Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.

Answers

Answer 1

Assume the smaller one is x, then the other ones will be x+2 and x+4

x(x+2) + 2 = 5(x+4)

x^2 + 2x - 5x - 18 = 0

-> x^2 - 3x - 18 = 0

-> (x-6)(x+3) = 0

-> x = 6 or -3, since x must be positive, then x = 6

So the numbers are: 6, 8, 10

Related Questions

What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45?

Answers

I assume your empty box is the product lol:)

So the product is: 28.2753. No tricks, better to use calculator, but you can do by hand too, not that hard.

28.2753 its the answer just use google calculator it's easy to use

A normal curve is ___________ about the mean. consequently, 50% of the total area under a normal distribution curve lies on the left side of the mean, and 50% lies on the right side of the mean.

Answers

In statistics, when you gather data points for the same test, you construct a distribution graph. For example, you make a statistics based on the score of a class for a 145-item test. You graph it based on frequency such as, 10 students got 50 points and so and so forth. When that test have a few outliers and have more or less the same score, you form a normal distribution graph. It is more commonly known as the Gaussian Bell Curve. An example would be shown in the picture.

A normal distribution curve is symmetric about the mean. As a result, the area under the curve on the left side of the mean would be equal to the area under the curve on the right side of the mean. So, each would constitute 50%.

salas little brother is learning to talk. he has a vocabulary of 30 words. each week his vocabulary grows by about 6%. at this rate how many words will he know 5 weeks from now

Answers

30 * (1+0.06)^5=

30* 1.338225578 = 40.146

he will know 40 words in 5 weeks

angle LMP and angle PMN are complementary. Find the value of x.

A. 22.5
B. 7.5
C. 15
D. 30

Answers

complimentary angles add up to 90 degrees

2x + 4x = 90
6x = 90
x = 90/6
x = 15 <==

The answer is C because if you multiply 15 * 4 and 15 * 2 it will sum to 90

Alice wants to buy some paper towels. She has two options. She can either buy a package of four rolls or she can buy one roll now and buy another when she runs out. Which of these options is better? Give reasons for your answer.

Answers

buying 4 rolls. If she buys 4 rolls, whenever she used up one roll she already has 3 to replace it. If she buys one roll and then one later, when she uses up the one roll she will have to go buy more

Answer:

Correct Answer: Alice should buy the package of four paper towels because buying in bulk means she gets each roll of towels for less money.

Step-by-step explanation:

At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours.
Let x the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?

Answers

Final answer:

The speed of the plane with no wind is 451 miles per hour.

Explanation:

Let's solve this problem step-by-step:

We are given that the airplane travels 2460 miles against the wind in 6 hours at maximum speed. This means that the speed of the airplane relative to the ground is its maximum speed minus the speed of the wind. So, the equation is: x - y = 2460/6 or x - y = 410 (where x is the maximum speed of the plane and y is the speed of the wind). We are also given that the airplane can travel the same distance with the wind in 5 hours. This means that the speed of the airplane relative to the ground is its maximum speed plus the speed of the wind. So, the equation is: x + y = 2460/5 or x + y = 492. To find the speed of the plane with no wind, we can add the two equations: (x - y) + (x + y) = 410 + 492. This simplifies to: 2x = 902. Dividing both sides by 2, we get: x = 451. Therefore, the speed of the plane with no wind is 451 miles per hour.

What is the work done by moving in the force field f~ (x, y) = h2x 3 + 1, 2y 4 i along the parabola y = x 2 from (−1, 1) to (1, 1)?

a.compute directly

b.use the theorem?

Answers

The force field seems to be

[tex]\mathbf f(x,y)=\langle2x^3+1,2y^4\rangle[/tex]

(though it's not entirely clear whether that's it...)

