How do we check if a solution is extraneous? Use these equations as examples to help you explain:

How Do We Check If A Solution Is Extraneous? Use These Equations As Examples To Help You Explain:

Answers

Answer 1
Multiplying both sides of a rational equation by a variable expression introduces the possibility of extraneous solutions. Therefore, we must check the solutions against the set of restrictions. If a solution is a restriction, then it is not part of the domain and is extraneous.

Related Questions

I would appreciate if someone could answer this

Answers

Answer:

x = 15

LN and MO both equal 43

Step-by-step explanation:

LN and MO are diagonals in rectangle

Diagonals of a rectangle are congruent Hence, 4x - 17 = 2x + 13

Now we solve for x

4x - 17 = 2x + 13

Add 17 to both sides

4x = 2x + 30

Subtract 2x from both sides

2x = 30

Divide both sides by 2

x = 15

Now we want to find the values of LN and MO

To do so we substitute 15 for x in it's given expression ( note: because LN = MO we only need to do this process once )

LN = 4x - 17

Substitute 15 for x

4(15) - 17

Multiply

60 - 17

Subtract

LN and MO = 43

A market research firm conducts telephone surveys with a 42% historical response rate. What is the probability that in a new sample of 375 telephone numbers, at least 150 individuals will cooperate and respond to the questions

Answers

Answer:

The right answer is "0.7823".

Step-by-step explanation:

Given that,

P = 42%

or,

  = 0.42

n = 375

[tex]\hat{P}[/tex] = 0.4

The z-score will be:

= [tex]\frac{\hat{P}-\mu_P}{\sigma_p}[/tex]

By putting the values, we get

= [tex]\frac{0.4-0.42}{\sqrt{\frac{0.42\times (1-0.42)}{0.375} } }[/tex]

= [tex]-0.784706[/tex]

hence,

The probability will be:

⇒ [tex]P(\hat {P}>0.04)[/tex] = [tex]P(z>-0.7847)[/tex]

                        = [tex]1-P(z<-0.7847)[/tex]

                        = [tex]1-0.21770[/tex]

                        = [tex]0.7823[/tex]

A grocery store chain uses loyalty cards that offer discounts on sale attheir store. The probability that a randomly chosen shopper has a loyaltycard is 0.8. A group of shoppers have been selected at random to completea customer satisfaction survey. Let Xi be a random variable that equals 1 when a customer has a loyalty card and 0 otherwise.

Required:
a. Construct a joint probability table for the random variables X, and X.
b. Define the event that the first four customers sampled have loyalty cards in terms of the random variables X, X2, X3, and Xd. Then compute the probability of this event.

Answers

The answer is a cause

Please answer this, I am confused (5^2)(7^2)(3^2)

Answers

Given:

The expression is:

[tex](5^2)(7^2)(3^2)[/tex]

To find:

The value of the given expression.

Solution:

We have,

[tex](5^2)(7^2)(3^2)[/tex]

On simplification, we get

[tex](5^2)(7^2)(3^2)=(25)(49)(9)[/tex]

[tex](5^2)(7^2)(3^2)=11025[/tex]

Therefore, the value of the given expression is 11025.

A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours

Answers

Answer:

The Sample Size Need To be at least 114

Step-by-step explanation:

According to the Question,

Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.

The Maximum Error(E) is given as 1.5 hours and the standard deviation(σ) is 6.2 hours.

Now, For 99% Confident the level of value α is 0.01.

α/2 = 0.01/2 ⇒ 0.005

Thus, From The table, We get that the value of [tex]Z_{alpha/2}[/tex] is 2.58.

Hence, the sample size n can be found as

n = {[tex]\frac{(Z_{alpha/2} * Standard Deviation)}{E}[/tex]}²

n = {2.58 × 6.2}² / 1.5²

n = 113.72 .

So, The Sample Size Need To be at least 114.

What is half of 3/4 in fraction?

Answers

Answer:

3/8

Step-by-step explanation:

1/2 times 3/4= 3/8

In general, half of all the customers you speak to will ask about any upcoming pricing discounts or promotions. Of those who do ask, only 20% qualify for the discount. So that means if I speak to 300 customers, how many will qualify for the discount

Answers

Answer:60

Step-by-step explanation:

300 of 20% is 60

The number of qualified customers for the discount will be 60.

What is the percentage?

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

It is given that half of all the customers you speak to will ask about any upcoming pricing discounts or promotions. Of those who do ask, only 20% qualify for the discount. So that means if I speak to 300 customers.

The number of qualified customers will be calculated as below:-

The qualified customers are 20% of 300.

Number = 300 x (20/100)

Number = 300 x 0.2

Multiply the number 330 with 0.2 to get the final value.

Number = 60

Therefore, the number of qualified customers for the discount will be 60.

