Mathematics High School

Sally found that a solution of x = 2 was extraneous for her function. What would be a possible denominator in Sally's function?
4x + 8
2x + 12
x^2 − 4
x^2 − 16

Answers

Answer 1
x^2-4 will be the answer ..

as denominator must not be zero to get a valid answer.

hope it helps
Answer 2

Answer:

[tex]x^2-4[/tex]

Step-by-step explanation:

Sally found that a solution of x = 2 was extraneous for her function.

Extraneous solution is a solution that makes the denominator 0

Possible denominator are given . LEts plug in 2 for x and check which option gives us 0

[tex]4x+8=4(2)+8= 16[/tex]  

[tex]2x+12=2(2)+12=4+12= 16[/tex]

[tex]x^2-4= (2)^2-4= 4-4=0[/tex]

[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]

[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.

So x=2 was extraneous solution for [tex]x^2-4[/tex]

Related Questions

A quadratic equation is shown below:

25x2 + 10x + 1 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answers

hello : 

help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 )  Δ > 0  the equation has two reals solutions : x =  (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions

5x - 10y = 15 if 3x + 7y = 31

Answers

5x - 10y = 15...reduces to x - 2y = 3
3x + 7y = 31

x - 2y = 3....multiply by -3
3x + 7y = 31
---------------
-3x + 6y = -9 (result of multiplying by -3)
3x + 7y = 31
---------------add
13y = 22
y = 22/13

x - 2y = 3
x - 2(22/13) = 3
x - 44/13 = 3
x = 3 + 44/13
x = 39/13 + 44/13
x = 83/13

solution is (83/13, 22/13) <=
3(5x-10y=15)-5(3x+7y=31)

15x-30y-15x-35y=45-155

-65y=-110

y=22/13, making 3x+7y=31 become

3x+154/13=31

39x+154=403

39x=249

x=83/13

So the solution to the system of equation is the point (83/13, 22/13)


Draw a model to represent the problem 6/12 divided by 1/4

Answers

The expression 6/12 divided by 1/4 is 2 and the model is attached

Drawing a model to represent the problem

From the question, we have the following parameters that can be used in our computation:

6/12 divided by 1/4

This can be expressed as

6/12 multiplied by 4

So, we have

0.5 multiplied by 4

When the product is evaluated, we have

2

Hence. 6/12 divided by 1/4 is 2 and the model is attached

.help me with this please thanks

Answers

i would say B . 
They are not like terms because they are not all the same

Two pools are being filled with water. To start, the first pool contains 2200
liters of water and the second pool contains 1840
liters of water. Water is being added to the first pool at a rate of 21.25
liters per minute. Water is being added to the second pool at a rate of 32.5
liters per minute.
(PLEASE ANSWER QUICK)


Answers

2200 + 21.25X = 1840 +32.50X

subtract 1840 from each side

360+ 21.25X= 32.50X

subtract 21.25x from each side

360=11.25X

x= 360/11.25 = 32 minutes pool will have the same amount

 

21.25*32 = 680+2200 = 2880 liters

32.5*32 = 1040 + 1840=2880 liters

 

 it will take 32 minutes and they will have 2880 liters each


Find the sum of the geometric sequence. (1 point) 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen

Answers

GP = 1/2 , 1/4 , 1/8 , 1/16
1st) the common ratio is (1/4 : 1/2 ) = 1/2, so r =1/2
2nd) the sum of a GP is:

S= a(1-rⁿ)/(1-r)

S=(1/2).[1-(1/2)⁴]/(1-1/2) = 15/16

Answer:

31/16

Step-by-step explanation:

If y varies directly with x and y = 10 when k = 10, what is the value of x?

Answers

y = k *x
y=10 ; k=10

10 = 10*x
x = 10/10 = 1

x =1


The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is

Answers

[tex]\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\ \left. \qquad \qquad \right.(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right][/tex]

[tex]\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &7500\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4\\ t=years\to &3 \end{cases} \\\\\\ A=7500\left[ \cfrac{\left( 1+\frac{0.12}{4} \right)^{4\cdot 3}-1}{\frac{0.12}{4}} \right][/tex]

Answer:

$180,997.50.

Step-by-step explanation:

1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.

2. Select the rate-per-period column corresponding to the period interest rate.

3. Locate the value in the cell where the periods row intersects the rate-per-period column.

4. Multiply the annuity payment by the table value from step 3.

Future value = annuity payment × table value

FV = $7500.00 * 24.133 = $180,997.50

Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?

Answers

75%...................

D: region D helppppppppp

Answers

you only hace to change x equal 0 and y equal 0, answer is D

HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5

a  (3x-1)(2x+5)
b  (3x-5)(2x-1)
c  (3x-1)(2x-5)
d  (3x-5)(2x+1)

Answers

c  (3x+1)(2x-5)
You have to try whatever factoring method you've been taught, but this is the answer.

The solution is: the following expression factored completely,

6x^2-13x=5 is: c  (3x-1)(2x-5)

What is an expression?

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Here, we have,  

we have,

6x² - 13x  = +5

6x² - 13x  - 5 = 0

6x² - 15x + 2x - 5 =0

so, we get,

(3x-1)(2x-5) = 0

The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.