The parabolic path can be parameterized by

[tex]\mathbf r(t)=\langle t,t^2\rangle[/tex]

where [tex]-1\le t\le1[/tex]. Then the work done by the field along the path is

[tex]\displaystyle\int_C\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=-1}^{t=1}\langle2t^3+1,2t^8\rangle\cdot\langle1,2t\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_{-1}^1(2t^3+1+4t^9)\,\mathrm dt[/tex]
[tex]=2[/tex]

Not sure what theorem is being referred to in part (b). Perhaps you mean the gradient theorem? In which case you would need to show that there's a scalar function [tex]f(x,y)[/tex] such that [tex]\nabla f(x,y)=\mathbf f(x,y)[/tex]. We have

[tex]\nabla f(x,y)=\left\langle\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y}\right\rangle=\left\langle2x^3+1,2y^4\right\rangle[/tex]

from which we have

[tex]\dfrac{\partial f}{\partial x}=2x^3+1\implies f(x,y)=\displaystyle\int(2x^3+1)\,\mathrm dx[/tex]
[tex]\implies f(x,y)=\dfrac12x^4+x+g(y)[/tex]

[tex]\implies\dfrac{\partial f}{\partial y}=g'(y)=2y^4[/tex]
[tex]\implies g(y)=\dfrac25y^5+C[/tex]

[tex]\implies f(x,y)=\dfrac12x^4+x+\dfrac25y^5+C[/tex]

We have a candidate for a potential function, so we apply the gradient theorem, which asserts that the value of the line integral is path independent and can be determined by evaluating the potential function at the endpoints of the path. We then have

[tex]\displaystyle\int_C\mathbf f(x,y)\cdot\mathrm d\mathbf r=f(1,1)-f(-1,1)[/tex]
[tex]=\dfrac{19}{10}-\left(-\dfrac1{10}\right)[/tex]
[tex]=2[/tex]

as expected.

Who can help me with that one please ? Thanks!

Answers

∠APB is an inscribed angle
The measure of the intercepted arc is twice that of the inscribed angle ⇒
arc AB = 2 * ∠APB = 2 * 108 = 216°

Two numbers have a sum of 30 and a product of 209. what is the positive difference between them?

Answers

y + x = 30
xy = 209
y = 30 -x
x(30-x) = 209
30x - x^2 = 209
x^2 - 30x + 209 = 0
x = 19
y = 11

the difference is 19-11 = 8

The numbers are 11 and 19.

Given to us,Sum of the two numbers = 30,Product of the two numbers = 209,

Assumption

Let's assume that the first number be a and the second is b.

equation 1,

a + b = 30

equation 2,

ab = 209

Therefore, in equation 1,

[tex]a\times b = 209\\b= \dfrac{209}{a}[/tex]

substitute the value of b in equation 1,

[tex]a+b=30\\\\a+\dfrac{209}{a}=30\\\\\dfrac{a^2+209}{a} =30\\\\a^2 +209 = 30a\\a^2-30a +209 = 0[/tex]

[tex]a^2 -30a+209= 0\\a^2 -19a-11a+209= 0\\a(a-19)-11(a-19)=0\\(a-11)(a-19)=0[/tex]

Substituting the factor against 0,

[tex](a-11) = 0\\a = 11\\\\(a-19)=0\\a = 19[/tex]

Therefore, the numbers are 11 and 19.

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X+y/3 =5 solve for (x)

Answers

Given x+y/3=5, to make x the subject we proceed as follows;
x+y/3=5
subtract y/3 from both sides we get:
x+y/3-y/3=5-y/3
hence;
x=5-y/3
this can also be written as:
x=(15-y)/3

PLEASE HELP!!! IMAGE ATTACHED FIND THE AREA OF THE FIGURE ABOVE

Answers

The area of the rectangle is equal to length times width, or 9*11=99 in^2.
The area of the parallelogram is equal to base times height, or 9*11=99.
The area of a triangle is equal to half of base times height, or 11*6/2=33.
Add these values together to get 231 or C

Answer:

231in

Step-by-step explanation:

To the nearest hundredth, what is the circumference of a circle with a radius of 4 units.

A. 201.06
B. 50.27
C. 12.57
D. 25.13

Answers

C = 2 * (pi) * r
C = 2 * 3.14 * 4
C = 25.12.....its gonna be 25.13...because I rounded (pi)

Answer:

it Is D

Step-by-step explanation:

just did it

-8-(3x+6)=4-x

Wow I'm dumb lol

Answers

hello:
solve for x :
-8-(3x+6)=4-x
-8 -3x-6 =4-x
-3x+x = 8+6+4
-2x =18
x = 18/-2
x= -9

The average grade mark received on 4 tests was 94. if he drops his lowest grade of 85, what will his new average be

Answers

After dropping his lowest marks of 85 the new average test mark is 97.

Given, average test score of 4 tests is 94.

Average concept:

Average = sum of all the observations / total number of observations.

