vertices

see the attached figure

The shorter diagonal is SU

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]S(6, 1),U(3, 3)[/tex]

substitute

[tex]SU=\sqrt{(3-1)^{2}+(3-6)^{2}}[/tex]

[tex]SU=\sqrt{(2)^{2}+(-3)^{2}}[/tex]

[tex]SU=\sqrt{13}\ units[/tex]

Answer:

Man cant really get more in depth than the other answer!

Answer is √(13) :D

Answer:a -10

Step-by-step explanation:

-10 +8 = 2

ANSWER

[tex]x = - 10[/tex]

EXPLANATION

The given equation

[tex]x + 8 = - 2[/tex]

This is a linear equation in x.

To solve this equation, we add the additive inverse of 8 to both sides to get;

[tex]x + 8 + - 8 = - 2 + - 8[/tex]

We simplify to get:

[tex]x + 0 = - 10[/tex]

This implies that,

[tex]x = - 10[/tex]

The correct answer is A.

Your question is so confused. Are you looking for the measure of angle B?

Below is my work on how to find the angle B.

Answer:

B = 46°

Step-by-step explanation:

Cos(B) = Adj./Hypo.

Cos(B) = AB/BC

Cos(B) = 20/29

Cos(B) = 0.6897

B = Cos^-1(0.6897)

B = 46°

For this case we have to define trigonometric relations of rectangular triangles that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]cos (B)= \frac {20} {29}\\cos (B)= 0.689655172414[/tex]

So:

[tex]B = arccos (0.689655172414)\\B = 46.39718103[/tex]

Rounding off we have that B is 46 degrees

Answer:

46 degrees

Answer:

[tex]648\ yd[/tex]

Step-by-step explanation:

step 1

Find the circumference of the complete circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=35\ yd[/tex]

substitute

[tex]C=2\pi(35)[/tex]

[tex]C=70\pi\ yd[/tex]

step 2

Find the measure of the arc length for a central angle of 280 degrees

Remember that the circumference subtends a central angle of 360 degrees

so by proportion

[tex]\frac{70\pi}{360}=\frac{x}{280}\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd[/tex]

step 3

Find the perimeter of the playground

[tex]P=54.44\pi+45=54.44*3.14+45=215.96\ yd[/tex]

Multiply by 3

[tex]215.96*(3)=647.87\ yd[/tex]

Round to the nearest integer

[tex]647.87=648\ yd[/tex]