When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.

The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is

... C (3x-1)(2x-5)

Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c  (3x-1)(2x-5)

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I need help with all of these

Answers

13. "Colinear" -> "on the same line" -> A,B,E
14. "Coplanar" -> "on the same plane" -> B,C,D,E
15. Planes are name by 3 non-colinear points --> Plane ACE

18. Two points -> G &F
       A line -> Line GF
19. Plane T and Plane S

What is the length of diagonal ac in parallelogram ABCD if the diagonal BD = 10cm which is twice the diagonal AC?

Answers

Final answer:

The length of the diagonal AC in parallelogram ABCD is 5 cm.

Explanation:

Given that the diagonal BD is twice the length of diagonal AC, we can represent the length of diagonal AC as x. So, the length of diagonal BD would be 2x. From the given information, we know that BD = 10 cm. Therefore, we can write the equation 2x = 10 to solve for x. Dividing both sides of the equation by 2 gives x = 5. So, the length of diagonal AC is 5 cm.

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Final answer:

In the given parallelogram, the length of the diagonal AC is 5 cm, given that the length of the diagonal BD is twice that of AC.

Explanation:

The question pertains to the properties of a parallelogram. In this case, it has been provided that diagonal BD (10 cm) is twice the length of the other diagonal AC. This implies that the length of diagonal AC is half the length of BD. Therefore, to find the length of AC, take the length of BD and divide by 2:

AC = BD / 2 = 10 cm / 2 = 5 cm

So, the length of diagonal AC is 5 cm.

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Two cards are drawn at random from a standard deck of cards without replacement. What is the probability that both cards will be from the clubs suit?

Answers

Answer:

The answer is 1/17.

Step-by-step explanation:

You will draw one club which will be 13/52. You will NOT replace it so you will draw a second card 12/51.

You will need to multiply them to find the probability.

First simplify your two fractions.

13/52 = 1/4   AND  12/51= 4/17

Multiply the two together and you will get 4/68 = 1/17

Hope this helps :)

at maximum speed, an airplane travels 1680 miles against the wind in 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours.

Answers

The speed of the airplane with the wind is 420 mph, and against the wind is 336 mph. The speed of the wind is 84 mph.

To find the speed of the wind, we use the following formulas:

Against the wind, the airplane travels 1680 miles in 5 hours. So, the speed against the wind is : [tex]\( S_a = 1680 \div 5 = 336 \)[/tex] mph

With the wind, the airplane travels the same distance of 1680 miles in 4 hours. So, the speed with the wind is: [tex]\( S_w = 1680 \div 4 = 420 \)[/tex]mph

Let W be the speed of the wind.

Against the wind: [tex]\( S_a = S_w - W \)[/tex]

[tex]\[ 336 = 420 - W \]\[ W = 420 - 336 = 84 \][/tex]

So, the speed of the wind is 84 mph.

A solution of phosphoric acid has a boiling point of 158 degrees Celsius. What is the boiling point of the solution in degrees Fahrenheit?

Answers

Final answer:

The boiling point of a phosphoric acid solution that is 158 degrees Celsius is 316.4 degrees Fahrenheit. This is found by using the formula F = C * 9/5 + 32.

Explanation:

To convert the boiling point of a solution from degrees Celsius to Fahrenheit, we use the formula F = C * 9/5 + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.

In this case, the temperature in Celsius that you want to convert is 158 degrees. So you can substitute this value in the formula as follows:

F = 158 * 9/5 + 32

When you perform the calculation, you find that the boiling point of the phosphoric acid solution is 316.4 degrees Fahrenheit.

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The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem?

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answers

f(x) = -x^2 + 20x - 75 = (x-5)*(-x + 15)
The two x-intercepts are x = 5 and x = 15, which are the two values of x where f(x) = 0. The vertex is located halfway between these two points, so where x = 10. When x = 10, f(x) = 25, so the vertex of this graph is (10, 25).

Part A: The vertex is (10, 25). The vertex represents the point where the profit is a maximum. When 10 photos are printed, the profit is $25.

Part B: The two x-intercepts are x = 5 and x = 15. This shows where the profit is $0. When 5 photos or 15 photos are printed, the profit is $0.

Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy

Answers

Let's say that the dogs eat 50 lbs of food in 50 days. That would mean they eat 50/50 = 1 pound per day. Notice I divided the weight over the number of days. The dog eats 1 pound per day, for 365 days, so in total it eats 365*1 = 365 pounds. This is just a hypothetical example. 

In general, if x is the number of days to eat 50 pounds of food, then x/50 is the expression representing the amount eaten per day (in pounds). Finally 365*(x/50) is the expression representing the total amount eaten over the whole year.

This is why the final answer is choice C

Suppose a rectangular garden has a length of 3c + 15 feet and a width of 4c feet. write an expression for the area of the garden in square feet.

