[50 pts] An even number, n, times the next consecutive number, n + 2, is equal to 168. Find the original number.

Answers

Answer 1

We are given:

An even number 'n', multiplied by the next consecutive even number is 168

Solving for n:

From the given statement, we can say that:

n(n+2) = 168                      [n multiplied by the next even number 'n+2']

n² + 2n = 168

n² + 2n - 168 = 0               [subtracting 168 from both sides]

We can see that we now have a quadratic equation, solving using splitting the middle term

n² + 14n - 12n - 168 = 0

n(n + 14) -12(n + 14) = 0      [factoring out common terms]

(n-12)(n+14) = 0

Here, we can divide both sides by either (n-12) OR (n+14)

Checking the result in both the cases:

(n + 14) = 0/(n-12)                     (n-12) = 0/(n+14)

n + 14 = 0                                 n - 12 = 0

n = -14                                      n = 12

Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n


Related Questions

You want to buy a $25,000 car. The company is offering a 2 % interest rate for 48 months (4 years). What
will your monthly payments be?
O $500.71
O $815.05
O $542.38
$6, 276.06

Answers

The answer is $542.38

PLEASE HELP, TWENTY POINTS PLUS BRAINLIEST
Write an explicit function to represent the following sequence.
3,9, 27, 81,...

Answers

The equation would be if y is the numbers in the sequence (like 3, 9, 27) and x is the is the number in the order (like 3 is 1, 9 is 2, 81 is 4) the the equation would be y = 3^x.

Complete the statement to show an equivalent ratio. ) 18:10 is equivalent to ? : 5.​

Answers

Answer:

9

Step-by-step explanation:

[tex] \frac{18}{10} = \frac{?}{5} \\ \\? = \frac{18 \times 5}{10} \\ \\? = \frac{90}{10} \\ \\ ? = 9[/tex]

Answer:9

Step-by-step explanation:because if you divide 10 by 2 it’s 5 and if you divide 18/2 it’s 9

4 days =____ hours


????????????????????????

Answers

4 days = 96 hours.......

Expand the linear expression 4(10x - 4).
40x - 16
40x + 16
40x - 4
10x - 16

Answers

Answer:

the correct answer is 40x-16

Step-by-step explanation:

here,

=4(10x-4)

=40x-16

While standing on a 50 foot high roof, Santa throws an ornament up into
the air with an initial velocity of 40 feet per second. How long will it take to
hit the ground? Round your answer to the nearest tenth.*
PLEASE HELP ASAP!

Answers

Answer: 1.25

Step-by-step explanation: you gotta divide 50 and 40.

(23 PTS) WILL GIVE BRAINLIST

Answers

Answer:

Step-by-step explanation:

g(x) would be

8

4

2

0

- 2

Which of the following inequalities matches the graph? (1 point)
-10
-0
10
1. x>-3
2. x<-3
3. y>-3
4. y<-3

Answers

Given:

The graph of an inequality.

To find:

The inequality.

Solution:

From the given graph it is clear that the boundary line is a vertical line parallel to y-axis at the distance of 3 units from the left of y-axis. So, the equation of boundary line is

[tex]x=-3[/tex]

Now, the shaded portion lies on the left of the boundary line. It means the values which are less than 0 are included in the solution set.

The boundary line is a dotted line. So, x=-3 is not included in the solution set.

So, the required inequality is

[tex]x<-3[/tex]  

Therefore, the correct option is B.

PLEASE HELP MEEE!! ASAP! I will mark brainliest

Answers

Answer:

The last 1 (D)

Step-by-step explanation:

The lines have to be straight nd have to pass through the origin

Answer:

i have this problem before and i believe it was c and if not b

Step-by-step explanation:

It’s time to lock down the design details for the redesigned Brick and Egyptian candles. Because of manufacturing constraints, the base length for each candle has to be at least 2 cm and can be no more than 10 cm. Make a recommendation for the base dimensions of each candle. Explain how you determined your base dimensions. Your reasoning does not have to be all math related.

Answers

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

Please help me out!!

Answers

Answer:

D.  9(3.1416)

Step-by-step explanation:

help meeeeeeeeehhhhhh​

Answers

Answer:

0

Step-by-step explanation:

i used a calculator & it was 0 meters

For a dinner party, a catering company charges a set fee $150 plus $20 per person. How much will it cost for 35 people to attend the event?

Answers

Answer:

$700 for 35 people but if you want to add the fee it will be $850

What is the equation of the line

Answers

it’s either y = 0 or x = 0, i believe it’s x= 0 but it could be the other

Answer:

x=-9

Step-by-step explanation:

Mrs. Robertson is carpeting her rectangular living room.
The room is 10 feet wide and 15 feet long. What is the
area to be carpeted?

Answers

Answer:

150 ft

Step-by-step explanation:

The formula for area is, height x width (h x w) or base x height (b x h)

10 feet is the base and 15 is the height, multiply those and you get 150

Evaluate the following for when x=5

4(x-2)(x-3)+7(x-2)(x-5)-6(x-3)(x-5)

Answers

Answer:5x^(2)-21x+4

Step-by-step explanation:

HELP GIVING AWAY 55 POINTS!!!!
Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentrate for a party. How much of the 60% pineapple juice concentrate should be used? please answer ASAP and explain thought process

Answers

Answer:

12 quarts

Step-by-step explanation:

Let the amount of pineapple juice be x quarts, the concentration of juice is as following equation:

4*0.2 + x*0.6 = (4 + x)*0.50.8 + 0.6x = 2 + 0.5x0.6x - 0.5x = 2 - 0.80.1x = 1.2x = 12

What is 7.5 - 1.5 x 3?