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Sally generates an input-output table using two rules. The input rule is “add 2 2” and the starting number is 3 3. The output rule is “add 4 4” and the starting number is 6 6. The table is shown. ​ ​ Which ordered pairs follow the same rules as the pattern in the table? Select two answer choices. A (9,12)(9,12) B (11,22)(11,22) C (15,25)(15,25) D (17,36)(17,36) E (21,42)(21,42)

Answers

9514 1404 393

Answer:

  B  (11, 22)

  E  (21, 42)

Step-by-step explanation:

The numbers in the input sequence are ...

  [tex]i_n=i_1+d(n-1)\\\\i_n=3+2(n-1) = 2n+1[/tex]

The numbers in the output sequence are ...

  [tex]o_n=o_1+d(n-1)\\\\o_n=6+4(n-1)=4n+2=2(2n+1)\\\\o_n=2\times i_n[/tex]

So, the ordered pairs we're looking for have an output value that is double the input value.

The two that match this characteristic are ...

  B(11, 22) and E(21, 42)

Factorise 12x3-9x2 please help

Answers

Answer:

18

Step-by-step explanation:

12x3=36=36-9x2=18=36-18=18

Which expression is equivalent to 5^15 x 5^5

Answers

Answer:

[tex]5^{15} * 5^{5}[/tex]

= [tex]25^{20\\}[/tex]

Find the equal measures of 1. 28 m = ________ km 2. 3899 ml = ______ l 3. 79 kg = _____ g Show the process of each

Answers

Answer:

1. 0.028 km

2. 3.899 L

3. 79,000 g

Which of the following functions has a rate of change that stays the same?
A. y=-4+10
B. y=1/2x^2
C. y=3^x
D. y=x^2+2

Answers

Answer:

The answer is A because the rest are parabolas

NEED HELP DUE IN 3 MINUTES!!!!

Answers

Answer:

y = -1/3 x+9

Step-by-step explanation:

First find the slope between the two points

m = ( -1 -8)/(2 - 5)

    -9/-3

   =3

We want a line that is perpendicular so it is the negative reciprocal

-1 /(3)

The slope of the perpendicular line is -1/3

y= mx+b where m is the slope and b is the y intercept

y = -1/3x+b

We have a point of (6,7)

7 = -1/3 (6) +b

7 = -2 +b

Add 2 to each side

7 +2 = -2+b+2

9 = b

The equation of the line is y = -1/3 x+9

1/3 x9







Bc I need help

Triangle ABC IS dilated using the origin as the center of dllation to create triangle A'B'C'. What rule best represents the dilation applied to triangle ABC to ​

Answers

The scale factor is 3 so B would be your answer because all coordinates are multiplied by 3

Jackson made 36 calls in 2.25 hours. How many calls per hour did he make?

Answers

Answer:

16 calls

Step-by-step explanation:

make an equation based off this ratio -- 36 calls: 2.25 hours and x calls: 1 hour

36/2.25 = x/1

cross multiply to get 36=2.25x

divided by 2.25 on both sides

x=16

I neeed the answer plssss

Answers

Answer:

300km

Step-by-step explanation:

if 1 hr=80

then take 80 and multiply it by 3.75

hope this helps!

please give brainiest if you want<3

Answer:

300km

Step-by-step explanation:

Which equation represents the function y - 5 = –2(x+3) in slope-intercept form?
Oy= 2x + 1
Oy = 2x - 1
Oy= -2x - 1
Oy = -2x + 11
Oy = -23 - 11

Answers

Answer:

-2x-1

Step-by-step explanation:

when you graph the equation it gives you a decreasing slope with the y intercept of -1. the slope is 2 and since its decreasing it is -2. therefore its -2x-1

The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .

What is a straight line?

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

the function y - 5 = –2(x+3)

now, we have to find  in slope-intercept form.

now, we have,

function has a decreasing slope with the y intercept of -1. the slope is 2

and since its decreasing it is -2.

again, we have,

y - 5 = –2(x+3)

or, y = -2x - 6 + 5

or, y = -2x -1

here, slope = m = -2

and, y-intercept = c = -1

as, we know that,

slope-intercept form is: y = mx+ c

so, we get,  y = -2x -1

Hence, The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .

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Solve for M and N please help me

Answers

Answer:

M=4   N=6

Hope this helped!

Simplify the fraction to lowest terms.
56/
182

Answers

the answer to your question is 4/13.

Please, I'm desperate need of help I will mark Brainliest to the one who answers with the full process! Gold will Bless You!

Two angles of a triangle are 85° and 65°, and the longest side of the triangle is 34 cm. How long is the shortest side? Include a labelled diagram.

Answers

Add 65 and 85

65+85= 150

Next subtract 180-150

The answer is 30, so that is the missing angle is 30.

The side opposite to 30 is the shortest side

Here I added the picture!

Tell wether x and y show a proportional relationship.

x 1 2 3 4
y 4 8 12 16

Answers

Answer:

They do because y is always 4 times of x.

Step-by-step explanation:

Use slopes and y-intercepts to determine if the lines y=−2/3x+2 and −3x+2y=−4 are parallel.

