what is the product? 4k+2/k^2-4*k-2/2k+1

Answers

Answer 1

[tex]\bf \cfrac{4k+2}{k^2-4}\cdot \cfrac{k-2}{2k+1}\implies \cfrac{2(2k+1)}{k^2-2^2}\cdot \cfrac{k-2}{2k+1}\implies \cfrac{2\underline{(2k+1)}}{\underline{(k-2)}(k+2)}\cdot \cfrac{\underline{k-2}}{\underline{2k+1}} \\\\\\ \cfrac{2}{k+2}\cdot \cfrac{1}{1}\implies \cfrac{2}{k+2}[/tex]

Related Questions

describe the vertical asymptotes) and holes) for the graph of y=(x+2)(x+4)/(x+4)(x+1)
A. asymtotes: x=-1 and hole: x=4
B. asymtotes: x=2 and hole: x=-1
C. asymtotes: x= -1 and hole: x=-4
D. asymtotes: x=1 and hole: x=4
Can someone plzzzz help me!??

Answers

For this case what you should do is check the points where the function is NOT defined.
The function is not defined for those values where the denominator is equal to zero.
We have then:
y = (x + 2) (x + 4) / (x + 4) (x + 1)
Studying the denominator:
(x + 4) (x + 1) = 0
x = -4
x = -1
Answer:
C. asymtotes: x = -1 and hole: x = -4

Consider the quadratic equation. x^2=4x-5. How many solutions does the equation have? a.) one real solution b.) two real solutions c.)no real solutions d.)cannot be determined

Answers

C - you have to check the discriminant (the number under the radical in the quadratic formula). If it’s positive, there are two real solutions. If it’s zero, just one. And if it’s negative, there are no real solutions.

I am pretty sure it is b.)two real solutions

Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.

Answers

Hello!

Here's what you know:

· Kevin's age is 4 times Daniel's age.
· Kevin's age is 6 more than Daniel's age.

In numbers:
· 4d
· d + 6

where d is Daniel's age. Kevin's age is constant, and both expressions represent his age, so you can set them equal to each other to solve for d.

4d = d + 6
4d - 6 = d
-6 = -3d
2 = d

Daniel is 2 and Kevin is 8.

I hope this helps you!

Does the function model exponential growth or decay? g(t)=1.7 * 0.8^t

Answers

Answer:

decay

just answered this question.

Step-by-step explanation:

Answer:

decaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecay

Step-by-step explanation:

. (02.02 HC) Dominic earns $18 an hour plus $25 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the week. Part A: Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 35 hours. (3 points) Part C: Dominic earned $730 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points) (10 points)

Answers

Part A)
Let
E-----------> the amount of money earned
x----------> hours working in a week-----> $18 an hour
we know that
E=18x ---------> equation that shows the amount of money earned for working x hours in a week
conditioned to x<= 35 hours--------> is no overtime

Part B)
Let
T----------------> the amount of money earned
y -------------- > hours of overtime-------> $25 an hour
for x=35 hour----------> E=18*35=$630
T=630+25y------> equation that shows the amount of wages earned for working y hours of overtime and 35 hour in a week

Part C)
if Dominic earned $730 in 1 week
$630------------> earned for working 35 hours in a regular week
[hours of overtime]=(730-630)/25=100/25=4 hours

[total hours worked]=35+4=39 hours

the answer is 39 hours (35 hours regular +4 hours overtime)

Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?

Answers

check the picture below.

notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.

make sure your calculator is in Degree mode.

Answer:

37.5 miles is the answer.

Step-by-step explanation:

Since car is travelling with a speed = 50 mph

Angle between the highway and the track on which the car is travelling = 30°

Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track

Distance traveled by the car in 1.5 hours = speed × time

= 50 × 1.5 = 75 mi.

Therefore sin 30° = x/75

x = 75×sin30° = 75 × 1/2 = 37.5 mi.

Therefore the answer is 37.5 mi away.

look at the pictures below

Answers

the answer might be negative one over 4 because it is the same but the red line is on negative

The formula represents the surface area S of a cube with side lengths x.