Answers

3 answer gotta be longer

Answer:

3

Step-by-step explanation:

7.5 - 1.5 x 3

7.5-4.5

3

what is angle 1,2,3,4,5,6,7

Answers

1 is 51, 2 is 34, 3 is 95, 4 is 38, 5 is 47, 6 is 74, 7 is 59. If it says to put u it’s they’re all in degrees

2x-2y=-10 Standard to Slope Intercept form

Answers

Answer:

y=x-5

Step-by-step explanation:

2x-2y=10

1.) subtract 2x from both sides

-2y=-2x+10

2.) Divide by -2 to get y by itself

y=x-5

Answer:

y= x+5

Step-by-step explanation:

y =mx+b is slope intercept form

Raul opened a savings account with 4300. Each week, x, Raul pays the dog sitter 30 from his savings account. Write a function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.

Answers

Given:

Amount in the savings account = 4300

Each week, Raul pays the dog sitter 30 from his savings account.

To find:

The function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.

Solution:

Let x be the number of weeks.

Raul pays the dog sitter in 1 week = 30

Raul pays the dog sitter in x week = 30x

Remaining amount = Initial amount - Amount he pays the dog sitter

[tex]f(x)=4300-30x[/tex]

Therefore, the required function is [tex]f(x)=4300-30x[/tex].

Aiden was asked to find the product of 24.5 and 7.7. His work is shown below. Which statements about Aiden's work are true? Check all that apply Estimate: 25 x 8 = 200 Aiden did not make a good estimate. Actual: 24.5 x 7.7 = 1,886.5 Aiden should have estimated the product as 24 x 7. Aiden did not insert the decimal point correctly when estimating. Aiden did not insert the decimal point correctly after multiplying the actual amount. O Aiden's estimate and the actual product do not match closely enough.​

Answers

Answer:

sorry for the late answer, it looks like a b and d

Every time Megan takes a sip of water, the level of the water in her glass goes down 2 inches. Which shows the correct way to find the change in the level of Megan's water glass after 3 sips?


please help me

Answers

Answer:

It changes 3 inches

Step-by-step explanation:

Because every time she takes a sip it goes down, I can’t really explain it good but it changes 3 inches as she took 3 sips of water.

Answer:

Step-by-step explanation: 1 sip = 2 in

                                           3 sips = 6 in so 3 sips x 2 inches =  6 inches

Plis help me plis! I need help with this

Answers

T=PV/K

Starting with V=KT/P, multiply P on both sides to get PV=KT

Then divide K on both sides to leave T alone

And you get.....T =PV/K

Answer:

The light blue/greenish one that says T=PV/K or Greeland

Step-by-step explanation:

We can make the equation more simplier by multiplying both sides by P to remove fractions.

It would become VP=KT

The only answer with VP or PV is B, or the T=PV/K

also, to isolate T, divide the VP=KT by K on both sides to isolate T.

VP/K=T

What is 106% of $40?

Answers

Answer:

I think it's 42.4 hope this helps

Answer:

42.4 hope this helps

Step-by-step explanation:


Which of the following functions maps 3 to -5?
Of(x) = x + 8
O f(x) = x-5
O f(x) = 4 – x2
O f(x) = -x + 2

Answers

Answer:I think it’s B

Step-by-step explanation:

If I get this wrong i’m sorry

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3100 seats. The students left 1395 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?

Answers

Answer: 55% of the seats in the theater were filled by the 6th graders on the trip.

Step-by-step explanation:

Given: Total seats = 3100

Seats vacant=  1395

Seats occupied by 6th graders = 3100-1395 = 1705

The percentage of the seats in the theater were filled by the 6th graders on the trip = [tex]\dfrac{\text{Seats occupied by 6th graders}}{\text{Total seats}}\times100[/tex]

[tex]=\dfrac{1705}{3100}\times100\\\\= 55\%[/tex]

Hence, 55% of the seats in the theater were filled by the 6th graders on the trip.

Which inequality represents all values of x for which the product below is
defined?
please help very confused

Answers

Answer:

 C.  x ≥ 5

Step-by-step explanation:

You must meet both conditions:

 (x -5) ≥ 0 and (x +2) ≥ 0

For the first condition, ...

 x ≥ 5 . . . . add 5 to both sides

For the second condition ...

 x ≥ -2 . . . . subtract 2 from both sides.

Since both conditions must be met, we must have ...

 x ≥ 5

i hope this helps :)

what is the correct answer?​

Answers

Answer:

yes, by AAA~

Step-by-step explanation:

to find the missing angles subtract 180 - 125 - 27 = 28

then we have all of the angles and we can see they are congruent

Yes by aaa your welcome

In the expression 2a-5+4a-9, name the constants​

Answers

Answer:

-5 and -9 are the constants, can also be written -14

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