Average of 4 test marks = 94

94 = Sum of all the marks obtained in 4 tests / 4

Sum of all the marks obtained in 4 tests = 94 × 4

Sum of all the marks obtained in 4 tests = 376

Now the lowest marks of 85 are removed,

Remaining sum of 3 test marks = 376 - 85

Remaining sum of 3 test marks = 291

New average of 3 tests:

Average of 3 test marks = 291/3

Average of 3 test marks = 97

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Which of the following is the correct expanded form for the series below?

A. 1+1+1/2+1/6
B.1+1/2+1/6+1/24
C.1+2/3+1/2+2/5
D.4+2+2/3+1/6

Answers

Answer: Option A is correct that is [tex]1 +1+\frac{1}{2} +\frac{1}{6}[/tex]

Explanation:

we will substitute the values of n in given expression

[tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]

when substituting n=1 we get in [tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]=[tex]\frac{1}{1!}[/tex]

when n=2 we get [tex]\frac{2}{2!}[/tex]

when n =3 we get [tex]\frac{3}{3!}=\frac{3}{6}=\frac{1}{2}[/tex] ;3 factorial that is 3! = 3 *2*1 = 6

when n=4 we get [tex]\frac{4}{4!}=\frac{4}{24}=\frac{1}{6}[/tex];4! = 4*3*2*1 = 24

Note: factorial means the product of the terms getting multiplied till 1

suppose n! will be equal to n(n-1)(n-2)(n-3).......1

Final answer:

The correct expanded form for the series is Option B, which represents the sum of inverse factorials up to 1/3! The other options do not accurately depict the factorial series.

Explanation:

The correct expanded form for the series given would be the option that correctly represents the sum of the factorial terms in the sequence. The series in the choices seems to depict a sum of inverse factorials. Factorials are mathematical expressions that involve multiplying a series of descending natural numbers. The factorial of a number n is represented as n! and is equal to n × (n-1) × (n-2) × … × 1. Therefore, 0! and 1! are both equal to 1, while 2! is equal to 2, 3! equals 6, and 4! equals 24, and so on.

By applying this logic to the options:

Option A is incorrect because 1/6 is equivalent to 1/3! not 1/4!.Option B, 1 + 1/2 + 1/6 + 1/24, correctly represents the sum 1/0! + 1/1! + 1/2! + 1/3!.Option C is incorrect as the sequence of numbers does not represent factorials.Option D is incorrect because the numbers do not follow the pattern of the inverse factorial sequence.

Therefore, the correct answer is Option B.

The original price of a couch is $650. It is on sale for $546. What is the percent change in the price off the couch?

Answers

%change=100(final-initial)/initial

%change=100(546-650)/650

%change= -16%

So 16% was taken off of the original price.

Raina makes eight dollars for each hour of work. Write an equation to represent her total pay p after working h hours

Answers

p=8h is the equation which shows the total pay is 8 times the number of hours worked.

P= 8h

P is her total pay
h is the amount of hours so if she works one hour she makes 8x 1
2 hours 8x2 and so on

At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]

Answers

he rides for 7 min and waits in line for 20 min, if he was to wait in line for 60 min then he would ride for 21 min, if you divide 20/60 then you'll get 3. Multiply the 7 with that 3 and you'll get "21".

Answer:

Step-by-step explanation:

True or false? in order to inscribe a circle in a triangle, the circle's center must be placed at the circumcenter of the triangle

Answers

Answer:

False.

Step-by-step explanation:

A inscribe circle in a triangle means to draw the biggest circle possible inside such triangle. To do that perfectly, we first have to find the incenter of the circle, which is the intersection of all three internal bisector of the triangle, that point is the center of the inscribed circle.

Therefore, the statement is false.

In addition, a circumcenter allow to perfectly draw a circumscribed circle, which is outside the triangle, which is not the case here.

An image showing the inscribed circle is attached.

Answer:

false

Step-by-step explanation:

What is the solution of y − 4x = 0 and 3x + 6y = 9?

Answers

You solve this by plugging one equation into the other. Usually you have to rewrite one equation to make this work. In this case I choose to rewrite y-4x=0 as y=4x.