S=6x^2

Solve for x.

Answers

The solution of x is √(S/6).

The formula to find the surface area of a cube with side lengths x is:

S = 6x2

To solve for x:

Divide both sides by 6: S/6 = x2

Take the square root of both sides to isolate x: x = √(S/6)

What is the sum of the polynomials (m+n+3)(m+n+4)

Answers

(m + n + 3)(m + n + 4)
First distribute the m in the first set of parentheses to the second set of parentheses. Do the same process with the n and the 3.
m^2 + mn + 4m + mn + n^2 + 4n + 3m +3n + 12
Combine Like terms. Final Answer:
m^2 + n^2 + 2mn + 7m + 7n + 12

Answer:

2m+2n+7

Step-by-step explanation:

Given: Two polynomial

[tex]P_1=m+n+3[/tex]

[tex]P_2=m+n+4[/tex]

We need to find the sum of polynomial.

[tex]Sum=P_1+P_2[/tex]

[tex]\Rightarrow (m+n+3)+(m+n+4)[/tex]

write like term together

[tex]\Rightarrow m+m+n+n+3+4[/tex]

Combine the like term

[tex]\Rightarrow 2m+2n+7[/tex]

Hence, The sum of two polynomial is 2m+2n+7

what is the approximate distance between the points (-5 1) and (-2 3) on a coordinate grid

Answers

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& 1~) % (c,d) &&(~ -2 &,& 3~) \end{array}~~ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-2-(-5)]^2+[3-1]^2}\implies d=\sqrt{(-2+5)^2+(3-1)^2} \\\\\\ d=\sqrt{3^2+2^2}\implies d=\sqrt{13}[/tex]

What number is 22 spaces to the right of negative 7?

Answers

Your calculator will tell you it is 15.

Final answer:

By adding 22 to -7, we find that the number 22 spaces to the right of -7 on the number line is 15.

Explanation:

The question asks for the number that is 22 spaces to the right of negative 7 on a number line. To find this, you can simply add 22 to negative 7. Here's the calculation: -7 + 22 = 15. Therefore, the number that is 22 spaces to the right of negative 7 is 15. To determine the number that is 22 spaces to the right of -7 on the number line, we need to add 22 to -7. Moving 22 spaces to the right indicates an increase in value by 22. Therefore, when we add 22 to -7, we get the final answer of 15. This calculation reflects the concept that moving to the right on the number line corresponds to increasing the numerical value, while moving to the left corresponds to decreasing it. In this case, starting from -7 and moving 22 spaces to the right results in a value of 15. Hence, 15 is the number that is 22 spaces to the right of -7.

Use the quadratic formula to determine the exact solutions to the equation.

x^2−2x−4=0

Enter your answers in the boxes.

x=__ or x=___

Answers

Answer: " x = 1 + √5 " or " x = 1 − √5" .
______________________________________________________
Given:
______________________________________________________

" x² − 2x − 4 = 0 " ;
______________________________________________

Solve for "x" by using the "quadratic formula" :

Note: This equation is already written in "quadratic format" ; that is:

" ax² + bx + c = 0 " ; { "a [tex] \neq [/tex] 0" } ;

in which: "a = 1" {the implied coefficient of "1" ;
since "1", multiplied by any value, equals that same value};

"b = -2 " ;

"c = -4 " ;
_______________________________________________________
The quadratic equation formula:

x = { - b ± √(b² − 4 ac) } / 2a ; {"a[tex] \neq [/tex]0"} ;
______________________________________________________
Substitute our known values:
______________________________________________________

→ x = { - (-2) ± √[(-2)² − 4(1)(-4)] } / 2(1) ;

→ x = { 2 ± √(4 − 4(-4) } / 2 ;

→ x = { 2 ± √(4 − (-16) } / 2 ;

→ x = { 2 ± √(4 + 16) } / 2 ;

→ x = { 2 ± √(20) } / 2 ;

→ x = { 2 ± √4 √5} / 2 ;

→ x = { 2 ± 2√5} / 2 ;

→ x = 1 ± √5 ;

_______________________________________________________
→ "x = 1 + √5" or "x = 1 − √5" .
_______________________________________________________

Explain why the function f(x)=x^2 is not invertible

Answers

It doesn't pass the horizontal line test. (A function will be invertible if a horizontal line only crosses its graph in one place, for any location of that line.)