Answers

A = L * W

A = 4c(3c + 15)
A = 12c^2 + 60c <==

The area of the rectangle is given by the equation A = 12c² + 60c

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

Let the length of the rectangle L = ( 3c + 15 ) feet

Let the width of the rectangle W = 4c feet

Now , the area of the rectangle A = length of the rectangle L x width of the rectangle W

Substituting the values in the equation , we get

Area of Rectangle A = ( 3c + 15 ) ( 4c )

On simplifying the equation , we get

Area of Rectangle A = ( 3c ) ( 4c ) + 15 ( 4c )

Area of Rectangle A = 12c² + 60c

Therefore , the value of A is 12c² + 60c

Hence , the area of the rectangle is A = 12c² + 60c

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Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant

Answers

x^2 - 4x = 5
(x - 2)^2 - 4 =  5
(x - 2)^2  = 9

x- 2 = +/- sqrt9  = +/- 3
x = 3 + 2 or -3 + 2
solution set is {-1 , 5}

The solution of the given equation is -1 or 5

What is an equation?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given is an equation, x²-4x = 5,

we need to transform it into a perfect square,

The equation is =

x²-4x = 5

Add 4 to each side,

x²-4x+4 = 5+4

x²-4x+4 = 9

(x-2)² = 9

Solving for x,

x-2 = √9

x-2 = ±3

x = -1 or x = 5

Hence, the solution of the given equation is -1 or 5

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ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP

Answers

3 because the next number to the right is a 0 and will not be rounded up.
3.05947821031
^
whole number

if 3.xxx... < .5, round to 3.
If 3.xxx... > or = .5, round to 4.

Because .059 < .5, it is therefore rounded to 3.

at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 when gas cost $2.20 per gallon on average

Answers

The average cost represents the slope of the line of the graph.
Increasing the slope of the graph increases the steepness of the line.
Therefore, increasing the average cost of gas from $1.50 to $2.20 will increases the steepness of the line. (i.e. the line becomes closer to the vertical line).

Find the product of (2x + 5y)2.

Answers

4x +10y is the product of (2x+5y)2
Distribute 2 to 2x and 5y using PEMDAS to get 4x+10y

1/2(6x-4)=2/3x How do i solve this?

Answers

Apply distributive property.

3x-2=2/3x

Multiply all terms by 3 so we won't have to deal with fractions.

9x-6=2x

Subtract 9x from both sides

-6=-7x

Divide both sides by -7

x= 6/7

Final answer: x=6/7

Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^2

Answers

It is r^3 in the volume formula.

V=(4πr^3)/3  multiply both sides by 3

3V=4πr^3  divide both sides by 4π

r^3=3V/(4π)  take the cube root of both sides

r=((3V)/(4π))^(1/3)

Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m

Answers

as x = 5 & z=12, 

2/3 = y /(xz) = y/(5*12) 

= y/60 

so y / 60 = 2/3 

y = (2*60)/3 

= 40

ROUND 43.0810194943 TO THE NEAREST TEN-THOUSANDTH HELP!

Answers

43.0810
Since the hundred thousandths is a 1 which is less than a 5, you have to round down.
43.0810 is the answer. The ten thousandths is always four numbers after the decimal.

HELP!!!!
Use the following data set and a separate piece of paper to make a line plot that will help you to answer questions 2-7.
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Add a box and whisker plot to the graph. Clearly mark the ends of box by drawing vertical lines and labeling their values on the horizontal axis. What are the ends of the box and whisker plot?

A. 1 and 6

B. 4 and 7

C. 4 and 8

D. 5 and 7

Answers

1,4,4,4,5,5,6,6,6,6,7,7,8,8,10

minimum = 1
Q1 = 4
Q2 (median) = 6
Q3 = 7
maximum = 10

The beginning and end of the " box " are Q1 and Q3.....4 and 7

Find the surface area of each figure to the nearest tenth. Show your work, please

Answers

Pyramid surface area (total): Lateral surface area + Base area

Lateral surface area = [tex] \frac{2p*a}{2} [/tex] where p is the base perimeter and a the apothem.

The base is a sqaure so, find the area of the square.

Base Area = 16*16 = 256 in²

Calculate the perimeter = 16*4 = 64 in

LSA = (64*17)/2 = (64*17)/2 = 1088/2 = 544 in²

TSA = 544+256 = 800 in²

Total surface of cone: LSA + Base Area

LSA = πra

Let's find the apotheme. Apply Pitagora, again the hypothenuse is the apotheme. The legs are the radius and the height.

a = √8²+3² = √64+9 = √73 ≈ 8,5 in.

Base area (area of the circle) = πr² = 3²*π = 9π in²

LSA = 3*8,5*π = 25,5π in²

TSA = 25,5π+9π = 34,5π = 34,5*3,14 = 108,3 in²

a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days

Answers

Given:
Initial mass, m₀ = 23 g
Decay constant, k = 0.13

Exponential decay obeys the equation
[tex]m(t)=m_{0} e^{-kt}[/tex]
where t = time, days

For half life, the mass is m = m₀/2.
Therefore
[tex]e^{-0.13t} = \frac{1}{2} \\ -0.13t = ln(0.5)\\t= \frac{ln(0.5)}{-0.13} =5.33[/tex]

Answer: The half life is 5.33 days

Answer:

5.3 is the right answer.

Step-by-step explanation:

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