A rational expression that will be undefined at x=1?

Answers

Answer 1

This rational. expression will be undefined when x=1. 3x+2÷(-x+1)

Answer 2

A rational expression of the form
[tex]r(x)= \dfrac{p(x)}{q(x)} [/tex]
will be undefined for the zeros of the expression [tex]q(x)[/tex]. For an expression with a zero equal to 1, the simplest way is to use [tex](x-1)[/tex] as a factor in [tex]q(x)[/tex]. In can be your only one, or you can mix in other factors.

But, so long as the denominator of [tex]r(x)[/tex] is equal to zero, as it is when [tex]q(x)=x-1[/tex], the expression will be undefined at that point x, because it would involve division by zero.

You could use as your sample:

[tex] \dfrac{x-7}{x-1} [/tex]

You can try to get fancy and square some factors or add in some radicals or trigonometric functions or anything else, so long as the 1 makes the denominator equal to zero!

Related Questions

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 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

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]

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

Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.

34.12°

123.98°

56.78°

75.52°

Answers

we have that
cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²

the answer is
the option 75.52°

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!

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)

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

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

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.

. (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)

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]

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:

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 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.

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" .
_______________________________________________________

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.

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]

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.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ2

This figure shows circle Z with chords AB and RS . mAR=55° mRB=66° AB=8 m RS=8 m What is mRS?

Answers

m AR = 55°
m RB = 66°
Like AB=8 m =RS →m RS = m AB

m AB = m AR + m RB
m AB = 55° + 66°
m AB = 121°

m RS = m AB
M RS = 121°

Answer: m RS is 121°

Answer:

The correct answer is, mRs = 121°

Step-by-step explanation:

From figure we get ,

mAR=55° mRB=66° AB=8 m RS=8 m

To find mRS

Using given information we can write,

mAB = mAR + mRB = 55 + 66 = 121°

Since AB=8 m RS=8 m,

AB = RS

⇒ mAB = mRS

mAB = 121°

Therefore mRS = 121°

The correct answer is given by,

mRS = 121°

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]

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

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.

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

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

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.

Learn more about Quadratic Equations:

https://brainly.com/question/2263981

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.

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

Johnny is five years older than his brother. the sum of their ages is 37. how old is Johnny

Answers

Johnny is 21 years old.
If you take 21 and add 16, you get 37.

21+16= 37
21-16= 5

johnny is 21 years old

Other Questions

What type of money did the greenback party recommend What statement is true about the polynomial Which is not a controlling idea in the essay the peach tree road race In "A Visit of Charity," why does Marian leave the room so quickly? A.She is frightened by Addie's tears. B.The nurse tells her it's time to go. C.She doesn't want to miss her bus. D.The old woman asks her for money What are the relative sizes of oocytes in a dormant follicle, a growing follicle, and a graafian follicle? In ________, a three-pronged symbol represents the "many" side of the relationship. a map is drawn with a centimeter representing 25 Miles. if the distance between two towns ia 3 centimeters on the map, what is the actual distance between the two towns? ELA 1 : DNA ELA 2 DNA Algebra 1 : DNA WHAT IS DNA MEANING Linda has heard that the acidic environment of the stomach is similar to that of a car battery. if the stomach is so acidic, why doesn't the acid eat away at the stomach lining and cause holes in the stomach? the stomach contracts during peristalsis, which pushes the acid out of the stomach and protects it. the stomach produces bacteria, which denature the acid in the stomach and protect it. the stomach is lined with a layer of mucus that protects it. the stomach produces bicarbonate, which neutralizes the acid in the stomach and protects it. The intent of the parties may be determined by evaluating what the parties said, how the parties acted, and did a territory keep it's independence after an imperialist country annexed it? Misusing capital letters can ________ a letter's effectiveness.1.Enhance2.Promote3.Disguise4.Limit Force exerted by the ball on the kickers foot. help me please asap ill mark brainliest nd plz be correct one face of a cube an area of 49 square centimeters. what is the volume of the cube What is eloquence? a. expressive languageb. humorous language c. disrespectful languaged.informal language According to the theory of plate to tonics how do two plates interact to form large mountain range Make a conjecture about the position, size and shape of a figure if a composition of transformation included a dilation The voltage of electricity traveling away from a power plant is very high. How high may it be? Why is the voltage so high? Is the underlined possessive noun singular or plural? the horses' barn