When you reflect the curve across the line y=x, it becomes multiple-valued, hence its inverse is not a function.

A circle has an arc of length 24pi that is intercepted by a central angle of 80 degrees. what is the radius of the circle?

Answers

circumference = 2pi r

80/360 x 2pi x r = 24pi
r = 54

The volume, V, of a soap bubble is related to its surface area, A. In cubic centimeters, this relationship is shown by the formula V = 0.094A 3/2. What is the surface area of a bubble with a volume of 5 cm3 ?

Answers

First let's rewrite the volume expression correctly:
V = 0.094 * (A) ^ (3/2)
Now we clear the area:
(A) ^ (3/2) = V / 0.094
A = (V / 0.094) ^ (2/3)
We now replace the volume:
A = (5 / 0.094) ^ (2/3)
A = 14.14364782 cm ^ 2
Answer:
The surface area of a bubble with a volume of 5 cm3 is:
A = 14.14364782 cm ^ 2

The surface area of a soap bubble with a volume of 5 cm³, given the relationship V = 0.094 [tex]A^{3/2[/tex], can be calculated by rearranging and solving the formula, resulting in an approximate surface area of 36.3 cm².

To find the surface area of a soap bubble with a volume of 5 cm³, using the given relationship V = 0.094 [tex]A^{3/2[/tex], we need to rearrange the formula to solve for A (the surface area). We will take the following steps to find A:

First, divide both sides of the equation by 0.094 to isolate [tex]A^{3/2[/tex] on one side:

[tex]A^{3/2[/tex] = V / 0.094

Next, substitute V = 5 cm³ into the equation:

[tex]A^{3/2[/tex] = 5 / 0.094

Calculate the right-hand side:

[tex]A^{3/2[/tex] ≈ 53.19

Finally, raise both sides of the equation to the power of 2/3 to solve for A:

A = [tex](53.19)^{2/3[/tex]

Calculating the right-hand side gives us the surface area A. After performing these calculations, we find that the surface area of a bubble with a volume of 5 cm³ is approximately 36.3 cm².

Are the two triangles are congruent ?

Answers

Yes, they're congruent because they're still in their original shape.

yes they are. they both have the same measurements.

Mr. Berger assigned the following system of equations to be solved for homework. 2x-3y = -12
4x+ y= -10
Which is the x-coordinate of the correct solution?

Answers

Answer:

A: x= -3

Step-by-step explanation:

The x- coordinate is of solution is -3.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

2x-3y = -12...........(1)

4x+ y= -10..............(2)

Now, multiply Equation (1) by 2 we get

4x - 6y = -24

4x + y = -10

________

-7y = -14

y= 2

and, 4x+ y= -10

4x + 2 = -10

4x = -12

x= -12/4

x= -3.

Hence, the x- coordinate is -3.

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Solve x + y + z = 12
2x – y – z = -6
x + 3y + 5z = 44

(4, 3, 5)

no solutions

(2, 4, -6)

(2, 4, 6)

Answers

The answer is (2,4,6)
Proof:

Solve the following system:{x + y + z = 12 | (equation 1){2 x - y - z = -6 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Swap equation 1 with equation 2:{2 x - y - z = -6 | (equation 1){x + y + z = 12 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:{2 x - y - z = -6 | (equation 1){0 x+(3 y)/2 + (3 z)/2 = 15 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Multiply equation 2 by 2/3:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2){0 x+(7 y)/2 + (11 z)/2 = 47 | (equation 3)
Multiply equation 3 by 2:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2)v0 x+7 y + 11 z = 94 | (equation 3)
Swap equation 2 with equation 3:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+y + z = 10 | (equation 3)
Subtract 1/7 × (equation 2) from equation 3:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+0 y - (4 z)/7 = (-24)/7 | (equation 3)Multiply equation 3 by -7/4:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Subtract 11 × (equation 3) from equation 2:{2 x - y - z = -6 | (equation 1){0 x+7 y+0 z = 28 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Divide equation 2 by 7:{2 x - y - z = -6 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Add equation 2 to equation 1:{2 x + 0 y - z = -2 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)Add equation 3 to equation 1:{2 x+0 y+0 z = 4 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Divide equation 1 by 2:{x+0 y+0 z = 2 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Collect results:

Answer: {x = 2, y = 4 , z = 6

PLEASE HELP! WILL MARK BRAINLIEST!

