The product of two consecutive even integers is 8. Find the integers.

Note: each set of brackets represents one solution.

The Product Of Two Consecutive Even Integers Is 8. Find The Integers.Note: Each Set Of Brackets Represents

Answers

Answer 1

Answer:

-4 and -2

2 and 4.

Step-by-step explanation:

Let n be the first even integer.

Then the consecutive even integer will be represented by (n+2).

We know that their product is 8. So:

[tex]n(n+2)=8[/tex]

Solve for n. Distribute:

[tex]n^2+2n=8[/tex]

Subtract 8 from both sides:

[tex]n^2+2n-8=0[/tex]

Factor:

[tex](n+4)(n-2)=0[/tex]

Zero Product Property

[tex]n+4=0\text{ or } n-2=0[/tex]

Solve for n for each case:

[tex]n=-4\text{ or } n=2[/tex]

Hence, we will have two correct solutions.

Case 1: -4 and -2. -4(-2) is indeed 8.

Case 2: 2 and 4. 2(4) is also 8.

Hence, our solutions are:

-4 and -2

2 and 4.


Related Questions

In the triangular prism shown below, which lines are parallel?
M
N
IK and IM
IM and IM
IM and KN
KN and IM

Answers

Answer:

JM and KN

Step-by-step explanation:

one thing you can do to eliminate some answer choices is to make sure that the statement doesn't repeat a letter

the correct answer would be something like AB and BC, it would be like AB and CD

from there, you just have to look and pick your answer

Answer:

the 3rd one

Step-by-step explanation:

2 (5x + 3)

solve and show like terms​

Answers

Answer:

10x+6

Step-by-step explanation:

you would times the 2 by the 5 and the 2 by the 3 which gives you 10x+6

The functions f(x) and g(x) are described below.
f(x) = 7x + 9

g(x) = 7x - 4

The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.

Answers

Answer:

13 units

Step-by-step explanation:

Because the c term (9 for f(x)) represents the y intercept. The y only moves the graph up or down. Since we are trying to get from 9 to -4 move down by 13 units.

What is the purpose of finding the average?

Answers

Answer:

The purpose of taking the average of a set of data is to give one a general idea of how the data set is acting or performing as a whole.

Step-by-step explanation:

y = -3x + 6

Slope:

y-intercept:


y = 4/3x - 1

Slope:

y-intercept:


y = -1/5x + 3

Slope:

y-intercept:​

Answers

Answer:

Step-by-step explanation:

y = mx  + c

Slope = m

y-intercept = c

1) y = -3x + 6

Slope = -3

y-intercept = 6

2) y = 4/3 x - 1

Slope = 4/3

y-intercept =  -1

3) y = -1/5x+3

Slope = -1/5

y-intercept = 3

Answer:

Step-by-step explanation:

y= -3x +6                         [tex]y=\frac{4}{3} x-1[/tex]

slope: -3                          slope=4/3x

y-intercept: (0,6)             y-intercept:(0,-1)

[tex]y=-\frac{1}{5} x+3[/tex]

slope: -1/5x

y-intercept: (0,3)

A random sample of online music video views and number of guitar sales was measured, and the computer output for regression was obtained: Coefficients Standard Error t Stat P-value Intercept 7.856710924 1.316226455 5.969118 0.001889 Music Video Views 0.094781123 0.027926367 3.393965 0.019378 R-sq. = 69.73%R-sq. (adj) = 63.68% Part A: Use the computer output to determine the LSRL. Identify all the variables used in the equation. Part B: What proportion of the variation of guitar sales is explained by its linear relationship to music video views? Explain. Part C: Determine if increased guitar sales were caused by online music video views. Explain your reasoning.

Answers

Answer:

Explained below.

Step-by-step explanation:

The regression analysis output is as follows:

                       Coefficients          Standard Error         t Stat            P-value

Intercept        7.856710924          1.316226455         5.969118       0.001889

Music Video   0.094781123         0.027926367        3.393965      0.019378

Views

R-sq. = 69.73%

R-sq. (adj) = 63.68%

A

There are two variables used in this study, the independent and the dependent variable.