After plugging it into the second, you get:

3x + 6*4x = 9 => 27x = 9 => x=1/3

Putting this solution back into y=4x gives us y=4/3

Which graph best represents the solution to the system of equations shown below?

y = -2x + 14
y = 2x + 2

Answers

The efficient way might be solving for the crossing point of the two lines:

Add 2 equations together, you will get:

2y = 16 -> y = 8

Then, x = 3

So the point will be (3,8)

Apparently, A will be the answer

Answer:

solution is (3,8)

option A

Step-by-step explanation:

[tex]y = -2x + 14[/tex]

[tex]y = 2x + 2[/tex]

Lets graph each equation

Given equation is in the form of y=mx+b

LEts graph each equation using a table

[tex]y = -2x + 14[/tex]

x y

0 14

1 12 points are (0,14) and (1,12)

[tex]y = 2x + 2[/tex]

x y

0 2

1 4 points are (0,2) and (1,4)

Graph both the table

The graph is attached below. both graph intersects at (3,8)

On a 10-item test, three students in professor hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. for this distribution of test scores, the standard deviation is equal to the square root of

Answers

The standard deviation is 5 because (2+5+8)/3=5. So the equal square root is square root of 25

Two way Frequency table question

Answers

Answer: choice A

---------------------------------------------------------------------
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Work Shown:

P(TV) = (number who watch tv)/(number total)
P(TV) = 30/100
P(TV) = 0.30

P(Girl) = (number of girls)/(number total)
P(Girl) = 55/100
P(Girl) = 0.55

P(TV)*P(Girl) = 0.30*0.55 = 0.165 which rounds to 0.17
We'll use this value later. So let's call this M = 0.17

Look in the "girl" row and "tv" column. The value 17 is here.
This is out of 100 people total, so
P(TV and Girl) = 17/100 = 0.17
Call this value N = 0.17

Because M = N = 0.17 approximately, this means that the two variables "TV" and "Girl" are approximately independent

So the equation P(TV and Girl) = P(TV)*P(Girl) is approximately true in this example.

This points to choice A being the answer.

Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values of x and y. Then evaluate the simplified expression. The value of x is , and the value of y is. The value of the expression, rounded to nearest hundredth, is .

Answers

Final answer:

To simplify the equation using logarithmic functions, take the natural logarithm of both sides and use properties of logarithms to solve for x and y. Then substitute the values in the simplified expression to evaluate it.

Explanation:

To simplify the expression on the left side of the equation using the properties of logarithmic functions, let's work step by step:

Take the natural logarithm (ln) of both sides of the equation. The natural logarithm cancels the exponential function.The natural logarithm of 5.6/16.0 is -1.050.Now, we have the equation ln(x) - ln(2y) = -1.050.Using the property of logarithms, subtracting the logarithms of two numbers is equivalent to dividing the numbers. So we have ln(x/2y) = -1.050.To find the value of x/2y, take the inverse natural logarithm (e^) of both sides.So we have x/2y = e^(-1.050).To solve for x, multiply both sides of the equation by 2y.Therefore, x = 2y * e^(-1.050).Once you have the values for x and y, substitute them into the simplified expression to find its value.

The average of six numbers is 4. a seventh number is added and the new average is 5. what is the seventh number?

Answers

the average of 6 numbers is 4....
t/6 = 4.....t = 24 (the total of the 6 numbers)

(24 + x) / 7 = 5
24 + x = 35
x = 35 - 24
x = 11 <== ur 7th number

According to the question, the seventh number is 11.

Use the concept of average defined as:

Average, also known as the mean, is a statistical measure that represents the central value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total count of numbers.

To find the seventh number,

If the average of six numbers is 4, then the total sum of those six numbers would be 6 multiplied by 4, which is 24.

Assume the seventh number is 'x'.

If the new average (after adding the seventh number) is 5, then the total sum of all seven numbers would be 7 multiplied by 5, which is 35.

To find the seventh number 'x',

Subtract the sum of the initial six numbers (24) from the sum of all seven numbers (35).

This gives us 35 - 24 = 11.

Hence,

The seventh number is 11.

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The last step in a proof contains the

Answers

The last step in a proof contains the conclusion.
hope this helps:)

The answer is "Conclusion". Feel free to ask more if needed.

The probability that an american industry will locate in shanghai, china, is 0.7, the probability that it will locate in beijing, china, is 0.4, and the probability that it will locate in either shanghai or beijing or both is 0.8. what is the probability that the industry will locate

Answers

The answer to this equation is 0.5

reflecting over which line will map the rhombus onto itself

Answers

y = -2x

because every point of the rhombus vertex will reflect on the opposite vertex.

a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. Describe what is being measured in this experiment and what variable is being manipulated?