Answers

the amount of representative that stayed 2 nights: 25
The amount of those who rented a car: 11
11/25 = 0.44 or 44%

The ratio of zoya's age to nelya's age is 1:4. twenty years from now, nelya will be twice as old as zoya will be then. find their present ages.

Answers

A) 4*z = nelya
B) 2 * (z + 20) = nelya + 20
Inputting equation A into B)
2z + 40 = 4z + 20
2z = 20
zoya's age is 10 and nelya's age is 40

Answer:

Zoya is 10 years old. Nelya is 40 years old.

Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3

Answers

Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3
[tex] \dfrac{x^3+10}{x^3+9}=1+\dfrac{1}{x^3+9} \\ \\ \\ \dfrac{x^3+10}{x^3+9}=\dfrac{(x^3+9)+1}{x^3+9}\\ \\ \\ \dfrac{x^3+10}{x^3+9}=\dfrac{x^3+10}{x^3+9} \\ \\ \\x\in R \qquad x\in (-\infty, +\infty) [/tex]

How do you do x ^4-4? What is the x values?

Answers

we know that
A difference of two perfect squares (A² - B²)  can be factored into  (A+B) • (A-B)
then
x ^4-4--------> (x²-2)*(x²+2)
(x²-2)--------> (x-√2)*(x+√2)
x1=+√2
x2=-√2

the other term
(x²+2)=0-> x²=-2-------------- x=(+-)√-2

i  is called the imaginary unit. It satisfies   i²  =-1
Both   i   and   -i   are the square roots of   -1
√ -2  =√ -1• 2   = √ -1 •√  2   =i •  √ 2
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x3= 0 + √2 i
x4= 0 - √2 i

the answer is

the values of x are
x1=+√2
x2=-√2
x3= 0 + √2 i
x4= 0 - √2 i

Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly distributed between 1.0 and 2.1 minutes. (a) determine the mean of x. (round your answer to 2 decimal places.)

Answers

mean = total amount of minutes / number of observations
= (1.0+2.1) / 2
=1.55

Quadrilateral JPRAQuadrilateral JPRA is similar to quadrilateral KDEWquadrilateral KDEW . PR=27 mmPR=27 mm , DE=15 mmDE=15 mm , and WE=25 mmWE=25 mm .

What is AR?

Answers

the sides that correspond that are listed are PR & DE and WE & AR. Corresponding sides of similar plolygons are proportional so we can set up a proportion to find the missing side length AR.

[tex] \frac{PR}{DE} = \frac{AR}{WE} [/tex]

substitute

[tex] \frac{27}{15} = \frac{AR}{25}[/tex]

Cross multiply

27*25 = AR*15
Simplify
675 = 15*AR
Divide both sides by 15

45=AR

The area of a rectangular wall of a barn is 96 square feet. its length is 4 feet longer than twice its width. find the length and width of the wall of the barn?

Answers

area = 96
width = x
length = 2x + 4

x(2x + 4) = 96
2x^2 + 4x - 96 = 0
(x - 6)(x + 8) = 0
x = 6 or x = - 8 (rejected, length cannot be negative)

x = 6
2x + 4 = 2(6) + 4 = 16

The length is 16 feet and the width is 4 feet

Final answer:

To find the dimensions of the barn's wall, we set up the equation w x (2w + 4) = 96 and solved for w to find the width is 8 feet. Then, we used the width to find the length, which is 20 feet.

Explanation:

To solve the problem of finding the dimensions of the rectangular wall of the barn, we need to set up and solve an algebraic equation. Let's call the width of the wall w feet. According to the problem, the length is 4 feet longer than twice the width, so we can express the length as 2w + 4 feet.