The independent variable is the number of online music video views and the dependent variable is the number of guitar sales.

B

The coefficient of determination R² specifies the percentage of the variation in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).

Thus, the proportion of the variation of guitar sales that is explained by its linear relationship to music video views is 69.73%.

C

The least square regression line is:

[tex]y=7.856710924+0.094781123\cdot x[/tex]

The least square regression line implies that there is a positive relationship between the guitar sales and music video views. That is as the number of music video views increases the guitar sales increases. And vice-versa.

Thus, increased guitar sales were caused by online music video views.

1. Sally decided to go early Christmas shopping at a local Wal-Mart. There was
a Black Friday sale and she bought a TV that was originally $200. The TV
was marked down 25%. How much did Sally pay after it was marked down?
(1 point)

Answers

Answer:

150$

Step-by-step explanation:

In order to find the answer to this question you must find twenty-five percent of two-hundred.

50% of 100 = 50

100% of 100 = 100

100% of 200 = 200

50% of 200 = 100

25% of 200 = 150

= 150$

Hope this helps.

Which statement best describes the leaf structures of monocots and dicots?

Dicots have narrow leaves with parallel veins, and monocots have broad leaves with a network of veins.
Monocots have narrow leaves with parallel veins, and dicots have broad leaves with a network of veins.
Dicots have narrow leaves with a network of veins, and monocots have broad leaves with parallel veins.
Monocots have narrow leaves with a network of veins, and dicots have broad leaves with parallel veins.

Answers

Answer:

can you space it plz

Step-by-step explanation:

Answer:

The correct answer is choice B.

Step-by-step explanation:

Monocots differ from the dicots In the structural features of the leaves, the stems, roots, and flowers. The differences start from the very beginning of the plant's life cycle: the seed. Monocots have one cotyledon, while dicots have two. When it comes to leaves,  monocots have narrow leaves with the typical parallel leaf veins. Dicots have broad leaves with a network of netted leaf veins.

Nick walked 3/4 of a mile in 12 minutes.How long would it take him to walk three miles at this pace

Answers

Answer:

48 minutes

Step-by-step explanation:

First do 3 divided by 3/4 and that gives you 4. Then multiply 4 by 12 and you get 48.

Answer:

45

Step-by-step explanation:

I love math, so this was fun! First, we need to know how long it would take him to walk 1 mile. We know it took 12 minutes to walk 3/4 of a mile, so we just need to figure out how long each quater is. For this problem, each quarter of a mile is 3 minutes, and so we just need to multiply that by 4. then, we know it would take him 15 mintues to walk a mile. Then, just multiply that by 3! Hope this helps, sorry I can't spell :)

If (x – 2k) is a factor of f(x), which of the following must be true? f(2k) = 0 f(–2k) = 0 A root of f(x) is x = –2k. A y intercept of f(x) is x = 2k.

Answers

Answer:

f(2k0=0

Step-by-step explanation:

answer a

The correct statement about function is,

⇒ f (2k) = 0

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;

(x – 2k) is a factor of function f(x),

Since, (x – 2k) is a factor of function f(x),

Hence, x = 2k is a factor of function f(x),

Thus, We get;

⇒ f (2k) = 0

Thus, The correct statement about function is,

⇒ f (2k) = 0

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Laney pays $0.99 for each song she downloads from the internet. In total, She paid $24.75 for songs from the internet. How many songs does Laney Download

Answers

25 song because 24.75 divided by 0.99 is 25 which means she downloads 25 songs

Answer:

25

Step-by-step explanation:

Divide the total cost ($24.75) by the price per song ($0.99) to get the amount of songs bought.

Eighth grade

Find the slope of the line that passes through (8, 10) and (4, 1).