Answers

Answer:

the answer is no

Step-by-step explanation:

y = -2/3x+2

2y = 3y-4

y = 3/2y-2

but here's a comment: it is perpendicular because it is it's opposite reciprocol

Select the correct answer.
Which expression is equivalent to the glven expression?
(3m-4)^3(3m^5)
A. 81/m^2 B.27/m^7 C. 27/m^2 D.81/m^7

Answers

The answer for this question is D

The correct expression which is equivalent to the given expression is,

⇒ 81 / m⁷

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (3m⁻⁴)³ (3m⁵)

Now, We can simplify as;

⇒ (3m⁻⁴)³ (3m⁵)

⇒ (3³m⁻¹²) (3m⁵)

⇒ (27m⁻¹²) (3m⁵)

⇒ 81 m⁻¹²⁺⁵

⇒ 81 m⁻⁷

⇒ 81 / m⁷

Thus, The correct expression which is equivalent to the given expression is,

⇒ 81 / m⁷

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I would really appreciate if someone could answer this:)

Answers

Answer:

first you need to know that the the sum of the co-interior angle is  180 degree and the sum of the opposite side of  parallelogram is always equal.

now x+140=180(being co - interior angle)

or, x= 180-140

therefore, x =40 degree

y= 140 degree because sum of the opposite side of  parallelogram is always equal.

x= z=40 degree (sum of the opposite side of  parallelogram is always equal.

when you are again confused go in this link

 ----> https://www.scholr.com/ncert-solutions/consider-the-following-parallelograms-fi/40087/

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plz it's do to day HELP PLZ​

Answers

Answer:

9 units^3

Step-by-step explanation:

V = l*w*h

   = 1 1/2 * 4 * 1 1/2

Change to improper fractions

  = 3/2 * 4 * 3/2

   = 36/4

   = 9 units^3

Identify the x-intercept points of the parabola

Answers

Answer:

(3,0) and (-1,0)

Step-by-step explanation:

The X intercept are the point(s) where the line croses the X axis (the horizontal/leftright line). the points for this graphing system are always listed (x,y) so to find a certain point you find the X value then the Y value

Simplify (2 1/6 - 1 2/3) - 2 2/3​

Answers

Answer:

[tex]- 2\frac{1}{6}[/tex]

Step-by-step explanation:

[tex](2\frac{1}{6} -1\frac{2}{3}) - 2 \frac{2}{3}[/tex]

[tex](\frac{13}{6} -\frac{5}{3}) - 2 \frac{2}{3}[/tex]

[tex](\frac{13}{6} -\frac{10}{6}) - 2 \frac{2}{3}[/tex]

[tex]\frac{3}{6} - 2 \frac{2}{3}[/tex]

[tex]\frac{3}{6} - \frac{8}{3}[/tex]

[tex]\frac{3}{6} - \frac{16}{6}[/tex]

[tex]- \frac{13}{6}[/tex]

[tex]- 2\frac{1}{6}[/tex]

The club with an occupancy of 100 will sell out at $25 per ticket. If the owner decides to increase the price by $5, then 2 less tickets will be sold. Determine the revenue function if x is the number of $5 increases.

Answers

Answer:

100 + (5X) = -2X

Step-by-step explanation:

Since the club with an occupancy of 100 will sell out at $ 25 per ticket, and if the owner decides to increase the price by $ 5, then 2 less tickets will be sold, to determine the revenue function if X is the number of $ 5 increases the following calculation must be performed:

100 + (5X) = -2X

So, for example, if the price were increased by $ 15, the equation would apply as follows:

15/5 = 3

100 + (5x3) = -2 x 3

100 + 15 = -6

115 = -6

0.36% as a fraction in simplest form

Answers

Answer: 9/2500

Step-by-step explanation:

We start with turning it into a fraction:

0.36/100

Then, we turn every number into a whole number by multiplying by whatever the last decimal place is called (hundreth= x100)

36/10000

Lastly, we simplify as much as we can by finding the least common denominator. In this case, the smallest whole number both 36 and 10000 can be divided by is 4:

(36/4)/(10000/4)

= 9/25000

Plz help me simply this

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt[5]{u^{10}*p^{15}}*\sqrt[4]{u^{16}*p^{18}}= \sqrt[5]{u^{2*5}*p^{3*5}}*\sqrt[4]{u^{4*4}*p^{16*2}}\\\\\\=\sqrt[5]{(u^{2})^{5}*(p^{3})^{5}}*\sqrt[4]{(u^{4})^{4}*p^{4*4}*p^{2}}\\\\=\sqrt[5]{(u^{2})^{5}*(p^{3})^{5}}*\sqrt[4]{(u^{4})^{4}*(p^{4)^{4}}*p^{2}}\\\\=u^{2}*p^{3} * u^{4}*p^{4}*\sqrt[4]{p^{2}}\\\\=u^{2+4}*p^{3+4}*\sqrt[4]{p^{2}}\\\\= u^{6}p^{7}\sqrt[4]{p^{2}}[/tex]

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