The area of the rectangle is given by multiplying the length by the width. We know the area is 96 square feet, so our equation to solve is w × (2w + 4) = 96.

Expanding this equation gives us 2w^2 + 4w - 96 = 0. This is a quadratic equation that we can solve by factoring, completing the square, or using the quadratic formula.

Factoring the quadratic equation, we look for factors of -96 that add up to 4. These factors are 12 and -8. So, we can write our equation as (2w + 12)(w - 8) = 0.

Setting each factor equal to zero gives us two possible solutions for w: w = -6 or w = 8. Since width cannot be negative, we discard w = -6 and keep w = 8 feet. The length is then 2(8) + 4 = 16 + 4 = 20 feet.

Therefore, the width of the barn's wall is 8 feet, and the length is 20 feet.

Complete the statement If x/7 = 5/3, then x+7/7 =?

Answers

Lets get started :)

[tex] \frac{x}{7} = \frac{5}{3} [/tex]
We can cross multiply, to find the value of x
3x = 7 x 5
3x = 35
We have to divide by 3 on either sides to isolate x
[tex] \frac{3x}{3} = \frac{35}{3} [/tex]
3 and 3 cancels out

x = [tex] \frac{35}{3} [/tex]

Then, x + [tex] \frac{7}{7} [/tex] ( 7 divided by 7 is 1)
[tex] \frac{35}{3} [/tex] + 1 = [tex] \frac{38}{3} [/tex]

Workers have 1600 m of fencing to enclose a rectangular area where a music festival will be held. The table represents a quadratic function that shows how the area of the rectangle formed by the fence depends on the length of the rectangle.
Length (m) Area (m²)
0 0
100 70,000
200 120,000
300 150,000
400 160,000
500 150,000
600 120,000
700 70,000
800 0

Select from the drop-down menu to correctly complete the sentence.

The x-coordinate of the vertex represents

the length that result in the largest possible area

the smallest possible area of the rectangle

the greatest possible length of any rectangle formed

the greatest possible area of a rectangle

Answers

This should get you a hundred on the 4.11 quiz. :)

The correct option is the x-coordinate of the vertex representing the length.

What is a quadratic equation?

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As it is given that the perimeter of the rectangular fencing is 1600 m.

Now, since the shape of the fence is rectangular, therefore, the x-coordinate of the vertex represents the length that results in the largest possible area, while the y-coordinate is the width of the rectangular fencing.

Hence, the correct option is the x-coordinate of the vertex representing the length.

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An angle measures 72° less than the measure of a complementary angle. What is the measure of each angle?

Answers

Complementary angles: Two angles that add to 90 degrees

Angle a: 90 degrees - 72 degrees = 18 degrees
Angle b: 72 degrees

Answer: [tex]81^{\circ}\ \text{ and }\ 9^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of two complementary angles is [tex]90^{\circ}[/tex].

Given : An angle measures 72° less than the measure of a complementary angle.

Let x be the angle , then the measure of other angle will be x-72.

Since they area complementary , then we have

[tex]x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81[/tex]

Therefore, the measure of angles are :

[tex]81^{\circ}\ \text{ and }\ (81-72)^{\circ}=9^{\circ}[/tex]

Answers anybody?????

Answers

The area is the same no matter how you calculate it.
.. (1/2)*20*12 = (1/2)*30*h
.. h = (2/3)*12 = 8 . . . . . feet

A rectangular prism has a volume of 360 in3. If the height measures 4 in., which base measurements could the prism have? 4 in. by 20 in. 45 in. by 45 in. 6 in. by 15 in. 5 in. by 19 in.

Answers

V = 360 in³
Let Ab = area of the base
h = 4 in

V = Ab × h

360 = Ab × 4

Ab = 360 ÷ 4

Ab = 90 in²

Ab = l × w
The product of the base measurements must be 90.
90 = l × w

⇒ 6 in × 15 in = 90 in² ⇒ The base measurements could be: 6 in by 15 in

Other Questions

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