Answers

Answer:

9/4 this Is a fraction

Step-by-step explanation:

1 - 10 = -9

4 - 8 = -4

-9 and -4 turn positive

If there are 21 students in class today, how much would it
cost for the class and your teacher to ride the Sandia
Aerial Tram? Show your work.
a.
Create an equation to represent the cost the class
and your teacher taking a ride on the Sandia Aerial
Tram. Let f(x) be the total cost.
b.
Does the above scenario represent a function,
explain your reasoning.
Rates: $25 Adults, $20 Seniors 62+ & Teens 13-20 yrs,
$15 Youth 5-12 yrs.
Students, write your response

Answers

Answer:

a. f(x) = 21 (20) +1 (25) = 445

b. The scenario is a function because each student just have to pay once.

What is the equation of a line that is parallel to y=4 that passes through (1, -5)

Answers

Answer:

y = - 5

Step-by-step explanation:

y = 4 is a horizontal line parallel to the x- axis

A parallel line must therefore be a horizontal line with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (1, - 5) with y- coordinate - 5, thus

y = - 5 ← equation of parallel line

Time = 2hour +12 mins per lightswitch
She charges her customers a call out fee of £35, plus £30 per hour.
How much should a customer be charged for wiring a house with 10 lightswitch?

Answers

Answer:

£395.

Step-by-step explanation:

Call out fee=35

30 per hour = 2 hour to be =60

but,12 minutes in hours= 12/60= 0.2

0.2 = 0.2*30 = 6

2 hours and 12 minutes would be charge as

30 + 6 = 36

36*10 = 360

call out fee + per hour = 35 + 360 + 395

What does 8EE4 represent?

Answers

It is a representation of a number

Gina Wilson All Things Algebra Unit 3 Parallel and Perpendicular Lines

Answers

Answer:

Parallel lines are lines that do not meet while perpendicular lines are aligned 90 degrees to each other.

Step-by-step explanation:

Imagine two straight lines, drawn side by side to each other with no angle between them. When they are drawn to infinite, no point of one line would touch the other.

Perpendicular lines are two or more line that meets at a point to form a right angle, that is, separated with an angle of 90 degrees to each other.

An electrician needs to buy 6 1/4 feet of electrical wire. There are 1 1/4 feet of wire on each spool. How many spools of wire should the electrician buy?​

Answers

Answer:

5

Step-by-step explanation:

1 1/4 multiplied by 4 is 5 add another 1 1/4 is 6 1/4

Find the coordinates of the point 7/10 of the way from A (-3,-5) to B (9.4)

Answers

Answer:

(-2/17, 5/17)

Step-by-step explanation:

Given the coordinates A (-3,-5) to B (9,4), we are to find the coordinate of the point cutting the line using the ratio 7:10

Using the midpoint formula;

M(X,Y) = {(ax1+bx2/a+b, (ay1+by2/a+b))

Given

x1 = -3, y1 = -5, x2 = 9, y2 = 4, a = 7 and b = 10

get the required coordinates;

X = ax1+bx2/a+b

X = 7(-3)+10(9)/7+10

X = -21+19/17

X = -2/17

Get the Y coordinate;

Y = ay1+by2/a+b

Y = 7(-5)+10(4)/7+10

Y = -35+40/17

Y = 5/17

Hence the required coordinate is (-2/17, 5/17)

Solve for k in the proportion.

18
12
=
k
8

Answers

22 makes more sense than 12

What is the slope of the line in the graph?
ch
4
3
2+
-54 -3 -1
1 2 3 3 4
4 5
X
-2
-3
4
-5

Answers

Answer:

I dont understand what your saying???

Step-by-step explanation:

The slope of the line in the graph is,

⇒ m = 1

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is,

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 1, 0) and (0, 1).

Now,

Since, The equation of line passes through the points  (- 1, 0) and (0, 1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 0) / (0 - (-1))

m = 1 / 1

m = 1

Thus, The slope of the line in the graph is,

⇒ m = 1

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Plot 1/2x-y=4 and 2y=x+6

Answers

Answer:

2x+y s with. 3x-2y 7 one of these. 3x+2y ex) (2x-y) (3x-2y)

Step-by-step explanation:

2x+y s with. 3x-2y 7 one of these. 3x+2y ex) (2x-y) (3x-2y)

hope this helped ^^

which line is perpendicular to y=2x+4?
a. y=2x-6
b. y=-1/2x+7
c. y=-1/4x+2
d. y=-4x+3

Answers

Answer:

B

In the equation y=mx+b m is the slope of the line.