Answers

The goal of any experiment is to test the hypothesis by adjusting the independent variables so you can see the trend of the dependent variable that you want to investigate. The independent variables are parameters that you manipulate. In this experiment, that would be the time of day. You have two independent variables: night and day. The speed of the mice is the parameter that you will measure. Once you do these set-up, you can conclude in the end the effect of the time of day on the speed of the mice.

(NEED HELP!!!)Which of the following lines is perpendicular to y= 3x + 2?

A. y=3x -1/2

B. y=-1/3x+6

C. y=1/3x+2

D. y=3x+1/2

Answers

The correct answer is: [B]: " y = (-⅓)x + 6 " .
____________________________________________________________

Answer:

[tex]y=\frac{-1}{3}x+6[/tex]

Step-by-step explanation:

We have to find the equation of the line from the options given which is perpendicular to the line y=3x+2.

In order to do so we must know that , the product of the slope of the two perpendicular lines is always -1

Hence

if the slope of line A is "m" and the line B which is perpendicular to A, will have [tex]-\frac{1}{m}\\[/tex]

Also , in the slope intercept form of any equation the coefficient of x is our slope. Hence the slope of y=3x+2., is 3

Hence the slope of any line perpendicular to this will be [tex]\frac{-1}{3}[/tex]

as the product of two slopes is -1

Hence in the given options only c options has the line whose slope is [tex]\frac{-1}{3}[/tex]

Other Questions

An oxygen atom with a charge of (+2) has ______________________.a. two more protons than the neutral atomb. two fewer protons than the neutral atomc. two more electrons that the neutral atomd. two fewer electrons than the neutral atom Andy has been consuming a set number of calories and recently added an additional 100 calories in the form of a daily snack. Although he is not trying to lose weight, he has lost one pound per week over the last two months. He wants to increase his level of activity and exercise, and he wants to return to his weight from two months ago. Which strategy should he follow to prevent becoming underweight? Increase his activity and exercise levels and add more calories to gradually gain weight Increase his activity and exercise levels and eat the same number of calories to gradually gain weight Increase his snacks to two or three per day until he reaches his target weight Increase his calories consumed and do less activity and exercise until he reaches his target weight A candy factory made 54 boxes of chocolates. Each box weighs 2 pounds. They packed the boxes in 6 cases with the same number of boxes in each case. How many pounds of chocolates were there in each case? Which is not a requirement for natural selection to occur? In the early reservation period, tribal membership (who belonged to the tribe) was determined by: Monozygotic twins are __________, while dizygotic twins are __________. the result of mitosis; the result of meiosis fraternal; identical always the same gender; always the opposite genders identical; fraternal The code of ethics dealing with experimentation on human subjects is The table below shows the surface area y, in square feet, of a shrinking lake in x days: Time (x) (days)5101520 Surface area (y) (square feet)90857061 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from 1, 0.98, 0.5, 0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points) How does curley react to lennies silence? determine the time (in a years and days) it would take for a $36,000 loan at a rate of 3% to cost the borrower $400 in interest? What is Hawthorne's purpose for the first four chapters of The Scarlet Letter? Which group of russians and ukranians made up the majority of people who? What caused the trend toward city life in the 1800s? How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240? A drawback of load bearing construction is The length of a spring is a linear function of the weight of the object compressing it. For a particular spring, the length decreases by 1.5 inches for every 3 pounds pressing down on it. When 4 pounds are on the spring, the length of the spring is 8 inches long. What is the length of the spring if 15 pounds are pressing down on the spring? Consider the following set of equations: Equation A: y = x + 5Equation B: y = 6x 2Which of the following is a step that can be used to find the solution to the set of equations? x = 6x + 2 x 2 = 6x + 5 x + 5 = 6x 2 x + 5 = 5x In Antigone by Sophocles, which element of tragedy is most apparent in Creons transformation from a proud and prosperous monarch in the beginning of the play to a defeated, lonely old man at the end of the play?A) peripeteiaB) hamartiaC) hubrisD) anagnorisis There were 490 people at play. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $990. How many adults and children attended Propane gas (C3H8) burns completely in the presence of oxygen gas (O2) to yield carbon dioxide gas (CO2) and water vapor (H2O). Steam Workshop Downloader