Therefore the coefficient in each of these equations is the slope.

A line with a perpendicular slope must have the inverse opposite of the actual line. For example if a line has a slope of 5, a perpendicular line to that line must have a slope of -1/5. If a line has a slope of 10, the perpendicular line has a slope of -1/10. If a line has a slope of 2 then the inverse opposite is -1/2 and that is the slope of the perpendicular line.

B is the only answer with the correct slope so B is the answer.

Step-by-step explanation:

Evaluate
4(x+3)(x+1)/(x+5)(x-5) x=3

Answers

Answer:

-6

Step-by-step explanation:

The value of the given expression will be equal to -3.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The solution to the expression is:-

=  4(  x  +  3  ) (  x + 1  )  /  (  x  +  5  )  (  x  -  5  )

=  4(  3 +  3  ) (  3  + 1  )  /  (  3  +  5  )  (  3  -  5  )

=  (  4  x  6  x  4 )  /  (  8  x   -2  )

=  -3

Therefore the value of the given expression will be equal to -3.

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wich expression is equivalent to 0.5 * 0.6?

Answers

Answer:

0.3

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

I hope this is what you where asking for?

Find value of x in triangle

Answers

Answer:

110

Step-by-step explanation:

Ik

Answer:

32

Step-by-step explanation

for this triangle the 2 missing angles are the same angle so subtract 116 from 180 to find the sum of the 2 angles then divide

estimate each product :
1/7 x 20

Answers

Answer:

2.85714285714

Step-by-step explanation:

just searched it.

estimate the other persons answer!!

The average profit/loss of a company (in thousands of dollars) was documented for 30 months. The 5th month showed a loss of $3000, however the 25th month
showed a profit of $5000. Assuming the profitloss is linear, write the equation of the line, in slope-intercept form, that represents the profit/loss for each month x. Use
this result to predict the profit/loss after 60 months
Hint: Use the ordered pairs (5. - 3) and (25,5).
2
The equation of the line in slope-intercept form is y= 5x -5.
(Type an equation using x and y as the variable. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
..There would be a of safter 60 months

Answers

Answer:

Step-by-step explanation: slope is (9-(-3))/(25-5)

12/20=0.6

point slope formula y-y1=m(x-x1), m slope (x1, y1) point

y-9=0.6(x-25)

y=0.6x-15+9

y=0.6x-6, x months and y profit.

for 60 months, y=0.6*60-6 or 36-6=$30000 profit

The price of shoes is $52.00. If you order them directly from the company on the internet, you can save money and the price is only $42.64. What is the percent change

Answers

Answer:18%

Step-by-step explanation:

50.00-42.64=9.36

9.36/52=.18

Answer:

18%

Step-by-step explanation:

$52.00-$42.64= $9.36

[tex]\frac{9.36}{52.00}[/tex] x100

=0.18 x 100

=18%

Given the following table, find the equation that matches it.​

Answers

Answer:

The equation that matches the table is y = -5x + 7 ⇒ C

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the slope of the lineb is the y-intercept (value y at x = 0)

The rule of the slope is m =  [tex]\frac{y2-y1}{x2-x1}[/tex] , where

(x1, y1) and (x2, y2) are two points on the line

From the given table

→ Choose any two points from the table

∵ Points (0, 7) and (1, 2) are in the table

x1 = 0 and y1 = 7

x2 = 1 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m = [tex]\frac{2-7}{1-0}=\frac{-5}{1}[/tex]

m = -5

→ Substitute it in the form of the equation above

∵ y = -5x + b

∵ b is the value of y at x = 0

∵ At x = 0, y = 7

∴ b = 7

y = -5x + 7

The equation that matches the table is y = -5x + 7

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